MECHANICAL BRANCH GUIDE

UNED S POSTGRADUATE STUDIES 22 nd INTERNATIONAL MASTER S IN THEORETICAL & PRACTICAL APPLICATION OF FINITE ELEMENT METHOD AND CAE SIMULATION MECHANICAL BRANCH GUIDE April 28 th 2016 SUPERIOR TECHNICAL SCHOOL OF MECHANICAL ENGINEERS INGECIBER, S.A. (U.N.E.D) p. 1

Contents International Master s in Theoretical and Practical Application p. 2 I. UNED S POSTGRADUATE STUDIES 1 II. INTRODUCTION 4 III. METHODOLOGICAL GUIDANCE 5 IV. EXPERT MODULE SUBJECTS 6 AF.1. - F.E.M GENERAL THEORY... 6 AF.2. - INTRODUCTION TO F.E.M PROGRAMMING... 11 AF.3. - NUMERICAL CALCULATION... 17 AF.4. - MATERIAL CONSTITUTIVE LAWS... 23 MSC NASTRAN. AP.1. - INTRO TO THE USE OF PRACTICAL SOFTWARE. I.... 29 MSC NASTRAN. AP.2. - INTRO TO THE USE OF PRACTICAL SOFTWARE. II.... 33 MSC NASTRAN. AP.3. - PRACTICAL SOFTWARE EXAMPLES... 38 ANSYS. AP.1. - INTRO TO THE USE OF PRACTICAL SOFTWARE. I.... 41 ANSYS. AP.2. - INTRO TO THE USE OF PRACTICAL SOFTWARE. II.... 45 ANSYS. AP.3. - PRACTICAL SOFTWARE EXAMPLES... 48 V. MODULE A DYNAMIC ANALYSIS 51 A.1. - FEM THEORY APPLIED TO STRUCTURE DYNAMIC ANALYSIS... 51 MSC NASTRAN. A.2. - INTRO TO DYNAMIC ANALYSIS WITH PRACTICAL SOFTWARE... 58 MSC NASTRAN. A.3. - DYNAMIC ANALYSIS PRACTICES... 62 ANSYS. A.2. - INTRO TO DYNAMIC ANALYSIS WITH PRACTICAL SOFTWARE... 65 ANSYS. A.3. - DYNAMIC ANALYSIS PRACTICES... 68 VI. MODULE B NON LINEAR ANALYSIS 71 B.1. - F.E.M THEORY APPLIED TO NON-LINEAR STRUCTURES CALCULATION... 71 MSC NASTRAN. B.2. - INTRO TO NONLINEAR ANALYSIS WITH PRACTICAL SOFTWARE... 73 MSC NASTRAN. B.3. - NONLINEAR ANALYSIS PRACTICES... 76 ANSYS. B.2. - INTRO TO NONLINEAR ANALYSIS WITH PRACTICAL SOFTWARE... 78 ANSYS. B.3. - NONLINEAR ANALYSIS PRACTICES... 81 VII. MODULE C HEAT TRANSFER ANALYSIS 83 C.1. - F.E.M THEORY APPLIED TO HEAT TRANSFER... 83 MSC NASTRAN. C.2. - INTRO TO HEAT TRANSFER WITH PRACTICAL SOFTWARE... 87 MSC NASTRAN. C.3. - HEAT TRANSFER PRACTICES... 90 ANSYS. C.2. - INTRO TO HEAT TRANSFER WITH PRACTICAL SOFTWARE... 93 ANSYS. C.3. - HEAT TRANSFER PRACTICES... 96 VIII. MODULE F FLUID MECHANICS 98 F.1. - FEM THEORY APPLIED TO FLUID MECHANICS... 98 CFD++. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE... 102 CFD++. F.3. - FLUID MECHANICS PRACTICES... 106 ANSYS CFD. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE... 109 ANSYS CFD. F.3. - FLUID MECHANICS PRACTICES... 111 XFLOW. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE... 113 XFLOW. F.3. - FLUID MECHANICS PRACTICES... 116 IX. MODULE J ELECTROMAGNETIC ANALYSIS 118 J.1. - FEM THEORY APPLIED TO LOW FREQUENCY ELECTROMAGNETIC ANALYSIS... 118

MAXWELL. J.2. - INTRO TO ELECTROMAGNETIC AN. WITH PRACTICAL SOFTWARE... 125 MAXWELL. J.3. - ELECTROMAGNETIC PRACTICES... 129 X. MODULE K COMPOSITE ANALYSIS OF STRUCTURES 131 K.1. - FINITE ELEMENT ANALYSIS OF COMPOSITE STRUCTURES... 131 MSC NASTRAN. K.2. - INTRO TO COMPOSITE STRUCTURES WITH PRACTICAL SOFTWARE... 135 MSC NASTRAN. K.3. - COMPOSITE STRUCTURES PRACTICE PROBLEMS... 138 ANSYS. K.2. - INTRO TO COMPOSITE STRUCTURES WITH PRACTICAL SOFTWARE... 141 ANSYS. K.3. - COMPOSITE STRUCTURES PRACTICE PROBLEMS... 143 XI. MASTER S FINAL PROJECT 146 p. 3

INTRODUCTION The principal objective of the Master s is to provide analysts and scientists with training in the Finite Element Method for use in the professional world, as a universityspecific Master s should do. With this objective in mind, the Master s is structured into foundation subjects, which give an overview of the Finite Element Method, and application and practical subjects where professional software currently on the market is used. In 2010, the directors of the Master s decided to make it an international course, and they made it available worldwide. Continuing the internationalization process, since 2015 the Master s counts on Enginsoft (Italy) and IDAC (United Kingdom), two prestigious companies of international renown, on the teaching of the application and practical subjects with ANSYS Mechanical and ANSYS CFD software. With this enlargement of the Master s, students will be able to study the mechanical branch with PATRAN/MSC Nastran - CFD++ - XFLOW or with ANSYS - ANSYS CFD ANSYS Maxwell and XFLOW. For the construction branch, students can choose between CivilFEM powered by Marc or CivilFEM for ANSYS. UNED and Ingeciber, their principal partner in the Master s, are investing in a determined internationalization of students and collaborators and want to offer participants the maximum number of options, with the objective of sharing experiences in the world of CAE on a global level. p. 4

METHODOLOGICAL GUIDANCE Due to the heterogeneous knowledge and experiences of the students of a course such as this, the provision of a multidisciplinary approach ranging from the most basic knowledge of certain essential subjects to other more difficult subjects which deepen knowledge in specific areas has been attempted. Furthermore, some freedom has been left to professors so they can approach each subject from their own perspective, losing uniformity, but gaining a variety of viewpoints. Nevertheless, the extensiveness of the FEM and virtual simulation makes more teaching hours necessary in order to cover all the specific aspects of the course, therefore every subject has been limited in its length and depth to its credits or corresponding hours. Students interested in a deeper understanding of certain aspects of the syllabus may start with the additional bibliography specified in the syllabus of each subject and should consult with the professor/tutor of the subject. It is very important to highlight that, in a distance learning course, the students must have the self-discipline to follow the timetable of teaching hours for each subject, according to the guidelines given and order of the course (section I from the general guide). During the weeks devoted to each subject in the schedule, and two additional weeks once the subject is finished, there are four hours per week of tutorships or consultation about the subjects taught. Finally, the continuous assessment booklets must be completed during the term of the corresponding subject and exams must be taken at the end of the term. If students do not take or do not pass their exams, they cannot obtain the corresponding diploma. p. 5

EXPERT MODULE SUBJECTS AF.1. - F.E.M GENERAL THEORY TEACHING STAFF Professor Juan José Benito Muñoz Associate Professor Ramón Álvarez Cabal Professor Mariano Rodríguez-Avial Llardent Mr. Enrique López del Hierro Fernández 1. - OBJECTIVES The aim of this subject is to consolidate the foundations of the Finite Element Method, by thinking mainly about its application in structure analysis, although the basic ideas can be generalized without any difficulty. Furthermore, it should be pointed out that the subject starts with the most basic concepts, initially treated intuitively in order to allow them to be easily assimilated. 2. - CONTENT The organization of basic ideas, already known to the student, is the beginning of the subject s syllabus, which tries to organize them using a matrix approach so that the structural calculation will be more effective. It will immediately set out the heart of the formulation of the direct rigidity method and the problem will be reassessed from a more powerful and general point of view. At the beginning it will deal with linear elements, which are easier to handle. Subsequently, the elastic-linear problems are set out, taking a further step in the generalization of ideas, and the C 0 shape functions are studied in detail. Finally, the theme of plates is discussed with the aim of laying the foundations for a later study about this important structural type and, above all, of presenting general ideas about the problems raised previously and the solutions adopted in the demanding cases of C 1 continuity. p. 6

INDEX I. Introduction. Classical Approximation 1.1.- Introduction 1.2.- Posing the Problem 1.3.- The Direct Stiffness (or Displacement) Method 1.4.- Matrix Formulation 1.5.- Conclusions 1.6.- Application examples II Foundations: Differential and Integral Formulations. Approximation to Exact Solution. Elements 2.1.- Introduction 2.2.- The State or Field Equation. Differential or Strong Formulation 2.3.- Direct Formulation 2.4.- The Principle of Virtual Work 2.5.- Energy Formulation 2.6.- Equivalence of Integral and Differential Formulations 2.7.- Approximation 2.8.- Galerkin s Method 2.9.- Spline Functions 2.10.- The Concept of an Element. Shape Functions 2.11.- Structure Stiffness Matrix and Load Vector. Calculation of Displacements 2.12.- Timoshenko s Beam III The Direct Stiffness Method 3.1.- Introduction 3.2.- Coordinate Systems 3.3.- Transformation of Coordinates. Axes Rotation 3.4.- Assembling the System of Equations 3.5.- The Boundary Conditions 3.6.- Calculation of Displacements 3.7.- Calculating Reactions and Internal Forces 3.8.- Examples p. 7

IV General Approach for the Finite Element Method. Application in Elastic and Steady-State Field Problems. 4.1.- Introduction 4.2.- Differential Approach to the Boundary Value Problem 4.3.- Integral Approach to the Boundary Value Problem 4.4.- Approximation 4.5.- The Finite Element Method 4.6.- Global Features. Application of Essential Boundary Conditions 4.7.- Application of FEM in Solving Linear Elastic Problems 4.8.- Steady-State Field Problems 4.9.- Convergence V Shape Functions of Continuity. Isoparametric Elements 5.1.- Introduction 5.2.- Normalized Coordinates 5.3.- Families of Shape Functions of Continuity 5.4.- Transformations 5.5.- Isoparametric Elements. Numerical Integration VI Thin Plate According To Kirchhoff Theory 6.1.- Introduction. Starting Hypothesis 6.2.- Differential Approach. Field Equations. Definition of Stress 6.3.- Integral Approach. Principle of Virtual Work 6.4.- Finite Element Discretization 6.5.- Requirement for continuity 1 6.6.- Nonconforming Plate Element 6.7.- Conforming Plate Element 6.8.- Conclusions VII Thick plates. Reissner-Mindlin Theory 7.1.- Introduction 7.2.- Differential Approach. Stress Definition 7.3.- Integral Approach 7.4.- Finite Element Discretization 7.5.- Shear Locking Solution p. 8

7.6.- Triangular Elements A.1.- Elementary stiffness matrices B.1.- Equivalent Nodal Loads C Rigid Nodes of Finite Size D Plane Stress and Strain D.1 Plane Stress (XY Plane) D.2 Plane Strain (XY Plane) E Numerical Integration E.1 Quadrature Rules E.2 Gaussian Quadrature E.3 Multiple Integrals F Historical Reference 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES ALARCÓN, A., ALVAREZ, R. & GÓMEZ-LERA, S.Cálculo Matricial de Estructuras.Barcelona, Spain: Ed. Reverté, S.A., 1986. ISBN: 84-291-4801-9. BATHE, K.J. Finite Element Procedures in Engineering Analysis. New Jersey, USA: Ed. Prentice-Hall, Inc.,2007. ISBN-10: 097900490X / ISBN-13: 978-0979004902. OÑATE, E. Cálculo de Estructuras por el Método de Elementos Finitos. Análisis Estático Lineal. Spain: Ed. CIMNE, 1995. ISBN: 9788487867002. ZIENKIEWICZ, O.C.& TAYLOR, R.L. The Finite Element Method: Its Basis and Fundamentals. 6 th edition. Oxford, UK: Ed. Elsevier Butterworth-Heinemann, 2005. ISBN-10: 0750663219/ ISBN-13: 9780750663212. Spanish version: ZIENKIEWICZ, O.C., TAYLOR, R.L. El Método de los Elementos Finitos. Formulación Básica y Problemas Lineales. 4 th edition. Barcelona, Spain: Ed. CIMNE - McGraw-Hill, 1994. ISBN: 9788495999528. 5. - CONTINUOUS ASSESSMENT BOOKLETS p. 9

In the distance learning booklets, the exercises and problems given must be directly resolved and it is necessary to use the software in order to compare the results obtained. 6. - SPECIFIC RECOMMENDATIONS It is advisable that the problems included in the distance learning booklets are resolved as the student moves forwards in the study of the learning units for the purpose of sequentially clarifying, as soon as possible, any doubts that may arise. 7. - TUTORSHIPS: OFFICE HOURS Student can contact tutors using subject s virtual classroom. Professor Juan José Benito Muñoz E-mail: jbenito@ind.uned.es Mondays, from 4:30 pm to 8:30 pm Telephones: (+34) 91-398-64-57 (+34) 91-398-64-58 Dpto. de Ingeniería y Fabricación E.T.S INGENIEROS INDUSTRIALES UNED Apdo. de Correos 60.149 28020 Madrid, Spain. 8. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 10

AF.2. - INTRODUCTION TO F.E.M PROGRAMMING TEACHING STAFF Professor Luis Gavete Corvinos 1. - OBJECTIVES The objectives of this course are focused on teaching students to use and introduce desired changes on a small computer program using the Finite Element Method. To that end, the student is provided with solid basis of programming with some basic algorithms related to data structure and numerical calculation. Thus, using this basis and simple programming language the programming of the Finite Element Method is addressed. We believe, therefore, that the objectives of the course are covered by the information provided, although students can improve the programming themselves so that the programs will be more effective. We have opted for clarity over the efficiency of the program. Therefore, we have used the BASIC language because of its ease of use and its wide dissemination. 2. - CONTENT The Introduction to F.E.M programming course is divided into three large sections. In the first section, called Programming introduction (Warnier Method in a freeware version), which is perfectly adapted to solving mathematical problems through numerical methods. This section includes the first chapters and it gives the basis to understand perfectly (starting from scratch) the programming of complex problems. Furthermore, it includes the basic algorithms which are often used in Finite Element Method programming. Obviously, this could be totally or partially ignored by those students who already have a good knowledge of programming. The second section constitutes the actual introduction to FEM programming, which is performed for the two dimensional linear elasticity case using the simplest finite element (three node triangle). This section includes two chapters, the first one addresses the two dimensional elasticity case including a simple graphic processor that p. 11

allows the user to see the model and the calculation results; the second one contains a brief introduction to storage improvements. Finally, the third section addresses error estimation in FEM It includes a simple application example as well as its programming. INDEX I. Structures 1.1. - Basic Rules 1.2. - Programming Methods 1.3. - Sequential Structure 1.4.-Repetitive Structure 1.5. - Exercises Resolved 1.5.1. - Exercise 1 1.5.2. - Exercise 2 1.5.3. - Exercise 3 1.5.4. - Exercise 4 1.5.5. - Exercise 5 1.6. - Alternative Structure 1.7. - Exercises Resolved 1.7.1. - Exercise 1 1.7.2. - Exercise 2 1.8. - Mix of Repetitive Structures with Alternative Structures (More Complex Programs) 1.9. - Decrease of the Storage Memory Needs II. Elementary Algorithmic 2.1. - Introduction 2.2. - Sorting Algorithm p. 12

2.3. - Search Algorithm 2.4. - Insertion Algorithm 2.5. - Coupled Algorithm (Search + Insertion) 2.6. Elimination Algorithm 2.7. - Merging Algorithm III. Numeric Algorithmic (I). Interpolation 3.1. - Linear Interpolation 3.2. - One Dimension Lagrange Interpolation 3.3. - Two Dimension Lagrange Interpolation IV. Numeric Algorithmic (II). Resolution of Linear Equation Systems 4.1. -Introduction: Gauss Method 4.2. - Improvements to Gauss Method 4.2.1. - PARTIAL PIVOTING METHOD 4.2.2. - TOTAL PIVOTING METHOD 4.3. - Cholesky Method V. Memory Improvement Algorithms 5.1. - Two Matrices Product 5.2. - Optimal Storage of a Symmetric Matrix 5.3. - Exercises Resolved 5.4. - Optimal Storage of a Symmetric and a Band Matrix VI. Introduction To Finite Element Method Programming 6.1. - Introduction 6.2. - Finite Element Method Discussed Program 6.2.1. - First Section Programming: Displacements Calculation 6.2.2. - Second Section Programming: Stresses Calculation 6.2.3. - Third Section Programming: Displacement Calculation 6.3. - Graphic Processor Programming 6.3.1. - Subroutine Draw p. 13

6.3.2. - Subroutine Number 6.3.3. - Subroutine Zoom 6.3.4. - Subroutine Deformed 6.3.5. - Graphic Processor Functioning 6.3.6. - Visual Basic Special Commands which Have Been Used in the Graphic Processor 6.3.7. - Application Example VII. Storage Improvements 7.1. - Introduction 7.2. - Storage Space Improvement 7.3. - Improved Procedure VIII. Introduction to Error Estimation in F.E.M. 8.1. - Error Measuring and Estimation 8.1.1.- A Priori Error Calculation 8.1.2.- A Posteriori Error Estimation 8.1.3.- A Posteriori Estimator Type 8.2. - A Posteriori Error Estimation in 2D Elasticity Problems 8.2.1. - Obtaining of a Recovered Solution 8.2.2. - Error Estimation in the Energy Norm. Z2Estimator 8.3. - Z2[11] Estimator Theorem 8.4. - Example 1 8.4.1. - Shape Function for the 3 Nodes Triangular Finite Element 8.4.2. - F.E.M. Process until the Stresses Calculation 8.4.3. - Error Estimation 8.4.4. - Deformation Energy Matrix Norm 8.5. Computer Program Commented 8.6. - Example 2 8.7. - Conclusions 8.8. - Full Computer Program 8.9. - Chapter 8 references p. 14

