# Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak Office: Inglis building mezzanine level (INO 31)

Save this PDF as:

Size: px
Start display at page:

Download "Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak (fc286@) Office: Inglis building mezzanine level (INO 31)"

## Transcription

1 Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak Office: Inglis building mezzanine level (INO 31)

2 Outline -1-! This part of the module consists of seven lectures and will focus on finite elements for beams, plates and shells. More specifically, we will consider! Review of elasticity equations in strong and weak form! Beam models and their finite element discretisation! Euler-Bernoulli beam! Timoshenko beam! Plate models and their finite element discretisation! Shells as an assembly of plate and membrane finite elements! Introduction to geometrically exact shell finite elements! Dynamics Page 2

3 Outline -2-! There will be opportunities to gain hands-on experience with the implementation of finite elements using MATLAB! One hour lab session on implementation of beam finite elements (will be not marked)! Coursework on implementation of plate finite elements and dynamics Page 3

4 Why Learn Plate and Shell FEs?! Beam, plate and shell FE are available in almost all finite element software packages! The intelligent use of this software and correct interpretation of output requires basic understanding of the underlying theories! FEM is able to solve problems on geometrically complicated domains! Analytic methods introduced in the first part of the module are only suitable for computing plates and shells with regular geometries, like disks, cylinders, spheres etc.! Many shell structures consist of free form surfaces and/or have a complex topology! Computational methods are the only tool for designing such shell structures! FEM is able to solve problems involving large deformations, non-linear material models and/or dynamics! FEM is very cost effective and fast compared to experimentation Page 4

5 Literature! JN Reddy, An introduction to the finite element method, McGraw-Hill (2006)! TJR Hughes, The finite element method, linear static and dynamic finite element analysis, Prentice-Hall (1987)! K-J Bathe, Finite element procedures, Prentice Hall (1996)! J Fish, T Belytschko, A first course on finite elements, John Wiley & Sons (2007)! 3D7 - Finite element methods - handouts Page 5

6 Examples of Shell Structures -1! Civil engineering Masonry shell structure (Eladio Dieste)! Mechanical engineering and aeronautics Ship hull (sheet metal and frame) Page 6 Concrete roof structure (Pier Luigi Nervi) Fuselage (sheet metal and frame)

7 Examples of Shell Structures -2! Consumer products! Nature Crusteceans Page 7 Ficus elastica leaf Red blood cells

8 Representative Finite Element Computations Wrinkling of an inflated party balloon Virtual crash test (BMW) Sheet metal stamping (Abaqus) buckling of carbon nanotubes Page 8

9 Shell-Fluid Coupled Airbag Inflation m 0.49 m 0.74 m m 0.86 m m Shell mesh: elements Fluid mesh: 48x48x62 cells Page 9

10 Shell-Fluid Coupled Airbag Inflation -2- Page 10

11 Detonation Driven Fracture -1Fractured tubes (Al 6061-T6)! Modeling and simulation challenges!! Page 11 Ductile mixed mode fracture Fluid-shell interaction

12 Detonation Driven Fracture -2- Page 12

13 Roadmap for the Derivation of FEM! As introduced in 3D7, there are two distinct ingredients that are combined to arrive at the discrete system of FE equations! The weak form! A mesh and the corresponding shape functions! In the derivation of the weak form for beams, plates and shells the following approach will be pursued 1) Assume how a beam, plate or shell deforms across its thickness 2) Introduce the assumed deformations into the weak form of three-dimensional elasticity 3) Integrate the resulting three-dimensional elasticity equations along the thickness direction analytically Page 13

14 Elasticity Theory -1-! Consider a body in its undeformed (reference) configuration! The body deforms due to loading and the material points move by a displacement! Kinematic equations; defined based on displacements of an infinitesimal volume element)! Axial strains Page 14

15 Elasticity Theory -2-! Shear components! Stresses! Normal stress components! Shear stress component! Shear stresses are symmetric Page 15

