Course information for TMHL63 Introduction to Computational Mechanics,

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1 Course information for TMHL63 Introduction to Computational Mechanics, HT Examiner and lecturer Carl-Johan Thore; Tel Teaching assistant Carl-Johan Thore; Lab. assistants Roar Remnert; Fredrik Rosenlund; Course secretary Lena Sundling; Course homepage Bachelor Level/TMHL63/2015/ht2 2015/TMHL63 ht html (note that the underscores may be lost if you copy the address) Aim At the end of the course, the student shall be able to 1. give an account of how computations are used in the design process 2. give an account of the theoretical basis of FEM 3. give an account of the inherent structure of an FE program 4. give an account of potential sources of error associated with FE analyses 5. use a well known FE software to solve problems 6. give an account of the importance of result evaluation In order to reach goal no 1, guest lecturers will be invited to the course. In order to reach goals no 2, 3, and 4, we will use classical lectures, teaching classes and laboratory classes. Fulfilment of goal no 5 will be guaranteed by using the commercial software ANSYS in the laboratory work. Topics associated with goal no 6 will continuously be discussed during the course. 1

2 Course literature Cook RD, Malkus DS, Plesha ME and Witt RJ, Concepts and Applications of Finite Element Analysis (fourth edition) The book can be bought at Bokakademin in Kårallen, Campus Valla. Alternative literature There s plenty of course. Here are two nice introductory texts: B Torstenfelt, Finite Elements from the early beginning to the very end N Ottosen and H Petersson, Introduction to the Finite Element Method More advanced texts include the following: TJR Hughes, The Finite Element method Linear static and Dynamic Finite Element Analysis D Braess, Finite Elements Theory, fast solvers, and applications in solid mechanics Examination Written exam and mandatory laboratory work. The written exam will be graded according to U/Fx, 3/C, 4/B and 5/A. You are allowed to bring the course book by Cook et. al to the exam. Examples of old exams are available at the course homepage. Lab instructions are found on the course homepage. The work will be carried out and reported in groups of 2 students (occasionally 3 students). Too late accounts and/or reports will not be considered! It is not allowed to use material from other groups in your own lab work accounts and project report. If such behaviour is seen, it will be reported as an attempt to cheat. Deadlines: Lab Lab 2 No deadline, results are to be discussed in the lab. Lab Lab NOTE: Corrected lab reports handed in after 25/ will not be considered at all! 2

3 Course plan TC = Teaching class 1D spring- and rod systems, 1D heat transfer Lec 1 Course intro. and Spring systems Lec 2 Rod systems TC 1-2 Lec 3 1D stationary heat transfer Mathematical formulations in mechanics Lec 4 The principle of minimum potential energy (PEM) Lec 5 Strong and weak form, PVW, Galerkin TC 3 Introduction to FE-software Lec E Guest Lecture 2D (plane) trusses Lec 6 2D trusses TC 4 Lab 1 Beams and 2D frames Lec 7 Beams Lec 8 2D frames TC 5 2D stationary heat transfer. 2D elastostatics Lec 9 2D stationary heat transfer. Linear triangle element Lab 2 Lec 10 2D elastostatics. Linear triangle element (CST) TC 6 Lec 11 The QUAD4-element. Isoparametry TC 7 Lab 3 Elastostatics; cont. Lec 12 Higher order 2D elements and 3D elastostatics Solution of linear systems Lec 13 Solution of linear systems TC 8 Repetition TC 9 Dynamics Lec 14 Lec 15 Lab 4 Repetition Vibrations in Beams FE-treatment of dynamical problems 3

4 Outlook, non-linear FEM, and computational methods in Fluid Mechanics Lec E Guest lecture Lec E CFD with Matts Karlsson Lec 16 Introduction to non-linear FEM 4

5 Reading instructions for the book by Cook et al listed above. Chapters not listed may be omitted. Notation and the way the theory is presented differ, sometimes just a little, sometimes a lot, from the lectures. Chapter 1 Everything. Chapter 2 Sections , 2.11 covers material discussed in Lec 1-2 and 6-7. Section 2.8 contains material discussed in Lec 13. Chapter 3 Sections Some details are a bit difficult and go beyond the scope of this course; these parts can be skimmed over. The material is mainly covered in Lec Chapter 4 Sections for Lec 4, and Section 4.7 for Lec 5. Chapter 5 Sections 5.1. This material is briefly covered in Lec 5. Chapter 6 Sections This material is mainly discussed in Lec 11. Chapter 9 Section 9.1. Sources of error are discussed throughout the course. Chapter 11 Sections Skim section This chapter contains material discussed in Lec 14 and 15. Chapter 12 Section is relevant for Lec 9. Chapter 17 Sections Sections can be skimmed. This material is relevant for Lec 16. Appendix A Everything matrix theory is used throughout the course. Appendix B Sections B.1 and B.2. Section B.3 can be skimmed. This material is discussed in Lec 13. The sections at the end of each of the listed chapter containing application examples is also recommended reading. 5

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