IX. Bibliography Annex: Creating a Form 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES ALARCÓN, A., ALVAREZ, R., GÓMEZ-LERA, S. Cálculo Matricial de Estructuras. Barcelona, Spain: Ed. Reverté, S.A., 1986. ISBN: 84-291-4801-9. BROWN, D.K. An Introduction to Finite Element Method Using BASIC Programs.2 nd edition. London, UK: Ed. Spon Press, 1998. ISBN-10: 0412005719/ ISBN-13: 9780412005718. CEBALLOS, F.J. Visual Basic. Curso de Programación. 2 nd edtion. Madrid, Spain: Ed. Ra- Ma, 1999. ISBN: 9788478973576. MICHAVILA, F & GAVETE, L. Programación y Cálculo Numérico. Barcelona, Spain: Ed. Reverté, 1985. ISBN: 9788429126778. OÑATE, E. Cálculo de Estructuras por el Método de Elementos Finitos. Análisis Estático Lineal. Spain: Ed. CIMNE, 1995. ISBN: 9788487867002. ZIENKIEWICZ, O.C., TAYLOR, R.L. The Finite Element Method: Its Basis and Fundamentals. 6 th edition. Oxford, UK: Ed. Elsevier Butterworth-Heinemann, 2005. ISBN-10: 0750663219/ ISBN-13: 9780750663212. Spanish version: ZIENKIEWICZ, O.C., TAYLOR, R.L. El Método de los Elementos Finitos. Formulación Básica y Problemas Lineales. 4 th edition. Barcelona, Spain: Ed. CIMNE - Mc.Graw-Hill, 1994. ISBN: 9788495999528. p. 15

5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor Luis Gavete Corvinos E-mail: lu.gavete@upm.es Mondays, from 11:30 am to 2:00 pm Fridays, from 12:30 am to 2:00 pm Telephone: (+34) 91-336-64-66 Dpto. Matemática Aplicada a los Recursos Naturales E.T.S. INGENIEROS DE MINAS U.P.M C/ Ríos Rosas, 21 28003 Madrid, España. 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 16

AF.3. - NUMERICAL CALCULATION TEACHING STAFF Professor Luis Gavete Corvinos 1. - OBJECTIVES The purpose of this text is to introduce basic numerical calculation techniques employed in the Finite Element Method to the student and to serve as the first contact base with the numerical methods. Thus, all the mathematical concepts have been simplified as much as possible and a series of examples has been provided in order to facilitate the student work. As it is a distance learning course, it is necessary for the text to be accompanied by the required self-taught manual. Furthermore, the numerical techniques needed in order to do static and dynamic analysis by finite elements in linear and nonlinear cases have been covered. 2. - CONTENT The text consists of two simple introductory chapters containing basic introductory concepts about matrices and numerical calculation to allow the student to move forward to the second part of numerical calculation. This second part has a chapter on interpolation (focused on Lagrange Interpolation) with some spline function concepts. Subsequently, the numerical integration is covered, focusing on Gauss integration. Three chapters are dedicated to the basic concepts of numerical Algebra: a) equation systems; b) nonlinear equation systems; c) eigenvalues and eigenvectors. The intention is to cover the most common algorithms areas in the finite elements programs. There is also a chapter based on the resolution of the second order differential equation systems which originate from the dynamic analyses, and there is another chapter which contains an introduction to the equations in partial derivatives and methods of resolving them. p. 17

INDEX II. Matrices and Matrix Norms 1.1. -Basic Definitions 1.2. - Vector and Matrix Norms III. Numerical Calculation Introduction 2.1. - Introduction 2.2. - A Numerical Calculation Algorithm 2.3. - Summary 2.4. - Criteria in the Election of Algorithm IV. Interpolation 3.1. - The Interpolation Problem 3.2. - Other Interpolation Problems 3.2.1. - Taylor s Interpolation Problem 3.2.2. - Hermite s Interpolation Problem 3.3. - The General Problem of Interpolation 3.4. - Construction of the Interpolation Polynomial: Lagrange Formula 3.5. - Newton s Interpolation Formula 3.6. - Study of the Interpolation Error 3.7. - Piecewise Polynomial Interpolation 3.8. - Splice Cubic Interpolation (A.S.C) 3.9. - Approximated Calculation of Derivatives 3.10. - Richardson s Extrapolation V. Numerical Integration 4.1. - Introduction 4.2. - Investigation Methods with a Variable 4.2.1. - General Approach. Formulas of Interpolation Type 4.2.2. - Newton-Cotes Formulas 4.2.3. - Gaussian Quadrature Formulas 4.3. - Multiple Integrals p. 18

4.4. - Numerical Integration in Triangular or Tetrahedral Regions 4.5. - Needed Numerical Integration Order VI. Linear Equation Systems 5.1. - Introduction 5.2. - Direct Methods: Gauss Method 5.3. - Special Matrix Types 5.4.-Direct Matrix Factorization 5.5. - Iterative Methods 5.6. - Ill-Conditioned Systems of Equations 5.6.1. - Data Entry Errors 5.6.2. - Rounding Errors 5.6.3. - Conditioning of Non-singular Matrices 5.6.4. Matrix Norm 5.6.5. - Most Used Matrix Norms 5.6.6. - Property 5.6.7. - Error Calculation 5.7. - Application to the Optimization Techniques to the Linear Equation Systems Resolution 5.7.1. - Introduction 5.7.2. - Methods for the Resolution of Symmetric Systems Defined Positives 5.7.2.1. - Gradient Method (Or the Maximum Decrease) 5.7.2.2. - Conjugated Gradient Method 5.7.2.3. - Pre-conditioning Conjugate Gradient Method VII. Non-linear Equation Systems 6.1. - Introduction 6.2. - Newton-Raphson Method to Resolve a Non-linear Equation 6.3. - Newton-Raphson Method for Systems (Non-linear) 6.4. - Newton-Raphson Method Applied to the Equations System Originated by the Finite Element Method 6.4.1. - Newton-Raphson Method with Initial Stiffness 6.4.2. - Convergence Control (of the Program) p. 19

VIII. Eigenvalues and Eigenvectors 7.1. - Introduction 7.2. - Generalities 7.3. - Eigenvalues and Eigenvectors 7.4. - Determination Methods of the Characteristic Polynomial 7.5. - Transformation Methods 7.6. - Iterative Methods 7.7. - Methods of Values Calculation and Characteristic Vectors in Finite Elements IX. Differential Equations and Systems 8.1. - Introduction 8.2. - Modal Superposition Method 8.3. - Direct Integration Methods 8.3.1. - Newmark s Direct Integration Method X. Equations in Partial Derivatives 9.1. - Partial Derivative 9.2. - Mathematical Formulations and Solution of Physical Problems 9.3. - Foundations 9.4. - Some Typical Problems 9.5. - Functionals and Operators 9.6. - Numerical Methods for the Resolution of Equations in Partial Derivatives 9.7. - Application Example 9.7.1. - Variational Method 9.7.2. - Collocation Method 9.7.3. - Subdomain Method 9.7.4. - Galerkin Method 9.7.5. - Least Square Method 9.8. - Finite Element Method 9.9. - Brief Development of F.E.M. History p. 20

XI. Bibliography 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES Software: manuals BATHE, K.J. & WILSON, E. Numerical Methods in Finite Element Analysis.Ed. Prentice Hall, 1976. ISBN-10: 0136271901 / ISBN-13: 978-013627901. BATHE, K.J. Finite Element Procedures in Engineering Analysis. New Jersey, USA: Ed. Prentice-Hall, Inc., 2007. ISBN-10: 097900490X / ISBN-13: 978-0979004902. BURDEN, R. L. & DOUGLAS FAIRES, J. Numerical Analysis.9 th edition. Boston, USA: Ed. Brooks/Cole Cengage Learning, 1985. ISBN-10: 0-538-7335-9 / ISBN-13: 978-0-538-7335-9. Spanish version: BURDEN, R. L. & DOUGLAS FAIRES, J. Análisis Numérico. Mexico: Ed. Grupo Editorial Iberoamérica, 1985. ISBN: 9789706861344. CONDE, C. & WINTER, G. Métodos y Algoritmos Básicos de Álgebra Numérica. Seville, Spain: Ed. Reverté, 1990. ISBN: 9788429150360. DAHLQUIST, G. & BJÖRCK, A. Numerical Methods. Mineola, New York: Ed. Dover Publications, 2003. ISBN: 9780486428079. GASCA, M. Cálculo Numérico I. Ed. Universidad Nacional de Educación a Distancia, 1990. LIPSCHUTZ, S. Álgebra Lineal. 2 nd 9788476157589. edition. Mexico: Ed. McGraw Hill, 1992. ISBN: LIPSCHUTZ, S. Linear Algebra. Ed. McGraw Hill, 2000.ISBN: 9780071362009. LUTHER.; OLIVEIRA, A. & SCHUTZ, F.J. Métodos Numéricos. Mexico: Ed. Limusa, 1978. p. 21

MICHAVILA, F. & GAVETE, L. Programación y Cálculo Numérico. Barcelona, Spain: Ed. Reverté, 1985. ISBN: 9788429126778. SEGERLIND, L.J. Applied Finite Element Analysis.2 nd edition. New York, USA: Ed. John Wiley, 1985. ISBN-10: 0471806625 / ISBN-13: 978-0471806622. STOER, J. & BULIRSCH, R. Introduction to Numerical Analysis. 3 rd edition. New York, USA: Ed. Springer Verlag, 2010. ISBN-10: 038795452X / ISBN-13: 978-0387954523. TURNER, P. Numerical Analysis. Lancaster, UK: Ed. Macmillan Press Ltd, 1994. 5. - TUTORSHIPS: OFFICE HOURS Students can contact the tutor using the subject s virtual classroom. Professor Luis Gavete Corvinos E-mail: lu.gavete@upm.es Mondays, from 11:30 am to 2:00 pm Fridays, from 12:30 am to 2:00 pm Telephone: (+34) 91-336-64-66 Dpto. Matemática Aplicada a los Recursos Naturales E.T.S. INGENIEROS DE MINAS U.P.M C/ Ríos Rosas, 21 28003 Madrid, España. 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 22

AF.4. - MATERIAL CONSTITUTIVE LAWS TEACHING STAFF Professor Enrique Alarcón Álvarez Mrs. Arancha Alarcon-Fleming Civil Engineer, PhD, PE, LEED AP 1. - OBJECTIVES The main objective of the subject is to show the possibilities of representing the nonlinear behavior of the materials through mathematical models. Therefore, it starts with hyperelastic materials, which allow us to observe the importance of thermodynamic concepts in materializing reversibility and, later, it sets out the Clausius-Duhem equation as a restriction to the satisfaction of any formulation. The thermodynamics of irreversible processes based on the local state principle allow the outlining of a global frame where the theories of viscoplasticity, damage, etc. are found, which, in themselves, constitute another objective of the course. 2. - CONTENT INDEX I. General Considerations 1.1. - Tensile Test 1.1.1. - Necking 1.2. - Idealization of the Macroscopic Behaviour 1.3. - Finite Deformations 1.4. - Type of Test to Characterize the Materials Behaviour 1.5. - Relaxation and Creeping II. Rheological Equations. Real Behavior Method 2.1. - State Equation 2.2. - Simple Rheological Models p. 23

2.2.1. - Elastic Solid 2.2.1.1. - Three-dimension Generalization 2.2.2. - Rigid Body Perfectly Plastic 2.2.2.1. - Three-dimension Generalization 2.2.3. - Viscous Body 2.2.3.1. - Three-dimension Generalization 2.3. - Complex Rheological Models 2.3.1. - Viscous Fluid 2.3.1.1. - Creep Behavior 2.3.1.2. - Relaxation Behavior 2.3.1.3. - Three-dimension Generalization 2.3.2. - Viscoelastic Solid 2.3.2.1. - Creep Behavior 2.3.2.2. - Three-dimension Generalization 2.3.3. - Generalized Viscous Models 2.3.3.1. - Generalized Maxwell Models 2.3.3.2. - Generalized Kelvin Models 2.3.4. - Elastic Body Perfectly Plastic 2.3.5. - Perfectly Viscoplastic Solid 2.3.6. - Other Behavior Models III. Calculation with Linear Rheological Models. Finite Element Method 3.1. - Linearity 3.2. - Linear Elasticity 3.3. - Finite Element Method (FEM) 3.4. - Linear Viscoelasticity 3.4.1. - Functional Formulation. Creeping and Relaxation Functions 3.4.1.1. - Creep Function 3.4.1.2. - Relaxation Function 3.4.1.3. - Alternatives Forms of Integral Representation 3.4.1.4. - Three-dimension Generalization 3.4.2. - Correspondence Principle p. 24

3.4.2.1. - Transformed Viscoelastic Equations 3.4.2.2. - Resolution Method 3.4.3. Viscoelastic Calculation through Finite Element Method 3.4.3.1. - Representation through State Variables 3.4.3.2. - Integration of the State Variables 3.4.3.3. - Incremental Formulation of the Viscoelastic problem IV. Plasticity 4.1. - One-dimensional Behavior 4.1.1. - Elasticity Limit. Hardening 4.1.2. - Yield surface. Hardening 4.1.3. - Charge and Discharge Criteria 4.1.4. - Idealized Behavior Equations 4.1.4.1. - Solid Perfectly Plastic 4.1.4.2. - Hardening Plastic Solid 4.15. - Hardening Rule 4.2. - Plasticity Theory. General Formulation 4.2.1. - Yield Surface 4.2.1.1. - Von MisesYield Surface 4.2.1.2. - TrescaYield Surface 4.2.2. - Load-Unload Criteria 4.2.3. - Yield Rule 4.2.4. - Plastic Consistency 4.2.5. - Hardening 4.2.5.1. - Isotropic Hardening 4.2.5.2. - Kinematic Hardening 4.2.5.3. - Mix Hardening 4.3. - Plasticity. Analysis by Finite Elements 4.3.1. - Newton-Raphson Method 4.3.2. - Nonlinear Finite Element Method: Algorithm 4.3.3. - Residual Vector Evaluation: Integration of the Elastoplastic Behavior Equations p. 25

4.3.3.1. - Generalized Trapezoidal Rule 4.3.4. - Tangent Operator Evaluation V. Mechanic of Degradable Mean 5.1. - Mechanic Representation 5.1.1. - Degradation Variable 5.1.2. - Effective Stress 5.1.3. - Principle of Equivalence in Deformation 5.1.3.1. - Elastic Behavior 5.1.3.2. - Plastic Behavior 5.1.3.3. - Fragile Material 5.2. - Three-dimension Generalization 5.2.1. - Elasticity- Degradation Coupling 5.3. - Three- Dimension Degradation Criteria 5.3.1. Damage Equivalent Stress Criterion 5.3.1.1.1. - Release Rate of Elastic Energy 5.3.2. - Asymmetric Criteria in Deformation 5.4. - Evaluation of the Degradation 5.4.1. - Degradation Micro-mechanics 5.4.2. - Formulation of the Degradation Law 5.4.3. - Three-dimensional Fracture Criterion 5.4.4. - Determination of the Material Parameters 5.4.5. - Pure Fragile Degradation 5.4.6. - Ductile Degradation 5.5. - Plasticity-Degradation Attachment 5.6. - Degradation Mechanic: Numerical Analysis of Fracture Prediction in Structures 5.6.1. - Uncoupled Analysis 5.6.2. - Local Coupled Analysis 5.6.3. - Total Coupled Analysis 3. - BASIC TEXT AND OTHER TEACHING MATERIALS p. 26

Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES LEMAÎTRE, J. & CHABOCHE, J.L. Mecanique des Materiaux Solides.Ed. Dunod, 1988. ISBN: 9782100013975. LUBLINER, J. Plasticity Theory.New York, USA: Ed. Dover Publications, 2008. ISBN: 9780023721618. MAUGIN, G.A.The Thermodynamics of Plasticity and Fracture.New York, USA: Ed. Cambridge University Press, 1992. ISBN: 9780521397803. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor: Dr. Enrique Alarcón Álvarez E-mail: enrique.alarcon@upm.es Mrs. Arancha Alarcon-Fleming E-mail: Mondays, from 4:30 pm to 8:30 pm Telephones: (+34) 91-336-53-40 (+34) 91-336-30-21 Dpto. Estructuras E.T.S. INGENIEROS INDUSTRIALES U.P.M. C/ José Gutiérrez Abascal, 2 28006 Madrid, Spain p. 27

6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 28

MSC NASTRAN. AP.1. - INTRO TO THE USE OF PRACTICAL SOFTWARE. I. TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1.- OBJECTIVES In an engineering project, the Finite Element Method requires the use of algorithms programmed by computer and the basis of calculation is set out, in most cases, using finite element commercial programs; so it is necessary to supplement the theoretical training in the Finite Element Method with the use of software. To that end, the MSC Patran/Nastran program has been chosen since it is a general purpose program, which in addition allows the use of a specific license for the Master s. The MSC brand, a standard of FE programs, permits the user to put into practice all the knowledge that has been taught on the course and in its specific modules. The aim of this subject, as its name indicates, is to introduce the student to the use of practical software based on the Finite Element Method and for the student feel sufficiently at ease from the beginning to acquire knowledge continuously during the course in the rest of the subjects of Theory and Practice. 2.-CONTENT This subject is eminently practical and both its content and its structuring are focused on the student becoming familiar with the use of the program from the beginning of the course since it will be useful throughout, and will be the means of materializing and applying the knowledge acquired during the study of the other subjects. The subject has been structured into the following chapters: p. 29