16 Elasticity Theory -3-! Equilibrium equations (determined from equilibrium of an infinitesimal volume element)! Equilibrium in x-direction! Equilibrium in y-direction! Equilibrium in z-direction! are the components of the external loading vector (e.g., gravity) Page 16

17 Elasticity Theory -4-! Hooke s law (linear elastic material equations)! With the material constants Young s modulus and Poisson s ratio Page 17

18 Index Notation -1-! The notation used on the previous slides is rather clumsy and leads to very long expressions! Matrices and vectors can also be expressed in index notation, e.g.! Summation convention: a repeated index implies summation over 1,2,3, e.g.! A comma denotes differentiation Page 18

19 Index Notation -2-! Kronecker delta! Examples: Page 19

20 Elasticity Theory in Index Notation -1-! Kinematic equations! Note that these are six equations! Equilibrium equations! Note that these are three equations! Linear elastic material equations! Inverse relationship! Instead of the Young s modulus and Poisson s ratio the Lame constants can be used Page 20

21 Weak Form of Equilibrium Equations -1-! The equilibrium, kinematic and material equations can be combined into three coupled second order partial differential equations! Next the equilibrium equations in weak form are considered in preparation for finite elements! In structural analysis the weak form is also known as the principle of virtual displacements! To simplify the derivations we assume that the boundaries of the domain are fixed (built-in, zero displacements)! The weak form is constructed by multiplying the equilibrium equations with test functions v i which are zero at fixed boundaries but otherwise arbitrary Page 21

22 Weak Form of Equilibrium Equations -1-! Further make use of integration by parts! Aside: divergence theorem! Consider a vector field and its divergence! The divergence theorem states! Using the divergence theorem equation (1) reduces to! which leads to the principle of virtual displacements Page 22

23 Weak Form of Equilibrium Equations -2-! The integral on the left hand side is the internal virtual work performed by the internal stresses due to virtual displacements! The integral on the right hand side is the external virtual work performed by the external forces due to virtual displacements! Note that the material equations have not been used in the preceding derivation. Hence, the principle of virtual work is independent of material (valid for elastic, plastic, )! The internal virtual work can also be written with virtual strains so that the principle of virtual work reads! Try to prove Page 23

### Finite Element Formulation for Plates - Handout 3 -

Finite Element Formulation for Plates - Handout 3 - Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the

### Finite Element Formulation for Beams - Handout 2 -

Finite Element Formulation for Beams - Handout 2 - Dr Fehmi Cirak (fc286@) Completed Version Review of Euler-Bernoulli Beam Physical beam model midline Beam domain in three-dimensions Midline, also called

### Finite Element Methods (in Solid and Structural Mechanics)

CEE570 / CSE 551 Class #1 Finite Element Methods (in Solid and Structural Mechanics) Spring 2014 Prof. Glaucio H. Paulino Donald Biggar Willett Professor of Engineering Department of Civil and Environmental

### Keywords: Structural System, Structural Analysis, Discrete Modeling, Matrix Analysis of Structures, Linear Elastic Analysis.

STRUCTURAL ANALYSIS Worsak Kanok-Nukulchai Asian Institute of Technology, Thailand Keywords: Structural System, Structural Analysis, Discrete Modeling, Matrix Analysis of Structures, Linear Elastic Analysis.

### Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 01

Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 01 Welcome to the series of lectures, on finite element analysis. Before I start,

### AN INTRODUCTION TO THE FINITE ELEMENT METHOD FOR YOUNG ENGINEERS

AN INTRODUCTION TO THE FINITE ELEMENT METHOD FOR YOUNG ENGINEERS By: Eduardo DeSantiago, PhD, PE, SE Table of Contents SECTION I INTRODUCTION... 2 SECTION II 1-D EXAMPLE... 2 SECTION III DISCUSSION...