Preliminary Work 1. Overview 2. Introduction to the Finite Element Method 3. Basics of MD Nastran and Patran 4. MD Nastran Elements Overview 5. Units Sections 1. Space Station Truss 1. Introduction to geometry 2. Coordinate Systems 3. Grid Points i. Workshop 1: Coordinate Systems 4. The CBAR Elements 5. Multiple Subcases 6. Post Processing CBAR Results i. Workshop 2: Bridge Truss 2. Case Study: Traffic Signal Pole 1. Material Properties 2. The CBEAM Element 3. Fields 4. Post Processing CBEAM Element i. Workshop 3: Tapered Plate 3. Case Study: Aircraft Wing Rib 1. Meshing 2. 2-D Elements 3. Single Point Constraints 4. Loads 5. Element Distortion i. Workshop 4 A-C Tension Coupon 6. Analysis of Composite Materials p. 30

i. Workshop 4 D- Composite Tension Coupon 4. Case Study: Intercooler Structure 1. Create Geometry 2. Mesh the Geometry 3. Create Boundary Conditions 4. Plot Results i. Workshop 5 A-B 2 ½ D Clamp Obtaining a proper model is frequently the longest step in the realization of an analysis using Finite Element Method software, especially in those cases in which the models present complex geometrical forms. Similarly, the accuracy of the results will largely depend on obtaining an element model with proper forms and sizes (mesh density). To that end, the use of Solid and Meshing Model generation techniques of the Patran / MSC NASTRAN software will be described in detail. Also, the following practice exercises from Patran s workbook will be provided. Pre-Work 1 Landing Gear Strut PWs1-1 2 Simply Supported Beam PWs2-1 3 Editing a Nastran Input File PWs3-1 Course Materials 1 Coordinate Systems WS1-1 2 Bridge Truss WS2-1 3 Tapered Plate WS3-1 4 Tension Coupon WS4-1 p. 31

3. - BASIC TEXT AND OTHER TEACHING MATERIALS The teaching material for this subject is composed of MSC Patran /Nastran software and NAS 120 Linear Static, Normal Modes, and Buckling Analysis Using MD Nastran and Patran original MSC base text for an introductory course of PATRAN/ MSC NASTRAN, as well as the related exercises from the workbook. Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES The software includes an interactive help section with specific help for each of the different themes dealt with. Patran / Nastran software includes a lot of documentation with many practical examples and technical papers. It is important that students familiarize themselves with the software help and its documentation. The Quick Reference Guide, available in the installation directory of NASTRAN (qrg.pdf) will also be used frequently. 5. - SPECIFIC RECOMMENDATIONS Practicing with the computer and consulting the Quick Reference Guide and the online help section of the software is recommended. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Thursdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 p. 32

MSC NASTRAN. AP.2. - INTRO TO THE USE OF PRACTICAL SOFTWARE. II. TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES AND CONTENT This subject goes in depth about PATRAN / MSC NASTRAN. An introduction to MSC Nastran and its language is also made. The sections of this subject are: 5. Case Study: Scuba Tank 1. Model Simplification Methods 2. Importing Geometry 3. Viewports 4. Mesh Density Control 5. Axisymmetric Elements i. Workshop 6: Support Bracket 6. Case Study: Car Design 1. Groups and lists i. Workshop 7: Spacecraft Fairing 2. 0-D Elements 3. Rigid Body Elements i. Workshop 8: RBE2 vs RBE3 7. Case Study: Communications Tower 1. Normal Modes Analysis i. Workshop 9: Normal Modes of a Rectangular Plate 8. Case Study: Slender Column Buckling p. 33

1. Linear Buckling Analysis i. Workshop 10 Buckling of a Submarine Pressure Hull 9. Linear Contact 1. Linar vs Nonlinear analysis 2. Contact Bodies 3. Contact Detection 4. Plate Contact Case Study i. Workshop 11: 3D Contact Appendix 1. Parasolid Modeling 2. Results Postprocessing 3. Model Checkout In addition, an introduction to the Nastran Input files, with their language and particular commands (.bdf files) is made. The next exercises from MSC NASTRAN s workbook will be also provided in order to complete the practical approach. Course Materials 5 2 1/2 D Clamp WS5-1 6 Support Bracket WS6-1 7 Spacecraft Fairing WS7-1 8 RBE2 vs. RBE3 WS8-1 9 Normal Modes of a Rectangular Plate WS9-1 10 Buckling of a Submarine Pressure Hull WS10-1 11 3D Linear Contact WS11-1 Supplemental p. 34

12 Parasolid Modeling WS12-1 13 Stiffened Plate WS13-1 14 Importing a Temperature Field WS14-1 15 Importing a Pressure Field WS15-1 2. BASIC TEXT AND OTHER TEACHING MATERIALS CONTENT The basic text that composes the subject is: NAS 120 Linear Static, Normal Modes, and Buckling Analysis Using MD Nastran and Patran. Another essential teaching material for this subject is the practice program itself and its online documentation. Other advanced training material will be provided during the course. It is also recommended to use, as reference, the Nastran Quick Reference Guide and the MD demonstration problems. This documentation is stored in the computer during the installation of the software. Software: Patran/MSC Nastran Software 3. BIBLIOGRAPHICAL REFERENCES The bibliographical references are the interactive documentation of the program (Help): p. 35

Documentation: C:\MSC.Software\MD_Nastran_Student_Edition\20102\Nastran\md20101\Doc\pdf_n astran\ nastran_library.pdf p. 36

4. - SPECIFIC RECOMMENDATIONS It must be taken into account that Patran, which is a Pre/Post processor, uses PCL language and Nastran, which is only a solver, has its own language (.bdf files) The objective of Patran is to generate an input file in order for Nastran to resolve it. To do this Patran has its own graphical user interface and the PCL command language. Nastran input files (.bdf files) created by Patran have their own language. These files can be also created from scratch with a text editor. Becoming familiar with these Nastran input files is part of the objective of the course. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Thursdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 p. 37

MSC NASTRAN. AP.3. - PRACTICAL SOFTWARE EXAMPLES TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1.-OBJECTIVES The objective of the course is to complete, with exercises which must be done using Patran/MSC Nastran, the concepts explained previously in the theoretical and application subjects of the Expert module. The exercises of this subject will be done as the chapters of the AP1 and AP2 courses are studied. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. 2.-CONTENT The exercises represent a review of the concepts introduced in the subjects taken up to now, as well as the orderly use of the Patran/MSC Nastran software. The exercises will be similar to the following ones: Advanced analysis of a warehouse with temperature jump 3D Truss Bridge structural analysis Offshore platform design for different structural loads Structural analysis and validation of a Space Satellite. Structural analysis of a steam condenser Pre-stress bolt design of a union. p. 38

3. - BASIC TEXT AND OTHER TEACHING MATERIALS The teaching material is given with the resolved exercises proposed. Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: - AF.1: FEM general theory - AF.2: FEM Introduction to programming - AF.3: Numerical calculation - AF.4 Material laws 5. - CONTINUOUS ASSESSMENT EXERCISES The student should follow the instructions specified in the virtual classrooms by the professors. 6. - SPECIFIC RECOMMENDATIONS This subject must be taken after having finished subject AP.1 using the user s guide, manual of procedures and the online documentation of the corresponding commands, so that the main teachings of the different chapters can be completed and assimilated through practice. Each exercise should not take more than three hours, although it is recommended that the student practices as much as possible with the menu in the post-process phase and analyzes and interprets the physical sense of the results obtained. 7. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. p. 39

Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Thursdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 8. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 40

ANSYS. AP.1. - INTRO TO THE USE OF PRACTICAL SOFTWARE. I. TEACHING STAFF Responsible Mr. Alessio Trevisan MSc Mechanical Eng Tutors Ms. Valentina Peselli MSc Aerospace Eng Mr. Daniele Calsolaro MSc Aerospace Eng Mr. Michele Camposaragna MSc Mechanical Eng. PhD Applied Mathematics Mr. Stefano Cavalleri MSc Mechanical Eng. PhD Mechatronics and Innovative Technologies Mr. Nicola Varotto MSc Civil Eng 1.- OBJECTIVES In an engineering project, the Finite Element Method requires the use of algorithms programmed by computer and the basis of calculation is set out, in most cases, using finite element commercial programs. Therefore it is necessary to supplement the theoretical training in the Finite Element Method with the use of software. To that end, the ANSYS Mechanical program has been chosen since it is a general purpose program, which in addition allows the use of a specific license for the Master s. A standard of FE programs, it permits the user to put into practice all the knowledge that has been taught on the course and in its specific modules. The aim of this subject, as its name indicates, is to introduce the student to the use of practical software based on the Finite Element Method and for the student to feel sufficiently at ease from the beginning to acquire knowledge continuously during the course in the rest of the subjects of Theory and Practice. 2.-CONTENT This subject is eminently practical and both its content and its structuring are focused on the student becoming familiar with the use of the program from the beginning of the course since it will be useful throughout, and will be the means of materializing and applying the knowledge acquired during the study of the other subjects. p. 41

ANSYS DesignModeler as well as ANSYS Mechanical will be studied during the course ANSYS DesignModeler (ANSYS Geometry) DesignModeler, which is the ANSYS Geometrical Preprocessor will be studied. With DesignModeler you will be able to create simple and complex geometry as well as modify geometry from standard CAD software. The study of DesignModeler has been structured into the following chapters: Basics of ANSYS DesignModeler Geometry Modeling Geometry Simplification and Repair Geometry Modeling For CFD Beam and Shell Modeling Introduction to Advanced Topics The following solved exercises will be provided: Micro-Workshop 1: Pattern Micro-Workshop 2: Enclosure Workshop 3.1: DesignModeler Basics Workshop 3.2: Sketching Workshop 4.1: Modeling Workshop 6.1A: Geometry Cleanup and repair Workshop 6.1B: Geometry Cleanup and repair Workshops 6.2: Beam and Shell Modeling Workshops 6.3: Beam Modeling (Cross-sections) Workshop 7a: Parametric Mixing Tank Workshop 7b: Automotive Aero Workshop 7c: 2D Conical Combustion Chamber Workshop 7d: Bracket Workshop 7e: Pulley Workshop 7f: Shell Modeling p. 42

ANSYS Mechanical (ANSYS Workbench) ANSYS Workbench is a project-management tool. It can be considered as the top-level interface linking all our software tools. Workbench handles the passing of data between ANSYS Geometry / Mesh / Solver / Postprocessing tools. The study of ANSYS Workbench has been structured into the following chapters: Introduction Chapter 2: Mechanical Basics Chapter 3: General Preprocessing The next solved exercises will be provided: Workshop 2.1: ANSYS Mechanical Basics Workshop 3.1: 2D Gear and Rack Analysis Workshop 3.2: Named Selections Workshop 3.3: Object Generator You will continue studying ANSYS Workbench in AP.2 subject 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The teaching material for this subject is composed of: The introduction to ANSYS DesignModeler 15.0 training material and the related exercises from the workbook as well as Introduction to ANSYS Mechanical 15.0 and the related exercises from the workbook. Both training materials are the original ANSYS base texts for an introductory course of ANSYS DesignModeler and ANSYS Mechanical Software: ANSYS DesignModeler and ANSYS Mechanical 4. - BIBLIOGRAPHICAL REFERENCES The software includes an interactive help section with specific help for each of the different themes dealt with. ANSYS software includes a lot of documentation with p. 43

many practical examples and technical papers. It is important that the students familiarize themselves with the software help and its documentation 5. - SPECIFIC RECOMMENDATIONS Practicing with the computer and consulting the ANSYS Help is recommended. 6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Alessio Trevisan a.trevisan@enginsoft.it Ms. Valentina Peselli v.peselli@enginsoft.it Mr. Daniele Calsolaro d.calsolaro@enginsoft.it Mr. Michele Camposaragna m.camposaragna@enginsoft.it Mr. Stefano Cavalleri s.cavalleri@enginsoft.it Mr. Nicola Varotto n.varotto@enginsoft.it p. 44

ANSYS. AP.2. - INTRO TO THE USE OF PRACTICAL SOFTWARE. II. TEACHING STAFF Responsible Mr. Alessio Trevisan MSc Mechanical Eng Tutors Ms. Valentina Peselli MSc Aerospace Eng Mr. Daniele Calsolaro MSc Aerospace Eng Mr. Michele Camposaragna MSc Mechanical Eng. PhD Applied Mathematics Mr. Stefano Cavalleri MSc Mechanical Eng. PhD Mechatronics and Innovative Technologies Mr. Nicola Varotto MSc Civil Eng 1. - OBJECTIVES AND CONTENT This subject goes studies ANSYS Mechanical in depth. It s the continuation of subject AP.1. The sections of this subject are: Chapter 4: Meshing in Mechanical Chapter 5: Static Structural Analysis Chapter 6: Modeling Connections Chapter 7: Remote Boundary Conditions Chapter 8: Multistep Analysis Chapter 9: Vibration Analysis Chapter 10: Thermal Analysis Chapter 11: Results and Postprocessing Chapter 12: CAD and Parameters The next exercises from ANSYS Mechanical workbook of the introductory course will be also provided in order to complete the practical approach. Workshop 4.1: Meshing Control p. 45

Workshop 5.1: Linear Structural Analysis Workshop 5.2: Beam Connections Workshop 6.1: Contact Offset Control Workshop 6.2: Using Joints Workshop 7.1: Remote Boundary Conditions Workshop 7.2: Constraint Equations Workshop 8.1: Multistep Analysis Workshop 9.1: Free Vibration Analysis Workshop 10.1: Steady State Thermal Analysis Workshop 11.1: Meshing Evaluation Workshop 12.1: Parameter Management Workshop APPENDIX: Meshing 2. BASIC TEXT AND OTHER TEACHING MATERIAL CONTENT The teaching material for this subject is Introduction to ANSYS Mechanical 15.0 and the related exercises from the workbook. Both training materials are the original ANSYS base texts for an introductory course of ANSYS Mechanical. Software: ANSYS Mechanical 3. BIBLIOGRAPHICAL REFERENCES The software includes an interactive help section with specific help for each of the different themes dealt with. ANSYS software includes a lot of documentation with many practical examples and technical papers. It is important that students familiarize themselves with the software help and its documentation 4. - SPECIFIC RECOMMENDATIONS Practicing with the computer and consulting the ANSYS Help is recommended. 5. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. p. 46

Mr. Alessio Trevisan a.trevisan@enginsoft.it Ms. Valentina Peselli v.peselli@enginsoft.it Mr. Daniele Calsolaro d.calsolaro@enginsoft.it Mr. Michele Camposaragna m.camposaragna@enginsoft.it Mr. Stefano Cavalleri s.cavalleri@enginsoft.it Mr. Nicola Varotto n.varotto@enginsoft.it p. 47

ANSYS. AP.3. - PRACTICAL SOFTWARE EXAMPLES TEACHING STAFF Responsible Mr. Alessio Trevisan MSc Mechanical Eng Tutors Ms. Valentina Peselli MSc Aerospace Eng Mr. Daniele Calsolaro MSc Aerospace Eng Mr. Michele Camposaragna MSc Mechanical Eng. PhD Applied Mathematics Mr. Stefano Cavalleri MSc Mechanical Eng. PhD Mechatronics and Innovative Technologies Mr. Nicola Varotto MSc Civil Eng 1.-OBJECTIVES The objective of the course is to complete, with exercises which must be done using DesignModeler and ANSYS Mechanical, the concepts explained previously in the theoretical and application subjects of the Expert module. The exercises of this subject will be done as the chapters of the AP1 and AP2 courses are studied. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. 2.-CONTENT The exercises represent a review of the concepts introduced in the subjects taken up to now, as well as the orderly use of the ANSYS DesignModeler and ANSYS Mechanical software. The exercises will be similar to the following ones: Advanced analysis of a warehouse with temperature jump 3D Truss Bridge structural analysis Offshore platform design for different structural loads p. 48

Structural analysis and validation of a Space Satellite. Structural analysis of a steam condenser Pre-stress bolt design of a union. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The teaching material is given with the resolved exercises proposed. Software: ANSYS DesignModeler and ANSYS Mechanical 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: - AF.1: FEM general theory - AF.2: FEM Introduction to programming - AF.3: Numerical calculation - AF.4 Material laws 5. - CONTINUOUS ASSESSMENT EXERCISES The student should follow the instructions specified in the virtual classrooms by the professors. 6. - SPECIFIC RECOMMENDATIONS This subject must be taken after having finished subject AP.1 using the user s guide, manual of procedures and the online documentation of the corresponding commands, so that the main teachings of the different chapters can be completed and assimilated through practice. 7. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Alessio Trevisan a.trevisan@enginsoft.it Ms. Valentina Pesello v.peselli@enginsoft.it p. 49

Mr. Daniele Calsolaro d.calsolaro@enginsoft.it Mr. Michele Camposaragna m.camposaragna@enginsoft.it Mr. Stefano Cavalleri s.cavalleri@enginsoft.it Mr. Nicola Varotto n.varotto@enginsoft.it 8. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 50

MODULE A DYNAMIC ANALYSIS A.1. - FEM THEORY APPLIED TO STRUCTURE DYNAMIC ANALYSIS TEACHING STAFF Professor Francisco Montans Leal Mr. Marcos Latorre Ferrús MSc Aeronautical Eng. 1. - OBJECTIVES The initial objectives are to analyze the problems that are presented when a structure calculation is going to be made with a commercial Finite Element program and to provide some criteria to resolve them, and later to focus on some specific structural types such as plates and sheets. Finally, it is also intended to provide the essential concepts and to identify the fundamental parameters which characterize the dynamic behavior of structural systems. 2. - CONTENT In the first chapter, we intend to present an overview of the problems and different decisions that an analyst must take when a structure analysis is performed. The second chapter deals with the plate and sheet theories. In addition, the plate theory is established for thin plate cases from the Kirchhoff hypothesis and for thick plates from the Mindlin-Reisner hypothesis. In both cases, the study addresses the case of linear elasticity for homogeneous, isotropic, perpendicular charged to their mid-surface plates of constant thickness. Both linear theory and the membrane theory are developed for the constant thickness of thin sheets, and also for the linear case and supposing homogeneous and isotropic material. In the last chapters, structural dynamic analysis is addressed. Thus, after a brief introduction and a review of the essential concepts, the treatment of the systems is p. 51

studied with a degree of freedom in order to continue, after the mass and consistent damping matrix has been introduced, with the study of structural systems whose dynamic response can be characterized through a number of finite degrees of freedom. INDEX I. Fundamentals of dynamics of structures 1. Single-Degree-of-Freedom Systems 1.1.- Introduction 1.2.- Free undamped vibrations 1.2.1.- Equation of motion 1.2.2.- Harmonic motion: more formal approach solution 1.3.- Free damped vibrations 1.3.1.- Underdamped motion 1.3.2.- Overdamped motion 1.3.3.- Critically damped motion 1.4.- Response to harmonic excitation 1.4.1.- Undamped system 1.4.2.- Damped system 1.4.3.- Dynamic response factor 1.4.4 Frequency response function method 1.4.5.- Laplace transform based analysis 1.5.- General forced response 1.5.1.- Impulse response function 1.5.2.- Response to an arbitrary excitation II. Multi-Degree-of-Freedom Systems 2.1.- Introduction 2.1.1.- Two-Degree-of-Freedom system 2.1.2.- Mathematical modeling of damping 2.1.3.- Solutions of the equation of motion 2.2.- Free undamped vibrations of MDOF systems 2.2.1.- Natural frequencies and mode shapes p. 52

2.2.2.- Orthogonality of mode shapes 2.2.3.- Modal matrices 2.2.4.- Normalization of modes 2.2.5.- Response of undamped MDOF systems 2.3- Free damped vibrations of MDOF systems 2.4.- Response of MDOF systems under arbitrary loads 2.5.- Response of MDOF systems under harmonic loads 2.6.- Systems with distributed mass and stiffness 2.6.1.- Vibration of beams 2.6.2.- Vibration of plates III. Introduction to signal analysis 3.1.-Introduction to signal types 3.1.1 Deterministic signals 3.1.2 Random signals 3.2.- Fourier Analysis of signal 3.2.1.- The Fourier Series 3.2.2.- The Fourier integral transform 3.2.3.- Digital signals II. Finite element procedures for the dynamic analysis of structures IV. Finite element discretization of continuous systems. Stiffness and Mass matrices 4.1.- Stiffness matrix 4.1.1 Beam elements 4.1.2 Continuum elements 4.2.- Mass matrices 4.2.1 Consistent mass matrix 4.2.2 Lumped mass matrix V. Computational procedures for eigenvalue and eigenvector analysis. 5.1.- The modal decomposition revisited. Mode superposition analysis 5.2.- Other eigenvalue and eigenvector problems 5.3.- Computation of modes and frequencies 5.4.- Reduction of the general eigenvalue problem to the standard eigenp. 53

value problem. 5.5.- Static condensation. 5.6.- Model order reduction techniques: the Guyan reduction 5.7.- Inclusion of damping matrices 5.8.- Complex eigenvalue problem: complex modes VI. Computational algorithms for eigenvalue and eigenvector extraction 6.1.- Some previous concepts 6.1.1.- Matrix deflation 6.1.2.- Rayleigh quotient 6.1.3.- Courant minimax characterization of eigenvalues and Sturm sequence 6.1.4.- Shifting 6.1.5.- Krylov subspaces and the Power 6.2.- Determinant search method 6.3.- Inverse iteration method 6.4.- Forward iteration method 6.5.- Jacobi method for the standard eigenvalue 6.6.- The QR decomposition and algorithm 6.7.- Jacobi method for the generalized eigenvalue 6.8.- Bathe s subspace iteration method and Ritz 6.9.- Lanczos method VII. Transient analyses in linear elastodynamics 7.1 Introduction 7.2 Structural dynamics and wave propagation analyses. The Courant condition 7.3 Linear multistep methods. Explicit and implicit algorithms. Dahlquist theorem 7.4 Explicit algorithms: central difference method 7.5 Implicit algorithms 7.5.1 Houbolt method 7.5.2 Newmark-β method 7.5.3 Collocation Wilson-θ methods 7.5.4 Hilbert-Hughes-Taylor (HHT) α method p. 54

7.5.5 Bathe-Baig composite (substep) method 7.6 Stability and accuracy analysis VIII. Transient analysis in nonlinear dynamics 8.1 The nonlinear dynamics equation 8.2.- Time discretization of the nonlinear dynamics equation 8.3.-Example: The nonlinear Newmark- β algorithm in predictor-d-form IX. Harmonic analyses 9.1.- Discrete Fourier Transform revisited 9.2.- Harmonic analysis using the full space 9.3.- Harmonic analysis using mode X. Spectral and seismic analyses 10.1.- Accelerograms and ground excitation 10.2.- The equation of motion for ground excitation. Accelerometers and vibrometers 10.3.- Elastic Response Spectra: SD, SV, SA, PSV, PSA 10.4.- Modal superposition methods for spectral analysis. Modal 10.5.- Static correction or mode acceleration method XI. Bibliography 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES 11 Bibliography In this section we include a dozen selected books for the reader s convenience. 1. K.J. Bathe. Finite Element Procedures. Prentice Hall 1996. p. 55

2. A.K. Chopra. Dynamics of Structures. Prentice Hall 1995. 3. R.W. Clough, J Penzien. Dynamics of Structures. McGraw-Hill 1975. 4. J.P. Den Hartog. Mechanical Vibrations. Dover 1985. 5. J.L. Humar. Dynamics of Structures. Balkema 2002. 6. T.J.R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover 2000. 7. L. Meirovitch. Fundamentals of Vibrations. Waveland 2010. 8. D.E. Newland. Mechanical Vibration Analysis and Computation. Dover 2006. 9. W.H.Press, S.A.Teukolsky, W.T. Vetterling, B.P.Flannery. Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd Ed. Cambridge 1992 10. S Rao. Vibration of Continuous Systems. Wiley 2007. 11. S Rao. Mechanical Vibrations. 5th edition of Prentice-Hall 2010. p. 56

12. O Zienkiewicz, R.L. Taylor. The Finite Element Method (3 volumes). 6th edition of Elsevier 2005. 5. - SPECIFIC RECOMMENDATIONS It is generally advisable to resolve the simple exercises by analyzing the results which are obtained with different meshes and to verify to what extent the hypotheses made are fulfilled in the theoretical approaches. On the other hand, it should not be forgotten that only with training in calculus can clear criteria be acquired. Therefore, it is recommended that students try to do similar exercises to the ones proposed as continuous assessment exercises, but use problems from their professional activity as a base. 6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Marcos Latorre Ferrús E-mail: m.latorre.ferrus@upm.es 7. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 57

MSC NASTRAN. A.2. - INTRO TO DYNAMIC ANALYSIS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Miguel Ángel Moreno Fernández de Yepes Civil Eng. PhD Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The purpose of the subject is to introduce the student to the basic concepts of dynamic analysis of structures by using the practice program to resolve different types of dynamic analyses, so that theoretical concepts studied in previous chapters can be assimilated. Real problems will be studied with a Finite Element program (Patran/Nastran). 2. - CONTENT The content of this subject is presented in two parts: software training notes and application exercises from the workbook. The Patran/Nastran training notes are structured in the following fourteen chapters: 1. Review of Fundamentals 2. Mass Modeling 3. Normal Modes Analysis 4. Normal Modes Analysis for Pre-Stiffened Structures 5. Model Checkout 6. Reduction in Dynamic Analysis 7. Response Method 8. Damping Overview 9. Transient Response Analysis p. 58

10. Frequency Response Analysis 11. Residual Vector Method 12. Enforced Motion 13. Random Analysis 14. Response/Shock Spectrum Analysis 15. Complex Eigenvalue Analysis 16. Glued Contact in Normal Modes Analysis Various exercises are also proposed, involving the following topics: Modal Analysis, Transitory Analysis, Analysis of Harmonic Response, Spectral Analysis and PSD Analysis. INDEX 1) Normal Modes Analysis of a 2 DOF Structure 2) A. Normal Modes Analysis B. Normal Modes Analysis with Coarse Mesh C. Normal Modes Analysis with Fine Mesh 3) Modal Analysis of a Circuit Board 4) A. Modal Analysis of a Car Chassis B. Modal Analysis of a Car Chassis without Rigid Body Modes 5) A. Modal Analysis of Tuning Fork using Fine Mesh with Tet 10 Elements B. Modal Analysis of Tuning Fork using Coarse Mesh with Tet 10 Elements C. Modal Analysis of Tuning Fork using Fine Mesh with Tet 4 Elements D. Modal Analysis of Tuning Fork using Coarse Mesh with Tet 4 Elements E. Modal Analysis of Tuning Fork using 1D Elements 6) A. Modal Analysis of a Tower B. Modal Analysis of a Tower with Soft Ground Connection 7) A. Normal Modes Analysis for Pre-stiffened Plate Model B. Modal Analysis for Pre-stiffened Turbine Blade at Different RPM p. 59

8) Effective Mass 9) Direct Transient Analysis 10) Direct Transient Analysis of a Car Chassis 11) Modal Transient Analysis 12) Modal Transient Analysis of the Tower Model with Seismic Input 13) Direct Frequency Response Analysis 14) Modal Frequency Response Analysis 15) Frequency Response Analysis of a Circuit Board 16) Modal Frequency Analysis of a Car Chassis 17) Direct Transient Response with Enforced Acceleration, Matrix Partition Approach 18) A. Random Analysis with Single Excitation Using MSC.Random 19) B. Random Analysis with Multiple Excitations Using MSC.Random Vibration Analysis of a Satellite Model Using MSC.Random 20) Calculate Response Spectra 21) Response Spectrum Analysis 22) Normal Modes, Glued Contact 23) Direct Transient Response with Enforced Acceleration, Large Mass Method 3. - BASIC TEXT AND OTHER TEACHING MATERIALS NAS122 - Dynamic Analysis Using MSC Nastran and Patran Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES For bibliographical references, it is useful to use the Nastran Quick Reference Guide, which is available in: C:\MSC.Software\MD_Nastran\md[ ]\doc\pdf_nastran\reference\qrg.pdf And also the Patran help in its dynamic analysis sections (opened from the Patran interface). p. 60

5. - SPECIFIC RECOMMENDATIONS This subject is very large and interesting; it offers a complete and exhaustive treatment of the different types of dynamic analysis that are made today using Finite Elements software. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 p. 61

MSC NASTRAN. A.3. - DYNAMIC ANALYSIS PRACTICES TEACHING STAFF Responsible Mr. Miguel Ángel Moreno Fernández de Yepes Civil Eng. PhD Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2. - CONTENT The exercises provided are similar to the ones shown below: 1) Frequency response of a bedplate. 2) Transient response of a bedplate. 3) Harmonic analysis of the behavior of a chimney subjected to wind loads (Vortex Shedding) 4) Response spectrum analysis of a Workbench 5) Airbus A-320 Aircraft Wing Random Analysis (PSD analysis). p. 62

3. - BASIC TEXT AND OTHER TEACHING MATERIALS The documentation provided with the resolved exercises given pertaining to the dynamic analysis of MSC composes the teaching material. Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: A.1. - Static and Dynamic Structural Analysis Foundations A.2. - Dynamic Analysis Course. Application with the Practice Program Patran and Nastran Documentation 5. - CONTINUOUS ASSESSMENT BOOKLETS The student must follow the instructions given in the virtual classroom by the professor. 6. - SPECIFIC RECOMMENDATIONS This subject must be taken at the same time that the subject A.2 using the user s guide and the online documentation of the corresponding commands and onscreen menus, so that the other chapter s main teachings can be completed and assimilated through practice. 7. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 p. 63

Fax: (+34) 91-386-45-80 8. - ADDRESS FOR SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 64

ANSYS. A.2. - INTRO TO DYNAMIC ANALYSIS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Miguel Ángel Moreno Fernández de Yepes Civil Eng. PhD Mr. Ambrosio Baños Abascal MSc Science Tutors Ms. Nurial Moral. MSc Science. PhD Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The purpose of the subject is to introduce the student to the basic concepts of dynamic analysis of structures by using the practice program to resolve different types of dynamic analyses, so that theoretical concepts studied in previous chapters can be assimilated. Real problems will be studied with a Finite Element program (ANSYS Mechanical). 2. - CONTENT The following analyses will be studied: p. 65

The content of this subject is presented in two parts: software training notes and application exercises from the workbook. The ANSYS Mechanical training notes are structured into the following chapters: Lecture 1: Introduction Lecture 2: Mechanical Basics Lecture 3: Damping Lecture 4: Modal Analysis Lecture 5: Harmonic Analysis Lecture 6: Linear Perturbation Analysis Lecture 7: Response Spectrum Analysis Lecture 8: Random Vibration Lecture 9: Transient Analysis Various exercises are also proposed, involving the following topics: Modal Analysis, Transitory Analysis, Analysis of Harmonic Response, Spectral Analysis and PSD Analysis. Workshop 1: Intro. (Fly Wheel) Workshop 2: Mechanical Basics Workshop 3: Damping in Mechanical Workbench Workshop 4A: Modal Analysis (Plate with a Hole) Workshop 4B: Modal Analysis (Model Airplane Wing) Workshop 5: Harmonic Response (Fixed-Fixed Beam) Workshop 7: Response Spectrum (Suspension Bridge) Workshop 8: Random Vibration (Girder Assembly) Workshop 9A: Transient Analysis (Caster Wheel Test) Workshop 9B: Transient Analysis of a Gantry Crane Workshop 9C: Applying Initial Rotational Velocity 3. - BASIC TEXT AND OTHER TEACHING MATERIALS ANSYS Mechanical Linear and Nonlinear Dynamics 15.0 p. 66

Software: ANSYS Mechanical ANSYS Help 4. - BIBLIOGRAPHICAL REFERENCES For bibliographical references, it is useful to use the ANSYS Help 5. - SPECIFIC RECOMMENDATIONS This subject is very large and interesting; it offers a complete and exhaustive treatment of the different types of dynamic analyses that are made today using Finite Element software. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Ms. Nuria Moral n.moral@enginsoft.it Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 p. 67

ANSYS. A.3. - DYNAMIC ANALYSIS PRACTICES TEACHING STAFF Responsible Mr. Miguel Ángel Moreno Fernández de Yepes Civil Eng. PhD Mr. Ambrosio Baños Abascal MSc Science Tutors Ms. Nurial Moral. MSc Science. PhD Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2. - CONTENT The exercises provided are similar to the ones shown below: Frequency response of a bedplate. Transient response of a bedplate. Harmonic analysis of the behavior of a chimney subjected to wind loads (Vortex Shedding) Response spectrum analysis of a workbench Airbus A-320 Aircraft Wing Random Analysis (PSD analysis). p. 68

3. - BASIC TEXT AND OTHER TEACHING MATERIALS The documentation provided with the resolved exercises given pertaining to the dynamic analysis of ANSYS Mechanical composes the teaching material. Software: ANSYS Mechanical. ANSYS DesignModeler 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: A.1. - Static and Dynamic Structural Analysis Foundations A.2. - Dynamic Analysis Course. Application with the Practice Program ANSYS Help 5. - CONTINUOUS ASSESSMENT BOOKLETS The student must follow the instructions given in the virtual classroom by the professor. 6. - SPECIFIC RECOMMENDATIONS This subject must be taken at the same time that the subject A.2 using the online documentation of the corresponding commands and onscreen menus, so that the other chapter s main teachings can be completed and assimilated through practice. 7. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Ms. Nuria Moral n.moral@enginsoft.it Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com p. 69

Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 8. - ADDRESS FOR SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 70

MODULE B NON LINEAR ANALYSIS B.1. - F.E.M THEORY APPLIED TO NON-LINEAR STRUCTURES CALCULATION TEACHING STAFF Professor José M a Sancho Aznal 1. - OBJECTIVES The purposes of this subject are to learn and understand the formulation, using the Finite Element Method, of nonlinear problems in structures from an engineering perspective, the application of large displacement problems, large deformations and stiffening by stress; as well as the introduction to nonlinear mechanics of solids, and in addition to the formulation of beam elements and their methods of solution. 2. - CONTENT INDEX I. Introduction to Nonlinear Problems 1.1. - Nonlinearity causes 1.2. - Some simple examples 1.3. - Non geometric linearity with a G.D.L 1.4. - Models with two G.D.L. Critical Loads II. Continuum Mechanics Applied to Nonlinear Analysis 2.1. - Movement Description. Lagrangian Formulations 2.2. - Polar Decomposition Theorem 2.3. - Cauchy and Piola-Kirchhoff stresses III. Matrix Formulation of Elements 3.1.- Incremental Equilibrium Equations 3.2.- Stiffness Matrix of a Hinged Bar 3.3. Stiffness Matrix of a Bar Subjected to Flexure p. 71

VI. Solution Methods 4.1.- Loads Increment 4.2.-Critical Steps 4.3. -Arch-length Methods 4.4. - Instability Points Calculation. Linearized Buckling 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Teaching Units 4. - BIBLIOGRAPHICAL REFERENCES Teaching units and references are in the same unit. 5. - TUTORSHIPS Students can contact tutor using the subject s virtual classroom Professor José M a Sancho Aznal E-mail: jmsancho@invi.uned.es 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 72

MSC NASTRAN. B.2. - INTRO TO NONLINEAR ANALYSIS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The first objective of the course is to find answers to some basic questions of nonlinear structural calculation such as the following: What is a nonlinear structure? What kind of problems requires a nonlinear analysis? What are the causes of nonlinear behavior? What is different in a non-linear analysis? What is different in a nonlinear analysis by finite elements? What are the essential peculiarities of a nonlinear analysis by finite elements? The second objective is to learn how to solve the questions through the use of a Finite Elements program like MSC Patran/Nastran. 2. - CONTENT The content of this subject is structured into different chapters in which the different nonlinearities are described, the proceedings to address them, examples of each one and recommendations for their treatment. In this subject the various types of nonlinear behavior, which can be grouped into three main groups, are studied with MSC Patran/Nastran: - Geometric nonlinearities - Material nonlinearities - Status change nonlinearities (Contacts) These topics will be seen in the following chapters: p. 73

1. Introduction to MD Nastran 2. Nonlinear versus Linear Analysis 3. Nonlinear Solution Strategy 4. Nonlinear Materials 5. Nonlinear Elements 6. Contact 7. Heat Transfer 8. Nonlinear Transient Dynamics Furthermore, some examples of the application of the different types of nonlinear behavior are presented in the workbook: 1. Linear and Nonlinear Analysis of a Cantilever Beam 2. Normal Modes Analysis of a Pre-stiffened Blade 3. Ball joint Analysis 4. Buckling of a Composite Plate 5. Rubber Door Seal 6. Interference Fit 7. Thermo-Structural Analysis of an Integrated Circuit Board 8. Dynamic Collapse of a Cylinder 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic text for the course is the Structural Nonlinearities User s guide of the Nastran software edited by MSC (NAS400) Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES From the aforementioned references, the following have been chosen: p. 74

- NAS400 Implicit Nonlinear Analysis using MD Nastran and Patran (module documentation) - Nastran Quick Reference Guide (installed with the software) 5.- SPECIFIC RECOMMENDATIONS This subject is very large as nonlinear problems are found in a wide range of technical applications. It is a good idea to study subject B.1 first. It is advisable for students to follow the resolution of the exercises after studying each chapter and to resolve the problems highlighted in the text of the subject as well as the exercises of subject B.3 in the continuous assessment booklet. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 p. 75

MSC NASTRAN. B.3. - NONLINEAR ANALYSIS PRACTICES TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Mariano Serrano MSc Mechanical Eng. Mr. Pablo Arrieta MSc Naval Eng. 1. - OBJECTIVES The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2.- CONTENT The exercises provided are similar to the ones shown below: 1. Large Displacements: arc with concentrated load 2. Buckling: Linear and nonlinear buckling analysis of a pile 3. Large Strains: Compression of an axisymmetric disc 4. Plasticity: Disc under cyclic load 5. Contact exercise: locking tab 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic documentation of the subject is provided with the resolved exercises given. Software: Patran/MSC Nastran Software p. 76

4. - BIBLIOGRAPHICAL REFERENCES The references are the same as in the application subject. 5. - CONTINUOUS ASSESSMENT EXERCISES The student must follow the instructions given in the virtual classroom 6. - SPECIFIC RECOMMENDATIONS This subject must be studied at the same time as subjects B.1 and B.2. At some points of B.2, students are asked to do some B.3 exercises. The five additional exercises can be completed after B.1 and B.2. 7. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Tuesdays, from 9:30 am to 1:30 pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 8. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 77

ANSYS. B.2. - INTRO TO NONLINEAR ANALYSIS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Gabriel Arias MSc Mechanical Eng. Tutors Ms. Elena Vallejo MSc Mine Eng. 1. - OBJECTIVES The first objective of the course is to find answers to some basic questions of nonlinear structural calculation such as the following: What is a nonlinear structure? What kind of problem requires a nonlinear analysis? What are the causes of nonlinear behavior? What is different in a nonlinear analysis? What is different in a nonlinear analysis by finite elements? What are the essential peculiarities of a nonlinear analysis by finite elements? The second objective is to learn how to solve the questions through the use of a Finite Elements program like ANSYS Mechanical. 2. - CONTENT The content of this subject is structured into different chapters in which the different nonlinearities are described, the proceedings to address them, examples of each one and recommendations for their treatment. In this subject the various types of non-linear behavior, which can be grouped in three main groups, are studied with ANSYS Mechanical: 1. Geometric nonlinearities 2. Material nonlinearities 3. Status change nonlinearities (Contacts) These topics will be seen in the following chapters: Overview General Procedures p. 78

Introduction to Contact Introduction to Metal Plasticity Buckling Nonlinear Diagnostics Furthermore, some examples of the application of the different types of nonlinear behavior are presented in the workbook: Workshop 2A: Small vs Large Deflection Workshop 2B: Performing a Restart Workshop 3A: Contact Stiffness Study Workshop 3B: Symmetric vs. Asymmetric Workshop 4A: Metal Plasticity Workshop 5A: Linear Eigenvalue Buckling Analysis Workshop 5B: Post Buckling Analysis Workshop 6A: Contact Diagnostics 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic text for the course is the ANSYS Mechanical Introduction to Structural Nonlinearities. Software: ANSYS Mechanical 4. - BIBLIOGRAPHICAL REFERENCES From the aforementioned references, the following have been chosen: - ANSYS Help (installed with the software) 5.- SPECIFIC RECOMMENDATIONS This subject is very large as nonlinear problems are found in a wide range of technical applications. It is a good idea to study subject B.1 first. p. 79

It is advisable for students to follow the resolution of the exercises after studying each chapter and to resolve the problems highlighted in the text of the subject as well as the exercises of subject B.3 in the continuous assessment booklet. 6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Gabriel Arias garias@cadfemuk.com Ms. Elena Vallejo evallejo@cadfemuk.com p. 80

ANSYS. B.3. - NONLINEAR ANALYSIS PRACTICES TEACHING STAFF Responsible Mr. Gabriel Arias MSc Mechanical Eng. Tutors Ms. Elena Vallejo MSc Mine Eng. 1. - OBJECTIVES The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2.- CONTENT The exercises provided are similar to the ones shown below: 1. Large Displacements: arc with concentrated load 2. Buckling: Linear and nonlinear buckling analysis of a pile 3. Large Strains: Compression of an axisymmetric disc 4. Plasticity: Disc under cyclic load 5. Contact exercise: locking tab 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic documentation of the subject is provided with the resolved exercises given. Software: ANSYS Mechanical 4. - BIBLIOGRAPHICAL REFERENCES p. 81

The references are the same as in the application subject. 5. - CONTINUOUS ASSESSMENT EXERCISES The student must follow the instructions given in the virtual classroom 6. - SPECIFIC RECOMMENDATIONS This subject must be studied at the same time as subjects B.1 and B.2. At some points of B.2, students are asked to make do B.3 exercises. The additional exercises can be completed after B.1 and B.2. 7. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Gabriel Arias garias@cadfemuk.com Ms. Elena Vallejo evallejo@cadfemuk.com 8. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 82

MODULE C HEAT TRANSFER ANALYSIS C.1. - F.E.M THEORY APPLIED TO HEAT TRANSFER TEACHING STAFF Professor Julio Hernández Rodríguez Associate Professor Pablo Gómez del Pino Mr. Claudio Zanzi PhD 1.- OBJECTIVES This course aims to provide the theoretical knowledge about heat transfer and the finite element method necessary for its specific application in the resolution of heat transfer problems, as well as in stationary or non-stationary systems. 2. CONTENT INDEX FIRST PART: HEAT TRANSMISSION BASIS I. Basic Heat Transmission Mechanisms 1.1.- General considerations 1.2.- Heat Flow. Gauss Theorem 1.3.- Heat Conduction 1.4. - Convection 1.5. - Thermal Radiation 1.6. - Combined Convection and Radiation II. Heat Transfer by Conduction 2.1. - Introduction 2.2. - Temperature Field in a Solid 2.3. - Contour Conditions p. 83

2.4. -2D Planar Wall in Steady State 2.5.- Overall Transmission Coefficient 2.6. - Variable Rate in Flat Plates III. Heat Transfer by Convection 3.1.- Introduction 3.2.- Dimensional Analysis 3.3.- Laminar Flow and Turbulent Flow 3.4.- Forced Convection along the Flat Plates 3.5. - Forced Convection within Ducts 3.6. Heat Transfer from a Cylinder in Cross Flow 3.7. Heat Transfer from Tube Banks in Cross Flow 3.8. - Free Convection IV. Heat Transfer by Radiation 4.1. - Radiation Intensity. Diffuse Emission 4.2. - Radiation Exchange between Black Bodies 4.3. - Radiation Exchange between Gray Bodies SECOND PART: FINITE ELEMENT METHOD IN FLUID-DYNAMICS AND HEAT TRANSMISSION PROBLEMS I. Introduction II. Fluid Mechanic Foundations. General Equations and Contour Conditions III. Equations Classification IV. Weighted Residual Methods V.Finite Element Method 5.1. - Introduction 5.2. - Spatial Discretization and Approximation Functions 5.3. - FEM Application Examples to Heat Transfer Problems 5.3.1. - Variational Formulation of an Stationary Problem of Heat Conduction 5.3.2. - Stationary and One-Dimensional Heat Conduction Example p. 84

5.3.3. - Comparison between the Variational Formulation and the Formulation based in the Galerkin Weighted Residuals Method 5.3.4. - Galerkin FEM Application to a Non Stationary Problem of Heat Transfer with Convection Effects VI. Exercises 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Teaching Units 4. - BIBLIOGRAPHICAL REFERENCES CHAPMAN, A.J. Heat Transfer.4 th edition. New York, USA: Ed. Collier-McMillan, 1984. ISBN-10: 0023214708 / ISBN-13: 978-0023214707. CUVELIER, C., SEGAL, A. & VAN STEENHOVEN, A.A. Finite Element Methods and Navier- Stokes Equations. Dordrecht, NL: Ed. Springer, 1986. ISBN-10: 90277221483/ ISBN-13: 978-9027721488. FLETCHER, C.A.J. Computational Techniques for Fluid Dynamics. 2 nd edition, vols.i and II. Sydney, Australia: Ed. Springer-Verlag, 1991. ISBN-10: 3540530584/ISBN-13: 978-3540530589. LEWIS, R.W.,ET AL.The Finite Element Method in Heat Transfer Analysis. West Sussex, UK: Ed. Wiley, 1996. ISBN-10: 0471943622/ ISBN-13: 9780471943624. MCADAMS, W.H.Heat Transmission. 3 rd edition. New York, USA: Ed McGraw-Hill, 1954.ISBN-10: 0070447993/ISBN-13: 9780070447998. PEYRET, R.& TAYLOR, T.D. Computational Methods for Fluid Flow. USA: Ed. Springer- Verlag, 1983. ISBN-10: 3540111476/ISBN-13: 9783540111474. TANNEHILL, J.C., ANDERSON, D.A., & PLETCHER, R.H. Computational Fluid Mechanics and Heat Transfer.2 nd edition. Philadelphia, USA: Ed. Taylor & Francis,1997.ISBN: 9781591690375. WENDT, J.F. Computational Fluid Dynamics: An Introduction. 3 rd Springer-Verlag, 2009. ISBN: 9783540850557. edition. Belgium: p. 85

ZIENKIEWICZ, O.C. Finite Element Method. 5 th edition. Oxford, UK: Ed. Butterworth- Heinemann, 2005. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor: Dr. Julio Hernández Rodríguez Mondays, from 4:00 pm to 8:00pm Telephone: (+34) 91-398-64-24 E-mail: jhernandez@ind.uned.es Dpto. de Mecánica E.T.S. INGENIEROS INDUSTRIALES UNED Apdo.deCorreos 60.149 28080 MADRID, ESPAÑA 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 86

MSC NASTRAN. C.2. - INTRO TO HEAT TRANSFER WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutor Mr. Amer Kasim MSc Mechanical Eng. 1.- OBJECTIVES In this course, students come into contact with and manage, from an analysis by finite elements perspective, the basic concepts of heat transfer such as: conduction, convection and radiation, at the same time as resolving stationary or transient heat transfer problems and other peculiarities of the thermal processes, which can be treated like nonlinearities. The software, which allows the numerical treatment of problems, is MSC Patran/Nastran. 2.- CONTENT The content of this subject is presented in two parts: software training notes and application exercises from the workbook: The Patran/Nastran training notes are structures in the following chapters: 1. Overview 2. MD Nastran Thermal Analysis 3. Conduction 4. Convection 5. Transient Thermal Analysis (SOL 159, 400, 600) 6. Radiation p. 87

7. Additional Topics 8. Basic Thermal Analysis Theory 9. Nonlinear Solvers The exercises from the workbook represent a review of the concepts related to heat transmission. A series of exercises containing the physics of thermal analysis will be proposed throughout the course: INDEX 1) Getting Started, Creating a Conduction Model 2) Circuit Board and Chips Using Conduction and Heating 3) Free Convection From Printed Circuit Board 4) Forced Air Convection From Printed Circuit Board 5) Axisymmetric Flow in a Pipe 6) Typical Avionics Flow 7) Thermal Contact Resistance 8) Transient Thermal 9) Transient Thermal Analysis of a Cooling Fin 10) Transient Analysis With Radiation Source 11) Heating a Block of Ice cream 12) Solution of a Simple Radiation to Space Problem 13) Directional Heat Loads 14) Radiation Enclosures 15) Thermal Stress Analysis With Directional Heat Loads 16) Thermal Stress Analysis of a Two-Metallic Plate 17) Import IGES File and Auto Tet Mesh 18) Create Group and List 19) MSC.Nastran Bulk Data 20) Shield 21) Thermal stress p. 88

22) MD Nastran SOL 400 3D Composite Element 23) Calculation of VF Using the Pixel Hemi-cube Method 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic text is NAS 104 MD Nastran Thermal Analysis and the Heat Transfer Analysis User s guide of MSC. Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES Expanding the aforementioned references, the following have been chosen: - Patran Analysis Guides - Nastran Quick Reference Guide (QRG) available at NASTRAN s installation directory 5.- SPECIFIC RECOMMENDATIONS Even though the subject is short in length, it has its own peculiarities, so the student must handle the heat transmission concepts very well and must apply them to each case. Before starting, the student must manage the concepts of conduction, convection and radiation well, and know what kinds of elements are useful to simulate these phenomena. At the same time, the student must know to distinguish whether the problem is stationary or transitory. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños Abascal a.banos@ingeciber.com Mr. Amer Kasim akasim@invi.uned.es Tuesdays, from 9.30am to 1.30pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 p. 89

MSC NASTRAN. C.3. - HEAT TRANSFER PRACTICES TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutor Mr. Amer Kasim MSc Mechanical Eng. 1.- OBJECTIVES The main objective of this subject is to complete, with exercises that have to be done using Patran/MSC Nastran, the concepts explained in the Theoretical and Application subjects of module C. 2.- CONTENT The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. The exercises provided are similar to the ones shown below: INDEX 1) Thermal analysis of an igloo. 2) Cryogenic tank thermal analysis. 3) Thermal analysis of a finned tube. 4) Concrete wall thermal analysis. 5) Radiation analysis of a system. p. 90

3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic documentation of the subject is provided with the resolved exercises given. Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: C1. - FEM Theory Applied to Heat Transfer C2. - Heat Transfer Course. Application with the Practice Program In addition to the accompanying documentation specified in C1 and C2, it is recommended to use: - Heat Transfer Analysis User s guide of MSC. - Nastran Quick Reference Guide (QRG) available in NASTRAN s installation directory. 5. - CONTINUOUS ASSESSMENT EXERCISES The student must follow the instructions given in the virtual classroom. Each exercise should not take more than three hours, although it is recommended that the student practices as much as possible with the menu in the post-process phase and analyzes and interprets the physical sense of the results obtained. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños Abascal a.banos@ingeciber.com Mr. Amer Kasim akasim@invi.uned.es Tuesdays, from 9.30am to 1.30pm Telephone: (+34) 91-386-22-22 Fax: (+34) 91-386-45-80 p. 91

7. - ADDRESS FOR SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 92

ANSYS. C.2. - INTRO TO HEAT TRANSFER WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Gabriel Arias MSc Mechanical Eng. Tutors Ms. Elena Vallejo MSc Mine Eng. 1.- OBJECTIVES In this course, students come into contact with and manage, from an analysis by finite elements perspective, the basic concepts of heat transfer such as: conduction and convection, at the same time as resolving stationary or transient heat transfer problems and other peculiarities of the thermal processes, which can be treated like nonlinearities. The software, which allows the numerical treatment of problems, is ANSYS Mechanical. 2.- CONTENT The content of this subject is presented in two parts: software training notes and application exercises from the workbook: The ANSYS Mechanical training notes are structured in the following chapters: Lecture 1: Introduction Lecture 2: Heat Transfer Fundamentals Lecture 3: Preprocessing Lecture 4: Boundary Conditions Lecture 5: Steady-State Heat Transfer Lecture 6: Nonlinear Thermal Analysis Lecture 7: Transient Thermal Analysis Lecture 8: APDL and Command Objects p. 93

Lecture 9: Thermal-Structural Coupled Analysis The exercises from the workbook represent a review of the concepts related to heat transmission. A series of exercises containing the physics of thermal analysis will be proposed throughout the course: Workshop 1: Thermal Conduction Bar Workshop 2: Heating Coil Workshop 3: Thermal Contact Workshop 4: Radiating System Workshop 5: Solenoid Workshop 6: Fin Tube Heat Exchanger Workshop 7: Soldering Iron Workshop 8: Phase Change 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic text is ANSYS Mechanical Heat Transfer 15.0. Software: ANSYS Mechanical 4. - BIBLIOGRAPHICAL REFERENCES Expanding the aforementioned references, the following have been chosen: - ANSYS Help available at ANSYS installation directory 5.- SPECIFIC RECOMMENDATIONS Even though the subject is short in length, it has its own peculiarities, so the student must handle the heat transmission concepts very well and must apply them to each case. Before starting, the student must manage the concepts of conduction and convection, and know what kinds of elements are useful to simulate these phenomena. At the same time, the student must know to how distinguish whether the problem is stationary or transitory. p. 94

6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Gabriel Arias garias@cadfemuk.com Ms. Elena Vallejo evallejo@cadfemuk.com p. 95

ANSYS. C.3. - HEAT TRANSFER PRACTICES TEACHING STAFF Responsible Mr. Gabriel Arias MSc Mechanical Eng. Tutors Ms. Elena Vallejo MSc Mine Eng. 1.- OBJECTIVES The main objective of this subject is to complete, with exercises that have to be done using ANSYS Mechanical, the concepts explained in the Theoretical and Application subjects of module C. 2.- CONTENT The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. The exercises provided are similar to the ones shown below: Thermal analysis of an igloo. Cryogenic tank thermal analysis. Thermal analysis of a finned tube. Concrete wall thermal analysis. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS The basic documentation of the subject is provided with the proposed and resolved exercises. p. 96

Software: ANSYS Mechanical and DesignModeler 4. - BIBLIOGRAPHICAL REFERENCES Subjects of this course: C1. - FEM Theory Applied to Heat Transfer C2. - Heat Transfer Course. Application with the Practice Program In addition to the accompanying documentation specified in C1 and C2, the use of ANSYS Help is recommended. 5. - CONTINUOUS ASSESSMENT EXERCISES The student must follow the instructions given in the virtual classroom. Each exercise should not take more than three hours, although it is recommended that the student practices as much as possible with the menu in the post-process phase and analyzes and interprets the physical sense of the results obtained. 6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Gabriel Arias garias@cadfemuk.com Ms. Elena Vallejo evallejo@cadfemuk.com 7. - ADDRESS FOR SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 97

MODULE F FLUID MECHANICS F.1. - FEM THEORY APPLIED TO FLUID MECHANICS TEACHING STAFF Professor Julio Hernández Rodríguez Associate Professor Pablo Gómez del Pino Mr. Claudio Zanzi PhD 1.- OBJECTIVES In the first section of this subject, fluid mechanics foundations are studied with a particular emphasis on deduction and analysis of mass conservation equations, movement quantity and energy. Furthermore, the characteristics of different flow types are described and the conditions in which the different simplified shapes of general equations can be applied are discussed. The comparative study of the different treatments, equations and contour conditions used will allow the student a better all-round understanding of the subject and the acquisition of indispensable knowledge in order to set out and carry out the numeric resolution of fluid mechanics problems of interest in engineering. In the second part of the subject, an introduction to the finite element method application to some of the flow types studied in the first part is made. 2.-CONTENT I. Introduction 1.1.- Basic characteristics of fluids 1.2.- Continuum hypothesis 1.3. - Forces in fluids 1.4. - Thermodynamic concepts 1.5. - Transport Phenomena II. Fluid Kinematics p. 98

2.1.- Description of the flow field. Substantial derivative. Acceleration of a fluid particle 2.2. - Concepts of pathline, streakline and streamline 2.3.- Some particular types of flow 2.4.- Analysis of relative motion near a point 2.5. - Circulation. Irrotational flow III. General equations of Fluid Mechanics 3.1. - Time derivatives of integrals extended to fluid volumes 3.2. - Mass-conservation equation 3.3. - Momentum-conservation equation 3.4. - Energy conservation equation 3.5. - Summary of Fluid Mechanics equations IV. Dimensional analysis and physical similarity V. Approximate forms of the conservation equations 5.1. - Introduction 5.2. - Kinematic simplifications 5.3. - Simplifications of the constitutive laws or of the state equations 5.4. - Approximations based on considerations about the dynamics of the problem. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Teaching Units 4. - BIBLIOGRAPHICAL REFERENCES ARIS, R. Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York, USA: Ed. Dover Publication, Inc, 1990. ISBN-13: 9780486661100 / ISBN-10: 0486661105 BAKER, A.J. Finite Element Computational Fluid Dynamics. USA: Ed. Hemisphere,1983.ISBN-10: 0070034656/ ISBN-13: 978-0070034655. BATCHELOR, G.K. An Introduction to Fluid Dynamics. USA: Ed. Cambridge University Press, 2000.ISBN-10: 0521663962 / ISBN-13: 978-0521663960. p. 99

CRESPO, A. Mecánica de fluidos. Madrid, Spain: Ed. Paraninfo, 1997.ISBN: 9788497322928. CUVELIER, C., SEGAL, A. & VAN STEENHOVEN, A.A. Finite Element Methods and Navier- Stokes Equations. Dordrecht, NL: Ed. Springer, 1986. ISBN-10: 90277221483/ ISBN-13: 978-9027721488. FLETCHER, C.A.J. Computational Techniques for Fluid Dynamics. 2 nd edition, vols. I and II. Sydney, Australia: Ed. Springer-Verlag, 1991. ISBN-10: 3540530584/ISBN-13: 978-3540530589. GRESHO, Ph.M. (1989). The Finite Element Method in Viscous Incompressible Flows, Lecture Notes in Engineering, Vol. 43, pp. 148-190, Springer. HIRSCH, C. Numerical Computation of Internal and External Flows. 2 nd edition, vols. 1 and 2. Oxford, USA: Ed. John Wiley and Sons, 2007. ISBN-13: 9780750665940/ ISBN-10: 0750665947. LIÑÁN, A. Mecánica de Fluidos. Spain: Ed. Publicaciones de la ETS de Ingenieros Aeronáuticos, 1967. PEYRET, R. & TAYLOR, T.D. Computational Methods for Fluid Flow.USA: Ed. Springer- Verlag, 1983. ISBN-10: 3540111476/ISBN-13: 9783540111474. PIRONNEAU, O. Finite Element Methods for Fluids. Chichester,UK: Ed. John Wiley and Sons, 1989. ISBN-13: 9780471922551 /ISBN-10: 0471922552. WENDT, J.F. Computational Fluid Dynamics: An Introduction. 3 rd Springer-Verlag, 2009. ISBN: 9783540850557. edition. Belgium: WILCOX, D.C. Turbulence Modeling for CFD. USA: DCW Industries, 2006. ISBN-13: 9781928729099. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor: Dr. Julio Hernández Rodríguez p. 100

Mondays, from 4:00 pm to 8:00pm Telephone: (+34) 91-398-64-24 E-mail: jhernandez@ind.uned.es Dpto. de Mecánica E.T.S. INGENIEROS INDUSTRIALES UNED Apdo.deCorreos 60.149 28080 MADRID, SPAIN 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 101

CFD++. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Pablo Arrieta MSc Naval Eng. Mr. Mariano Serrano MSc Mechanical Eng. 1. - OBJECTIVES AND CONTENT The objective of this subject of Module F is to introduce students to the field of CFD techniques, and in particular to familiarize them with MIME meshing software and of CFD++ software for fluid mechanics. This subject is divided into two parts: first of all the application texts and then the application exercises. The application texts start with an initiation guide to MIME in which the meshing process, followed by the program, are explained, as well as the different capabilities of this meshing tool. The user will begin by learning the structure of the graphic interface and will later learn to carry out superficial and volumetric meshing, by following the steps of Importing Geometry, Families Generation, Mesh Sizing and Check Mesh Diagnostic. It will also explain the use of complementary tools such as the establishment of areas of greater mesh density, called Density Regions, the refinement of the boundary layer using the Apply Prism Layers feature or the extension of the mesh from one surface to another by means of translation or rotation using the Mesh Matching feature. The subject then has seven chapters about CFD++ software: -Chapter 1 is a general revision of fluid mechanics and CFD techniques. -Chapter 2 looks in detail at the characteristics which define a fluid mechanics problem. This is done through the creation of Information Sets, Initial Conditions, Reference Quantities, Fluid Properties and Boundary Conditions. p. 102

-Chapter 3 demonstrates the capabilities and benefits of CFD ++ and shows how to use its graphic interface by means of an exercise about a NACA profile and another about an S-bend pipe. In the following chapters more advanced aspects of CFD++ are described. These will be useful when approaching more complicated fluid problems. -Chapter 4 is an introduction to turbulence, with an exhaustive description of the turbulence models that exist in CFD++ as well as recommendations for their use. -Chapter 5 describes the mechanism used in CFD++ to deal with heat transfer problems and how this kind of problem is set out through the graphic interface. -In Chapter 6 the steps for establishing compressible flow and high temperature flow problems in CFD++ are set out. -The characteristics of the transitory simulations in CFD++ are defined in chapter 7, specifically the integration method and the parameters to be chosen in the graphic interface. To put the knowledge acquired into practice, some training examples are proposed with their respective geometry files in the part corresponding to application exercises. The CFD++ training examples illustrate a variety of flow scenarios with each case highlighting a particular feature of the code or the graphic interface. These exercises have been extracted from the CFD++ User s Manual. Also, two exercises about MIME meshing techniques have been included. MIME Exercise 1-2D Airfoil Exercise 2-3D Missile Geometry CFD++ Exercise 1 - Laminar Flow in a Double- Throated Nozzle p. 103

Exercise 2 - Incompressible Flow in an S-Bend Exercise 3 - Low Speed Flow in a Pipe Exercise 4 - Low-Speed Flow Over a Backstep Exercise 5 - Conjugate Heat Transfer in a Ribbed Channel Exercise 6 - Unsteady Flow Over a Cylinder Exercise 7 - Low-Speed Cylinder Flow Exercise 8 - A High-Speed Ogive - Cylinder Flow Exercise 9 - Natural Convection within a Rectangular Cavity Exercise 10 - NACA0012 Exercise 11 - Incompressible Flow in a T-Junction Furthermore, in the additional information section the students have at their disposal the CFD++ User s Guide, with which it is possible to expand upon the subjects dealt with in the course. The files to complete the exercises of this User s Guide are also provided. 2. - BASIC TEXT AND OTHER TEACHING MATERIALS Teaching Units Software: MIME and CFD++ 3. - BIBLIOGRAPHICAL REFERENCES WHITE, F. M. Fluid Mechanics. 7 th edition. New York, USA: Ed. McGraw Hill, 1979. ISBN: 9780073529349. JOHNSON, R. W. The handbook of Fluid Mechanics. Heidelberg, Germany: Ed. Springer,1998.ISBN-10: 3540646124 /ISBN-13: 978-3540646129. p. 104

DAUGHERTY, R. L. Fluid Mechanics with Engineering Applications. 7 th McGraw Hill, 1985.ISBN-10: 0070154279 /ISBN-13: 978-0070154278. edition. Ed. SAAD, M.A. Compressible Fluid Flow. Upper Saddle River, US: Prentice Hall, 1985. ISBN- 13: 9780131613737 /ISBN-10: 0131613731. 4. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Tuesdays, from 9:30 to 13:30 Telephone: (+34) 91-386-22-22 p. 105

CFD++. F.3. - FLUID MECHANICS PRACTICES TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Pablo Arrieta MSc Naval Eng. Mr. Mariano Serrano MSc Mechanical Eng. 1.- OBJECTIVES AND CONTENT The objective of this subject is to assimilate the concepts taught in subject F1 and the use of the CFD++ program as a calculation tool (which has been developed intensively in subject F2), in order to enter the fluid mechanics field with clear concepts and with a calculation tool. For this purpose some exercises of progressive difficulty have to be resolved. At the same time the student will verify the evolution of different magnitudes related to the fluid that is being studied, as well as the nature of the type of flow which corresponds to the physical phenomenon studied. For this purpose, besides the CFD++ numerical solution, an analytic solution has been included when possible, in order to compare both results. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2. - BASIC TEXT AND OTHER TEACHING MATERIALS The exercises provided are similar to the ones shown below: Exercise 1 Advanced S-bend analysis. p. 106

Exercise 2 Emptying of a system containing two spherical tanks. Head losses analysis. Exercise 3 Study of a Pipe Junction Exercise 4 Analysis of porosity in a catalytic converter. Exercise 5 Filling a tank with a back step. Transitory analysis. Exercise 6 Irrigation System. Study of a five outlet pipe. Exercise 7 Forced Convection Analysis Exercise 8 Wind turbine site assessment. Use of grid tools in CFD++. Software: MIME and CFD++ 3. - BIBLIOGRAPHICAL REFERENCES WHITE, F. M. Fluid Mechanics. 7 th edition. New York, USA: Ed. McGraw Hill, 1979. ISBN: 9780073529349. JOHNSON, R. W. The handbook of Fluid Mechanics. Heidelberg, Germany: Ed. Springer, 1998.ISBN-10: 3540646124 /ISBN-13: 978-3540646129. DAUGHERTY, R. L. Fluid Mechanics with Engineering Applications. 7 th McGraw Hill, 1985.ISBN-10: 0070154279 /ISBN-13: 978-0070154278. edition. Ed. SAAD, M.A. Compressible Fluid Flow. Upper Saddle River, US: Prentice Hall, 1985. ISBN 13: 9780131613737 /ISBN 10: 0131613731. 4. - TUTORSHIPS: OFFICE HOURS Student can contact tutors using subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com p. 107

Tuesdays, from 9:30 to 13:30 Telephone: (+34) 91-386-22-22 5. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 108

ANSYS CFD. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE TEACHING STAFF Mr. Hasan Avsar. B.Sc. Astronautical Engineer 1. - OBJECTIVES AND CONTENT The objective of this subject of Module F is to introduce the students to the field of CFD techniques, and in particular to familiarize them with ANSYS CFD software for fluid mechanics. This subject is divided into two parts: first of all the application texts and then the application exercises. The subject has the following chapters about the ANSYS CFD software: Lecture 01: Introduction to ANSYS Lecture 02: Introduction to ANSYS Workbench Lecture 03: Introduction to ANSYS Meshing Lecture 04: Meshing Methods Lecture 05: Global Mesh Controls Lecture 06: Local Mesh Controls Lecture 07: Mesh Quality Lecture 08: Introduction to the CFD Methodology and CFX Lecture 09: Domains, Boundary Conditions and Sources Lecture 10: Post-processing Lecture 11: Solver Settings and Output File Lecture 12: Domain Interfaces Lecture 13: CFX Expression Language (CEL) & Additional Variables (AVs) Lecture 14: Best Practice Guidelines p. 109

To put into practice the knowledge acquired, some training examples are proposed with their respective geometry files in the part corresponding to application exercises. The ANSYS CFD training examples illustrate a variety of flow scenarios with each case highlighting a particular feature of the code or the graphic interface. Workshop 01: ANSYS Meshing Basics Workshop 02: Global Mesh Controls Workshop 03: Local Mesh Controls Workshop 04: Mixing Tee Workshop 05: Catalytic Converter Workshop 06: Electronics Cooling Workshop 07: Inline Mixer 2. - BASIC TEXT AND OTHER TEACHING MATERIALS Introduction to ANSYS CFD Professional Software: ANSYS CFD and ANSYS DesignModeler 3. - BIBLIOGRAPHICAL REFERENCES WHITE, F. M. Fluid Mechanics. 7 th edition. New York, USA: Ed. McGraw Hill, 1979. ISBN: 9780073529349. JOHNSON, R. W. The handbook of Fluid Mechanics. Heidelberg, Germany: Ed. Springer,1998.ISBN-10: 3540646124 /ISBN-13: 978-3540646129. DAUGHERTY, R. L. Fluid Mechanics with Engineering Applications. 7 th McGraw Hill, 1985.ISBN-10: 0070154279 /ISBN-13: 978-0070154278. edition. Ed. SAAD, M.A. Compressible Fluid Flow.Upper Saddle River, US: Prentice Hall, 1985. ISBN- 13: 9780131613737 /ISBN-10: 0131613731. 4. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Hasan Avsar h.avsar@invi.uned.es p. 110

ANSYS CFD. F.3. - FLUID MECHANICS PRACTICES TEACHING STAFF Mr. Hasan Avsar. B.Sc. Astronautical Engineer 1.- OBJECTIVES AND CONTENT The objective of this subject is to assimilate the concepts taught in subject F1 and the use of the ANSYS CFD program as a calculation tool (which has been developed intensively in subject F2), in order to enter the fluid mechanics field with clear concepts and with a calculation tool. For this purpose some exercises of progressive difficulty have to be resolved. At the same time the student will verify the evolution of different magnitudes related to the fluid that is being studied, as well as the nature of the type of flow which corresponds to the physical phenomenon studied. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. The solutions provided will include the meshing, setup and post-processing stages of the analysis. 2. - BASIC TEXT AND OTHER TEACHING MATERIALS The exercises provided are similar to the ones shown below: Exercise 1 Advanced S-bend analysis. Exercise 2 Emptying of a system containing two spherical tanks. Head losses analysis. Exercise 3 Study of a Pipe Junction Exercise 4 Analysis of porosity in a catalytic converter. Exercise 5 Filling a tank with a back step. Transitory analysis. Exercise 6 Irrigation System. Study of a five outlet pipe. p. 111

Exercise 7 Forced Convection Analysis Exercise 8 Wind turbine site assessment. Use of grid tools in CFD++. Software: ANSYS CFD and ANSYS DesignModeler 3. - BIBLIOGRAPHICAL REFERENCES WHITE, F. M. Fluid Mechanics. 7 th edition. New York, USA: Ed. McGraw Hill, 1979. ISBN: 9780073529349. JOHNSON, R. W. The handbook of Fluid Mechanics. Heidelberg, Germany: Ed. Springer, 1998.ISBN-10: 3540646124 /ISBN-13: 978-3540646129. DAUGHERTY, R. L. Fluid Mechanics with Engineering Applications. 7 th McGraw Hill, 1985.ISBN-10: 0070154279 /ISBN-13: 978-0070154278. edition. Ed. SAAD, M.A. Compressible Fluid Flow. Upper Saddle River, US: Prentice Hall, 1985. ISBN 13: 9780131613737 /ISBN 10: 0131613731. 4. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Hasan Avsar h.avsar@invi.uned.es 5. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 112

XFLOW. F.2. - INTRO TO FLUID MECHANICS WITH PRACTICAL SOFTWARE TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Pablo Arrieta MSc Naval Eng. Mr. Mariano Serrano MSc Mechanical Eng. 1. - OBJECTIVES AND CONTENT The objective of this subject of Module F is to introduce the students to the field of CFD techniques using particle-based methods, and in particular to familiarize them with XFlow software for fluid mechanics. This subject is divided in two parts: the base texts and the workbook. BASE TEXT S INDEX 1. Theoretical foundation: Numerical Methodology a. The Lattice-Boltzmann Method (LBM) b. Spatial discretization c. Turbulence modeling High fidelity WMLES 2. Introduction to XFlow CFD a. XFlow Technology Overview b. Benchmarks and validation cases c. General description of the XFlow GUI d. Geometry, Set-up and Post-processing 3. Single phase flow: a. Single phase b. Adaptative refinement and moving parts 4. Thermal analysis a. Natural and forced convection b. Solid conduction 5. Acoustics: a. Direct noise computation b. Aeroacoustics p. 113

6. Free surface flow a. Interface tracking b. Porous media 7. Multiphase & DPM a. Two-phase flows b. Discrete Phase Model 8. Advanced and parallel computing a. Distributed computation b. Scripting capabilities c. Batch launching with XFlow To put into practice the knowledge acquired, some training examples are proposed with their respective geometry files. The XFlow Application exercises illustrate a variety of flow scenarios with each case highlighting a particular application field. These exercises have been extracted from the XFlow Tutorial Guide. APPLICATION EXERCISES S INDEX 1. Theoretical foundation: Numerical Methodology (None) 2. Introduction to XFlow CFD (None) 3. Single phase flow: a. Simulation practice: Tutorial 01 - Flow around a cylinder b. Simulation practice: Tutorial 02 - Vehicle aerodynamics c. Simulation practice: Tutorial 03 - Advanced post processing d. Simulation practice: Tutorial 06 - Ball check valve 4. Thermal analysis a. Simulation practice: Tutorial 08 - Heat transfer b. Simulation practice: Tutorial 09 Radiation 5. Acoustics: a. Simulation practice: Tutorial 07 - Wind turbine 6. Free surface flow a. Simulation practice: Tutorial 04 - Dam break b. Simulation practice: Tutorial 05 - Breaking waves 7. Multiphase & DPM a. Simulation practice: Tutorial 10 - Cyclone flow 8. Advanced and parallel computing (None) p. 114

2. - OTHER TEACHING MATERIALS 1. Material: XFlow2014_InstallationGuide_v92 2. Material: XFlow2014_UserGuide_v92 3. Material: XFlow2014_ValidationGuide_v92 4. Material: XFlow2014_TutorialGuide_v92 5. Material: XFlow2014_FAQ_v92 3. - BIBLIOGRAPHICAL REFERENCES QUIAN, Y.H., D HUMIERES,D. and LALLEMAND, P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17:479, 1992. McNAMARA, G. and ZANETTI, G. Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters, 61:2332, 1988. HIGUERA, F.J. and JIMENEZ, J. Boltzmann approach to lattice gas simulations. Europhysics Letters, 9:663, 1989. CHEN, S. and DOOLEN, G. Lattice Bolzmann method for fluid flows. Annual Reviews of Fluid Mechanics, 30:329, 1998. SUCCI, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon Press, 2001. 4. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Tuesdays, from 9:30 to 13:30 Telephone: (+34) 91-386-22-22 p. 115

XFLOW. F.3. - FLUID MECHANICS PRACTICES TEACHING STAFF Responsible Mr. Ambrosio Baños Abascal MSc Science Tutors Mr. Pablo Arrieta MSc Naval Eng. Mr. Mariano Serrano MSc Mechanical Eng. 1.- OBJECTIVES AND CONTENT The objective of this subject is to assimilate the concepts taught in subject F1 and the use of the XFlow program as a calculation tool (which has been developed intensively in subject F2), in order to enter the fluid mechanics field with clear concepts and with a calculation tool. For this purpose some exercises of progressive difficulty have to be resolved. At the same time the student will verify the evolution of different magnitudes related to the fluid that is being studied, as well as the nature of the type of flow which corresponds to the physical phenomenon studied. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom to the tutors. Therefore only the statements and geometries will be provided at the beginning. Once the exercises have been sent and graded, a complete solution will be provided for checking. The solutions provided will include the pre-processing, setup and post-processing stages of the analysis explained in a detailed report. 2. - BASIC TEXT AND OTHER TEACHING MATERIALS The exercises provided are similar to the ones shown below: Exercise 1 Petronas Towers Exercise 2 Heat Exchanger Exercise 3 Helmoltz Resonator p. 116

Exercise 4 Porous Pipe Exercise 5 T-Junction Software: XFlow 3. - BIBLIOGRAPHICAL REFERENCES QUIAN, Y.H., D HUMIERES,D. and LALLEMAND, P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17:479, 1992. McNAMARA, G. and ZANETTI, G. Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters, 61:2332, 1988. HIGUERA, F.J. and JIMENEZ, J. Boltzmann approach to lattice gas simulations. Europhysics Letters, 9:663, 1989. CHEN, S. and DOOLEN, G. Lattice Bolzmann method for fluid flows. Annual Reviews of Fluid Mechanics, 30:329, 1998. SUCCI, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon Press, 2001. 4. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Ambrosio Baños a.banos@ingeciber.com Mr. Pablo Arrieta p.arrieta@ingeciber.com Mr. Mariano Serrano m.serrano@ingeciber.com Tuesdays, from 9:30 to 13:30 Telephone: (+34) 91-386-22-22 5. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 117

MODULE J ELECTROMAGNETIC ANALYSIS J.1. - FEM THEORY APPLIED TO LOW FREQUENCY ELECTROMAGNETIC ANALYSIS TEACHING STAFF Associate Professor José Ángel Sánchez Fernández Associate Professor Francisco Blázquez García 1.- OBJECTIVES The objective of the course is to understand the application of the finite elements theory in different electromagnetic systems with the final goal of studying its behavior and even conditioning its design. 2.- CONTENT After a brief review of the basic electromagnetic and mathematical foundations, Maxwell s equations are developed for different electromagnetic systems starting from the most basic, electrostatic systems in steady state, and finishing with the most complex, magneto-dynamic systems, where transitory magnetic magnitudes and mechanic magnitudes are involved. Chapter 1: Mathematical Foundations This first chapter aims to refresh the student s memory of some basic algebraic concepts like gradient, divergence and rotational operators applied to scalar and vector magnitudes. The basic purpose is to establish the terminology which is going to be used in this whole module. Chapter 2: Electromagnetic Foundations. Maxwell s Equations in Electrostatic, Magneto-static and Magneto-dynamics Fields After a short review of the basic concepts of electromagnetic fields such as electric and magnetic fields, electric displacement, magnetic induction, permittivity, permeability, p. 118

volume charge density and conductivity; the four Maxwell laws are presented in their most generic form. These laws acquire a specific expression when they are applied to each of the three low frequency electromagnetic branches: Electrostatic, Magneto-static and Magnetodynamic. In any case, when Maxwell Laws are adapted to volumes and real surfaces, they lose generality and cannot be adapted to other cases; for instance, the shape that they adopt for the study of an electric machine is not valid for any other device. However, they can be applied in integral form to many cases and, to obtain them, the Stokes theorem is applied. By particularizing Maxwell s equations for electric fields, the Electrostatic laws are developed, defining the concepts of electrical load (and associated phenomena: electric field, force, potential), electromotive force, refraction of the electric field, of dielectric stiffness and applying the Laplace law for insulator and conductor mediums. In the same way, by particularizing Maxwell s equations for stationary magnetic fields the Magneto-static laws are developed, analyzing in detail these equations, deducing the Biot-Savart law for H field calculation and studying concepts like field refraction, energy and magnetic properties of the materials (diamagnetic, ferromagnetic and permanent magnets). paramagnetic, Regarding ferromagnetic materials, a simple analysis about the importance of using materials of very high permeability for the magnetic circuit of electric machines to pursue high intensities of the field in the air gap is proposed. Regarding permanent magnets, a very basic analysis is proposed, which will analyze the saturation curve of permanent magnets and their functioning points within the curve when the magnetic circuit to which the magnet belongs contains at least one air gap. Finally, Maxwell s equations are developed in the magneto-dynamic case, where field variation in time is looked at. First of all the Lenz-Faraday law is deduced and the phenomenon of useful induced flows (induction machine) or parasites (Eddy-current) p. 119

is introduced. This chapter finishes by considering the penetration of fields in ferromagnetic and non-ferromagnetic materials. Chapter 3: Basic Foundations of the Finite Element Method for the Analysis of Electromagnetic Systems The development and the massive use of the finite element method have always been linked to the development of computational systems. The finite element method has been applied to electromagnetism using variational methods or the residual method. Nowadays, most software uses the latter method because it is established from the physics equations which it aims to resolve, because of this they are easier to understand and apply. The purpose of this chapter is to clearly introduce the essential concepts and show how the methods relate to each other with the purpose of making a basic program that resolves a specific problem, rather than making a thorough analysis of the different methods. Overall, the method proposed is based on discretizing all the space in first order elements (the triangle is the most basic element) where the potential varies in linear form. The chosen element has n nodes or degrees of freedom (3, in the case of a triangle) so knowing the potential of them, the potential value can be determined for any point of that domain. Moreover, the solution obtained using this method is not exact, thus by applying this solution to the target function the value obtained is different from zero, this difference is called residue. To force the residue to zero, it is necessary to apply a weighting function. Chapter 4: Application of the Finite Element Method to Different Electromagnetic Systems After presenting the finite element method, which is used in electromagnetism, it is particularized for different electromagnetic systems, paying special attention to its physical meaning and its characteristics for each system shown. This chapter begins showing some static cases, in both electric and magnetic fields. The interest in their study is because many dynamic cases can be studied as a p. 120

composition of static cases. By using Maxwell s equations, the Laplace and Poisson equations (partial derivatives of second order) are established, using the scalar and vector potentials as primary variables. Secondly, some cases with variable magnetic fields are presented which imply the emergence of eddy-currents. In principle, the resolution of these cases shows an additional complication that consists of the equations integration depending on the coordinates systems chosen, the application of a transformation matrix before obtaining the final result being necessary. Within this mode with eddy-currents, the simplest case to study is that in which the fields have a sinusoidal variation in time of constant frequency. Here, the equation to be solved is shown in terms of complex potential so, by solving only one matrix, the real and imaginary parts of the field are obtained and, therefore, their magnitude and phase angle regarding the flows. Furthermore, an additional advantage of this method is that it allows easy calculation of the impedances of the electrical circuit that excites the magnetic core. The essential limitation of the method is that it can only be used in linearity cases of the magnetic circuit, which for real ferromagnetic materials would mean working with low levels of magnetic saturation. In the more general case of eddy-currents study, it is necessary to use the discretization in time of the potential, which basically consists of replacing the temporal variables with incremental functions. This approach is more valid when the time interval chosen for the discretization is small, so obtaining accurate results requires a greater capacity and calculation time. In contrast to permittivity and conductivity which are considered constants, permeability is not in the case of ferromagnetic materials, since it depends on the intensity of the H magnetic field (B-H curve, or characteristic curve). In order to resolve the problem and set out the finite element matrix it is necessary to know the permeability of the nodes but, as the definitive value of this depends on the solution, it will be necessary to establish an iterative process to obtain a proper solution. Furthermore, in this chapter different alternatives to establish this iterative process are presented. p. 121

Finally, how the analysis of any electromagnetic system can be simplified when certain conditions of symmetry and periodicity exist is studied. Chapter 5: Study of Electromagnetic Systems Coupled with Electrical Circuits In the previous chapters all the electromagnetic systems proposed were excited with a known flow density. However, in reality, on many occasions the electromagnetic systems are fed in tension; therefore the equations of field and of tension in the excitement circuit must be resolved simultaneously. On some occasions, for instance in the control of electric machines, the electromagnetic systems are fed through an electronic converter so a detailed study of the influence of the harmonics introduced by these feeding systems is necessary. In the case of three-phase systems, the influence of the different connection types: series-parallel, star-delta, etc. will be also studied. Chapter 6: Study of Systems in Movement. Mechanical Efforts Calculation Some of the electromagnetic systems of frequent use like relays, switches and rotating electrical machines are subjected to mechanical and movement forces. Applying the finite element method to these systems has the extra complication of variation of the model s geometry due to movement, thus special attention must be paid to discretization in the areas close to the moving parts (air gap). In this chapter the technique to discretize the air gap in order to simulate the displacement of the model s moving parts without losing accuracy in the results obtained is presented. If the results obtained are considered exclusively in the case of electrical machines, it is essential to make a detailed analysis of the interaction between the electrical magnitudes and torque in order to establish the balance of energy. In this sense, this chapter shows different ways of calculating torque in the machine starting from electromagnetic magnitudes. p. 122

Chapter 7: Determination of the Magnetic Core Losses Overall, the core losses of a specific electromagnetic system can be divided into three components: losses to parasitic currents, hysteresis losses and additional losses. In this chapter the nature of each one of these three components and the method for calculating them using Finite Elements are described. On many occasions it is enough to use a simple method consisting of calculating the magnetic induction without considering the effects of the losses effects in it, by calculating the losses a posteriori using analytical expressions well known in the electrical engineering field. Nevertheless, when the losses in the magnetic core have an influence on the waveform of the current and consequently of the induction, it is necessary to integrate the loss models to calculate the field, which requires a more complex analysis. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Subject text. 4. - BIBLIOGRAPHICAL REFERENCES FRAILE MORA, J. Electromagnetismo y Circuitos Eléctricos. 4 th edition. Madrid, Spain: Ed. McGraw Hill, 2005. ISBN: 9788448198435. FRAILE MORA, J. Máquinas Eléctricas. 6 th edition. Madrid, Spain: Ed. McGraw Hill, 2008. ISBN: 9788448161125. SILVESTER, P.P. &FERRARI, R.L. Finite Elements for Electrical Engineers.3 rd edition. Cambridge, UK: Ed. Cambridge University Press, 1996. ISBN-13: 9780521449533/ ISBN- 10: 0521449537. MCLYMAN, W. T. Transformer and Inductor Design Handbook. Bosa Roca, USA: Ed.Taylor & Francis Inc., 2011. ISBN-13: 9781439836873 /ISBN-10: 1439836876. p. 123

TOLIYAT, H. A.& KLIMAN, G. B. Handbook of Electric Motors. 2 nd edition. New York, USA: Ed. Marcel Dekker, Inc., 2004. ISBN-13: 9780824741051/ ISBN-10: 0824741056. HANDI, E. S. Design of Small Electrical Machines. Chichester, UK: Ed. John Wiley & Sons Ltd, 1994.ISBN-13: 9780471952022/ ISBN-10: 0471952028. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor: Dr. José Ángel Sánchez Fernández Wednesdays, from 10:30 am to 12:30am Fridays, from 4:00pm to 6:00pm Telephone: (+34) 91-336-67-62 E-mail: joseangel.sanchez@upm.es Professor: Dr.Francisco Blázquez García Tuesdays, from 3:30pm to 7:30pm Telephone: (+34) 91-336-31-78 E-mail: fblazquez@etsii.upm.es Dr. José Ángel Sánchez Fernández Dpto. Ingeniería Civil: Hidráulica y Energética E.T.S. INGENIEROS CAMINOS, CANALES Y PUERTOS U.P.M. C/ Profesor Aranguren s/n 28040 Madrid, Spain 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 124

MAXWELL. J.2. - INTRO TO ELECTROMAGNETIC AN. WITH PRACTICAL SOFTWARE TEACHING STAFF Andrea Serra MsC Telecommunication Eng. PhD Information Eng. 1.- OBJECTIVES The objective of this subject is for the student to have contact with and to manage practically the basic concepts of low frequency electromagnetic calculation through the use of the finite element software provided. 2. - CONTENT The subject is structured into different topics which further the capacities of the ANSYS Maxwell electromagnetic module. The topics are: Lecture 1: Introduction to ANSYS Maxwell Lecture 2: Geometry Operations Lecture 3: Static Magnetic Solvers Lecture 4: Static Electric Solvers Lecture 5: Maxwell Transient Solvers Lecture 6: Meshing and Mesh Operations Lecture 7: Maxwell Postprocessing Lecture 8: Optimetrics Analysis Furthermore, some examples of the application are presented in the workbook: ANSYS Maxwell 2D Workshop 1: Basic Magnetostatic Analysis Workshop 2: Basic Eddy Current Analysis Workshop 3: Basic Electrostatic Analysis Workshop 4: Basic DC Conduction Analysis p. 125

Workshop 5: Basic Transient Sources and Circuit Workshop 6: Basic Transient Rotational Motion Workshop 9: Basic Postprocessing Workshop 10: Basic Parametric Analysis Workshop 11: Basic Optimetrics Analysis ANSYS Maxwell 3D Workshop 1: Basic Magnetostatic Analysis Workshop 2: Basic Eddy Current Analysis Workshop 3: Basic Electrostatic Analysis Workshop 4: Basic DC Conduction Analysis Workshop 5: Basic Transient Sources and Circuit Workshop 6: Basic Transient Rotational Motion Workshop 7: Basic Electric Transient Analysis Workshop 8: Basic Meshing Operations Workshop 9: Basic Postprocessing Workshop 10: Basic Parametric Analysis Workshop 11: Basic Optimetrics Analysis 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Introduction to ANSYS Maxwell 2015 (R16) Training Manual Software: ANSYS Electromagnetic Suite Release 16.2.0. ANSYS Maxwell 2015.2.0 4. - BIBLIOGRAPHICAL REFERENCES Books of General Electromagnetic Purpose KNOEPFEL, H. E. Magnetic Fields. A Comprehensive Theoretical Treatise for Practical Use.1 st edition. USA: Ed. Wiley- Interscience, 2000. ISBN: 0471322059. p. 126

JACKSON, J. D. Classical Electrodynamics. 3 rd edition. USA: Ed. Wiley, 1998. ISBN: 047130932X. LEVICH, B. G. Teoría Del Campo Electromagnético Y Teoría De La Relatividad Vol 1. ISBN: 84-291-4061. LEVICH, B. G. Física Estadística. Procesos Electromagnéticos En La Materia Vol 2. Spain: Ed. Reverté, 2002. ISBN: 84-291-4062-X. Books of the Finite Element Method Applied to the Electromagnetism BRANCHI,N. Electrical Machine Analysis Using Finite Elements. USA: Ed. CRC Press, 2005. ISBN: 0-8493-3399-7 DI BARBA, P., SAVINI, A. & WIAK, S.Field Models in Electricity and Magnetism. Italy: Ed. Springer, 2010. ISBN: 9789048177356 6. - TUTORSHIPS Students can contact tutors using the subject s virtual classroom. Mr. Andrea Serra a.serra@enginsoft.it p. 127

p. 128

MAXWELL. J.3. - ELECTROMAGNETIC PRACTICES TEACHING STAFF Andrea Serra MsC Telecommunication Eng. PhD Information Eng. 1.- OBJECTIVES The purpose of this subject is to do exercises with the ANSYS Maxwell software so that the student assimilates the concepts previously explained in subjects J1 and J2 of the Electromagnetism Module, and becomes familiarized with the use of the software. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements and geometries will be provided at the beginning. Once the exercises have been sent and graded, a complete solution will be provided for checking. The solutions provided will include the pre-processing, setup and post-processing stages of the analysis explained in a detailed report. 2.- CONTENT The exercises provided are similar to the ones shown below: Exercise 1: Magnetic Clutch Exercise 2: Loads Exercise 3: Skin Effect in a Solid Conductor of Rectangular Cross-Section Exercise 4: Switch: Flux Effect inside the Device Exercise 5: DC Electromagnet and Contact Exercise 6: Electromagnetic Gear Induction Heating Exercise 7: Metal Detector p. 129

Exercise 8: Use LMATRIX to Determine Keeper Force 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Basic text of the subject ANSYS Maxwell Software 4. - BIBLIOGRAPHICAL REFERENCES See the application subject (J.2). 5. - CONTINUOUS ASSESSMENT BOOKLETS The student must follow the instructions given in the virtual classroom. 6. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Mr. Andrea Serra a.serra@enginsoft.it p. 130

MODULE K COMPOSITE ANALYSIS OF STRUCTURES K.1. - FINITE ELEMENT ANALYSIS OF COMPOSITE STRUCTURES TEACHING STAFF Professor Francisco Montans Leal Mr. Marcos Latorre Ferrús MSc Aeronautical Eng. 1.- OBJECTIVES The objective of this module is to introduce the student to the basic concepts of the mechanical behavior of composite structures. In the first part of the module, these materials are studied from an analytical point of view, analyzing first the mechanical response of single laminas and then the more complex behavior of laminates. Common failure criteria and general design concepts are presented. The comparison with experimental data will provide the required foundation to the derived theories. In the second part of the subject, the basic formulations for the treatment of this type of material in a Finite Element code are introduced. A good understanding of all the concepts explained in the first part of the module is essential to successfully follow this computational approach. The content of this second part will be complemented with the practical sessions for Composite Structures. The background of the student should include a mechanics of materials course, in which the fundamentals of tensor analysis, elasticity theory and the strength of materials are treated. A basic knowledge on finite element procedures would be desirable. A brief review of the basics needed for each Chapter is given throughout the text. p. 131

2.- CONTENT 1. Introduction to Composite Materials a. What is a Composite Material? b. Types of Composite Materials. c. Advantages and disadvantages of composites. d. Use of composite materials in industry. 2. Mechanical Analysis of a Lamina a. Stress and strain tensors. b. Constitutive equations for isotropic solids. c. The linearized stress-strain behavior for transversely isotropic and orthotropic materials. d. Apparent material constants. Coupling coefficients. e. Failure criteria for composite laminas. f. Determination of the overall behavior of a lamina through the behavior of its constituents. Strength of materials approach. g. Determination of the overall behavior of a lamina through the behavior of its constituents. Theory of elasticity approach. h. Determination of the strength properties of a lamina from its constituents. 3. Mechanical Analysis of Composites a. Review of the theory of beams and plates. b. In-plane and out-of-plane analysis of the behavior of a layered material. c. Coupling coefficients. d. Symmetric and unsymmetrical laminates. e. Examples. 4. Failure and Design of Fiber-Reinforced Composites a. Types of mechanical failure in composite materials. b. Types of mechanisms that yield to failure in composite materials. c. Strength of laminates. d. Interlaminar stresses. Delamination. e. Buckling of composite materials. p. 132

f. Resonance in composite materials. g. Fatigue in composite materials. h. Fracture in composite materials. i. Considerations about a good design. Design requirements. Some basic optimization concepts. j. Design of structural members made of composite materials. k. Joints in composite materials. 5. Finite Element Formulations for Composites a. Finite element formulation for isotropic, transversely isotropic and orthotropic solids. b. Finite element formulation of plates. Approaches to the finite element formulation of a laminate. Recovery of strains and stresses. c. Modelling delamination in finite elements. d. A brief on finite element formulation of shells. Layout of fibers in a composite shell. e. Linear and nonlinear analysis of composite structures. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Course Learning Units 4. - BIBLIOGRAPHICAL REFERENCES JONES, R.M. Mechanics of Composite Materials. Taylor and Francis, 1999. GIBSON, R.F. Principles of Composite Material Mechanics. CRC Press, 2012. HALPIN, J.C. Primer on Composite Materials: Analysis. Technomic Publishing Company, 1992. CHRISTENSEN, R.M. Mechanics of Composite Materials. Wiley, 1979. REDDY, J.N. Mechanics of Laminated Composite Plates and Shells. CRC Press, 2004. KOLLÁR L.P., SPRINGER G.S. Mechanics of Composite Structures. Cambridge University Press, 2003. p. 133

AGARWAL B.D., BROUTMAN L.J., CHANDRASHEKHARA K., Analysis and Performance of Fiber Composites. John Wiley & Sons, 2006. KAW, A.K. Mechanics of Composite Materials. CRC Press, 2006. BARBERO, E.J. Introduction to Composite Materials Design. CRC Press, 2011. BARBERO, E.J. Finite Element Analysis of Composite Materials. CRC Press, 2008. 5. - TUTORSHIPS: OFFICE HOURS Students can contact tutors using the subject s virtual classroom. Professor Francisco Montans E-mail: Fco.Montans@upm.es Tutor: Mr. Marcos Latorre E-mail: m.latorre.ferrus@upm.es Tuesday and Thursday, from 16.00 to 18.00 6. - SENDING THE CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. p. 134

MSC NASTRAN. K.2. - INTRO TO COMPOSITE STRUCTURES WITH PRACTICAL SOFTWARE TEACHING STAFF Professor Francisco Montans Leal Mr. Miguel Ángel Sanz Gómez. MSc Mechanical Eng. 1.- OBJECTIVES The purpose of the subject is to introduce the student to the basic concepts of composite materials and finite element procedures. The main aspects about this subject will be exposed by the way of elementary problems in composite materials, and will be studied with the finite element program provided (Patran/MSC Nastran), taking into account the theoretical knowledge related in the previous subject. 2. - CONTENT The content is presented in two parts: software training notes, and application exercises from the workbook. The subject is structured into the following main topics: 1. Introduction to Composites in MSC Nastran. 2. Overview of Classical Lamination Theory and implementation in MSC Nastran. 3. Advanced Composite Elements in MSC Nastran and special remarks. 4. Classical Failure Theories on composite materials under finite element procedures. 5. Post-Processing on finite element models with composite materials. 6. Introduction to Advanced Failure Theories and Prediction. 7. Buckling Analysis on composite structures. 8. Practical Usage Guidelines with composite materials. Appendix A. Composite Theory. Exercises available: 1. Making a Composite Model p. 135

2. Forward Swept Wing -- Ply Direction Tailoring for Bending/Twist Coupling 3. Layup of Solid Composite Shell 4. Ply Direction Tailoring Strength 5. Progressive Failure Analysis (PFA) 6. Virtual Crack Closure Technique (VCCT) Double Cantilever Beam 7. Cohesive Zone Modeling (CZM) Lap-shear Joint 8. Transverse Shear Stress and Stiffness 9. Linear Buckling 10. Post-Buckled Strength 11. Ply Direction Tailoring for Strength Using the Optimizer 12. Ply Direction Tailoring for Stiffness Using the Optimizer 3. - BASIC TEXT AND OTHER TEACHING MATERIALS NAS113 - Composite Material Analysis using MSC NASTRAN Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES JONES, R.M. Mechanics of Composite Materials. Taylor and Francis 1999. KAW, A.K. Mechanics of Composite Materials. CRC Press 2006. BARBERO, E.J. Introduction to Composite Materials Design. CRC Press 2011. BARBERO, E.J. Finite Element Analysis of Composite Materials Design. CRC Press 2008. MSC Nastran Quick Reference Guide 5. TUTORSHIPS: OFFICE HOURS Students can contact the tutor using the subject s virtual classroom. Tutor: Mr. Miguel Angel Sanz Gómez e-mail: ma.sanz@invi.uned.es Tuesdays and Thursday, from 16:00 to 18:00 p. 136

Telephone: (+34) 91-336-63-67, ext. 114 Fax: (+34) 91-336-63-67 p. 137

MSC NASTRAN. K.3. - COMPOSITE STRUCTURES PRACTICE PROBLEMS TEACHING STAFF Professor Francisco Montans Leal Mr. Miguel Ángel Sanz Gómez. MSc Mechanical Eng. 1.- OBJECTIVES In this part of the course the student will find some additional exercises to help understand the behavior of composite materials, and acquire the ability to solve different types of composite structures. The exercises of this subject must be sent to the tutor to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. In addition to Nastran numerical solution, it may be possible introduce an analytic solution to understand the mechanical behavior (stresses, strains and displacements) of composite structures. 2.- CONTENT The exercises provided in this subject are similar to the ones shown below: 1. Analysis of a flat shell subjected to several loading conditions: solution and interpretation of results in terms of stresses, strains and displacements. Computation of membrane behavior with several ply tailoring lay ups. 2. Study of a cylindrical thin-walled tube loaded in torsion. Analysis on strength and stiffness behavior for different ply tailoring lay ups. p. 138

3. Computation of a solid beam with T shape and specific ply tailoring over the cross section (web and flange): analysis of strength and deflection under bending loads. 4. Final Problem: a flat plate with-without reinforcement of a central stringer, and several loading conditions. Over these elementary problems the specific concepts about mechanic of composite materials and finite element procedures, exposed in the previous subject, will be applied: Making a Composite Model, solution and interpretation of results. Ply direction tailoring for strength and stiffness. Layup of Solid Composite Shells and Beams. Failure Criteria and Progressive Failure Analysis (PFA) on laminated composite materials. Linear Buckling on composite structures. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS NAS113 - Composite Material Analysis using MSC NASTRAN Software: Patran/MSC Nastran Software Exercise s statements 4. - BIBLIOGRAPHICAL REFERENCES JONES, R.M. Mechanics of Composite Materials. Taylor and Francis 1999. KAW, A.K. Mechanics of Composite Materials. CRC Press 2006. BARBERO, E.J. Introduction to Composite Materials Design. CRC Press 2011. BARBERO, E.J. Finite Element Analysis of Composite Materials Design. CRC Press 2008. p. 139

GAY, D. Composite Materials Design and Applications. CRC Press 2003. VOYIADJIS, G.Z. Mechanics of Composite Materials with MATLAB. Springer 2005. MSC Nastran Quick Reference Guide 5. - CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. More exercises will be proposed in the virtual classrooms during the course. The exercises must be sent through the virtual classroom. 6. - TUTORSHIPS: OFFICE HOURS Students can contact the tutor using the subject s virtual classroom. Tutor: Mr. Miguel Angel Sanz Gómez E-mail: ma.sanz@invi.uned.es Tuesdays and Thursday, from 16:00 to 18:00 Telephone: (+34) 91-336-63-67, ext. 114 Fax: (+34) 91-336-63-67 p. 140

ANSYS. K.2. - INTRO TO COMPOSITE STRUCTURES WITH PRACTICAL SOFTWARE TEACHING STAFF Fabio Rossetti MSc Mechanical Eng. 1.- OBJECTIVES The purpose of the subject is to introduce the student to the basic concepts on composite materials and finite element procedures. The main aspects about this subject will be exposed by the way of elementary problems in composite materials, and will be studied with the finite element program provided (ANSYS Mechanical and ANSYS Composite Prep-post), taking into account the theoretical knowledge related in the previous subject. 2. - CONTENT The content is presented in two parts: software training notes, and application exercises from the workbook. The subject is structured into the following main topics: ANSYS Composite PrepPost Demonstration Composite Introduction ANSYS Composite PrepPost Introduction Rosettes The Oriented Element Sets Rules and Edge Sets Draping Solid Modeling Parameters in ANSYS Composite PrepPost Failure Criteria Progressive Failure and Crack Growth Analyses Tips and Tricks Exercises available: p. 141

Workshop 1: Introduction to ANSYS Composite PrepPost Workshop 2: Kiteboard Workshop 3: Helix Workshop 4: T-Joint Workshop 5: Rules Workshop 6: Draping Workshop 7: Solid Modeling Workshop 8: Solid Modeling and Ply Drop Offs Workshop 9: Parameters in ANSYS Composite PrepPost Workshop 10: Delamination Workshop 11: Submodeling Workshop 12: Temperature Dependent Material 3. - BASIC TEXT AND OTHER TEACHING MATERIALS ANSYS Composite PrepPost Training Software: ANSYS Mechanical and ANSYS Composite Prep-post 4. - BIBLIOGRAPHICAL REFERENCES JONES, R.M. Mechanics of Composite Materials. Taylor and Francis 1999. KAW, A.K. Mechanics of Composite Materials. CRC Press 2006. BARBERO, E.J. Introduction to Composite Materials Design. CRC Press 2011. BARBERO, E.J. Finite Element Analysis of Composite Materials Design. CRC Press 2008. 5. TUTORSHIPS: Students can contact tutor using the subject s virtual classroom. Mr. Fabio Rossetti f.rossetti@enginsoft.it p. 142

ANSYS. K.3. - COMPOSITE STRUCTURES PRACTICE PROBLEMS TEACHING STAFF Fabio Rossetti MSc Mechanical Eng. 1.- OBJECTIVES In this part of the course the student will find some additional exercises to help understand the behavior of composite materials, and acquire the ability to solve different types of composite structures. The exercises of this subject must be sent to the tutors to be reviewed and graded using the subject s virtual classroom. Therefore only the statements will be provided at the beginning. Once the exercises have been sent and graded a complete solution will be provided for checking. In addition to ANSYS numerical solution, it may be possible introduce an analytic solution to understand the mechanical behavior (stresses, strains and displacements) of composite structures. 2.- CONTENT The exercises provided in this subject are similar to the ones shown below: 5. Analysis of a flat shell subjected to several loading conditions: solution and interpretation of results in terms of stresses, strains and displacements. Computation of membrane behavior with several ply tailoring lay ups. 6. Study of a cylindrical thin-walled tube loaded in torsion. Analysis on strength and stiffness behavior for different ply tailoring lay ups. 7. Computation of a solid beam with T shape and specific ply tailoring over the cross section (web and flange): analysis of strength and deflection under bending loads. 8. Final Problem: a flat plate with-without reinforcement of a central stringer, and several loading conditions. p. 143

Over these elementary problems the specific concepts about mechanic of composite materials and finite element procedures, exposed in the previous subject, will be applied: Making a Composite Model, solution and interpretation of results. Ply direction tailoring for strength and stiffness. Layup of Solid Composite Shells and Beams. Failure Criteria and Progressive Failure Analysis (PFA) on laminated composite materials. Linear Buckling on composite structures. 3. - BASIC TEXT AND OTHER TEACHING MATERIALS Exercise statements Software: Patran/MSC Nastran Software 4. - BIBLIOGRAPHICAL REFERENCES JONES, R.M. Mechanics of Composite Materials. Taylor and Francis 1999. KAW, A.K. Mechanics of Composite Materials. CRC Press 2006. BARBERO, E.J. Introduction to Composite Materials Design. CRC Press 2011. BARBERO, E.J. Finite Element Analysis of Composite Materials Design. CRC Press 2008. GAY, D. Composite Materials Design and Applications. CRC Press 2003. VOYIADJIS, G.Z. Mechanics of Composite Materials with MATLAB. Springer 2005. 5. - CONTINUOUS ASSESSMENT EXERCISES The student will upload the continuous assessment exercises in the virtual classroom. More exercises will be proposed in the virtual classrooms during the course. The exercises must be sent through the virtual classroom. p. 144

6. - TUTORSHIPS: OFFICE HOURS Students can contact the tutor using the subject s virtual classroom. Mr. Fabio Rossetti f.rossetti@enginsoft.it p. 145

MASTER S FINAL PROJECT A. Master s Final Project Assignment In order to assign the master s final projects, there are two options: 1. Doing a master s final project proposed by the course The course has proposed various Master s Final Projects, related to the students specialties, so that students can choose the most appropriate one: Interpolation Methods and Numerical Approximation -1. Interpolation Methods and Numerical Approximation -2. Posteriori Error Estimation in the Finite Element Method. Fire Resistance 2D Analysis of the World Trade Center. Jules Verne s Cannon. Dynamic Analysis Of The Structural Response Of A Tall Building Subjected To Aircraft Impact. Design Methods of Reinforced Concrete Shells Comparison of Winkler Soil Models with a Three-dimensional Elastic Model. Buckling Analysis of Concrete Piles. Study of Embedment Depths in Diaphragm Walls. According to the project chosen, a tutor will be assigned to the student. 2. The student wishes to propose a specific project Students can propose their own topic for their final projects which may be of interest to the company where the student works, or it can be related to the student s personal interests or their future plans for professional activity. When proposing the final project, students must take into account the size limitations of the educational practice program unless they have access to university facilities with greater capabilities, or a commercial installation in their respective companies. p. 146

Similarly, the final project must be related to the Specialized Module Group covered. Students should indicate on the application form the professor/lecturer that they would like to be their tutor for their Master s Final Project. The professor/lecturer should correspond to the modules studied by the students. The Final Project must have the appropriate scope to be finally accepted. To apply, students must send the application form according to the these guidelines by e-mail to the following address: secretariat@ingeciber.com (the application form has a maximum of 3 pages). B. Awards for the Master s Final Project of the Theoretical and Practical Application Competition Explanation The Theoretical and Practical Application Master concludes, at its highest level, with the Master s Final Project. This project gathers all the knowledge acquired by the student throughout the study phase of the Expert and Specialist modules, and concentrates all the student s aptitudes and capabilities with a common goal in a sole project. The training acquired by students, in addition to their own personal career, will substantially influence the industrial capacities of our society, providing it with highly qualified technicians for its development, prosperity and wellness. For these reasons, we wish, on an annual basis, to reward the dedication of the students and the excellence of the best Master s Final Project presented on the course. The National Distance Learning University (UNED), through its Superior School of Industrial Engineers, rewards in this way the student s effort and contribution to the study of the practical application of the Finite Element Method. p. 147

Competition Foundations 1. Organization The competition is organized by the Superior School of Industrial Engineers of UNED, with its headquarters at the following address: calle Juan del Rosal, 12, 28040, Madrid. To contact the secretariat of the Master s, you should follow the established channels (secretariat@ingeciber.com) to send any correspondence. 2. Competition aim To reward the best Master s Final Project made in the corresponding Theoretical and Practical Application Master s. 3. Participation In order to participate in the Competition it is essential that the Master s Final Projects have received at least a grade of good (ECTS: C) during the academic year corresponding to the competition. All the projects done during the course which fulfill this characteristic will participate in the Competition. 4. Competition schedule The competition is annual. 5. Projects presentation All the students, who have received a mark of good or better in the Master s final project during the academic year in which the competition is held, will be automatically entered in the competition. If a student does not want to participate in the competition, they must notify the Master s secretariat. p. 148

The presentation implies agreement with the Competition Rules in their entirety. 6. Steering committee, selection criteria and awards of prizing The Directors of the Superior School of Industrial Engineers of UNED or the Commission delegated will be responsible for the judging of the files and the awarding of the prizes. The committee will be composed of the School Director or their delegate, the Director, the Coordinator and two Master s professors. The jury s decision will not be open to appeal and they will indicate the projects considered to merit the prize, and are also able to declare the prize unawarded. The winners will be contacted in due time and will be made public before the prizegiving. 7. Appraisal criteria The projects will be evaluated according to their grade of: - Difficulty: up to 5points - Originality and Innovation: up to 5 points 8. Awards The prize that the Jury of the Master s Final Project award will be the following: - The enrollment fees corresponding to the Master s Final Project. 9. Ownership and Submission of the projects The intellectual property of the winning projects and the material property of the documents that integrate them will correspond to the Author of these. The Superior School of Industrial Engineers of UNED reserves the right to keep in its documentary collection winning projects which it considers to be of special relevance or merit. p. 149