### CHAPTER 4 4 NUMERICAL ANALYSIS

41 CHAPTER 4 4 NUMERICAL ANALYSIS Simulation is a powerful tool that engineers use to predict the result of a phenomenon or to simulate the working situation in which a part or machine will perform in

### Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014

Finite Element Method Finite Element Method (ENGC 6321) Syllabus Second Semester 2013-2014 Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered

### ANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET

International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 119-130, Article ID: IJMET_07_01_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

### The elements used in commercial codes can be classified in two basic categories:

CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

### FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS With Mathematica and MATLAB Computations M. ASGHAR BHATTI WILEY JOHN WILEY & SONS, INC. CONTENTS OF THE BOOK WEB SITE PREFACE xi xiii 1 FINITE ELEMENT

### Back to Elements - Tetrahedra vs. Hexahedra

Back to Elements - Tetrahedra vs. Hexahedra Erke Wang, Thomas Nelson, Rainer Rauch CAD-FEM GmbH, Munich, Germany Abstract This paper presents some analytical results and some test results for different

### Elasticity Theory Basics

G22.3033-002: Topics in Computer Graphics: Lecture #7 Geometric Modeling New York University Elasticity Theory Basics Lecture #7: 20 October 2003 Lecturer: Denis Zorin Scribe: Adrian Secord, Yotam Gingold

### COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS

International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 2, March-April 2016, pp. 30 52, Article ID: IJARET_07_02_004 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=7&itype=2

### CAE -Finite Element Method

16.810 Engineering Design and Rapid Prototyping Lecture 3b CAE -Finite Element Method Instructor(s) Prof. Olivier de Weck January 16, 2007 Numerical Methods Finite Element Method Boundary Element Method

### New approaches in Eurocode 3 efficient global structural design

New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beam-column FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural

### Neural network for constitutive modelling in finite element analysis

Neural network for constitutive modelling in finite element analysis A. A. Javadi, T. P. Tan Department of Engineering, School of Engineering and Computer Science University of Exeter, Exeter, Devon, EX4

### Module 4: Buckling of 2D Simply Supported Beam

Module 4: Buckling of D Simply Supported Beam Table of Contents Page Number Problem Description Theory Geometry 4 Preprocessor 7 Element Type 7 Real Constants and Material Properties 8 Meshing 9 Solution

### Applied Finite Element Analysis. M. E. Barkey. Aerospace Engineering and Mechanics. The University of Alabama

Applied Finite Element Analysis M. E. Barkey Aerospace Engineering and Mechanics The University of Alabama M. E. Barkey Applied Finite Element Analysis 1 Course Objectives To introduce the graduate students

### EML 5526 FEA Project 1 Alexander, Dylan. Project 1 Finite Element Analysis and Design of a Plane Truss

Problem Statement: Project 1 Finite Element Analysis and Design of a Plane Truss The plane truss in Figure 1 is analyzed using finite element analysis (FEA) for three load cases: A) Axial load: 10,000

### LECTURE NOTES: FINITE ELEMENT METHOD

LECTURE NOTES: FINITE ELEMENT METHOD AXEL MÅLQVIST. Motivation The finite element method has two main strengths... Geometry. Very complex geometries can be used. This is probably the main reason why finite

### Coefficient of Potential and Capacitance

Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that

### Course in. Nonlinear FEM

Course in Introduction Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity continued Lecture 5 Geometric nonlinearity revisited

### Stability Of Structures: Basic Concepts

23 Stability Of Structures: Basic Concepts ASEN 3112 Lecture 23 Slide 1 Objective This Lecture (1) presents basic concepts & terminology on structural stability (2) describes conceptual procedures for

### CAD and Finite Element Analysis

CAD and Finite Element Analysis Most ME CAD applications require a FEA in one or more areas: Stress Analysis Thermal Analysis Structural Dynamics Computational Fluid Dynamics (CFD) Electromagnetics Analysis...

### Feature Commercial codes In-house codes

A simple finite element solver for thermo-mechanical problems Keywords: Scilab, Open source software, thermo-elasticity Introduction In this paper we would like to show how it is possible to develop a

### CAE -Finite Element Method

16.810 Engineering Design and Rapid Prototyping CAE -Finite Element Method Instructor(s) Prof. Olivier de Weck January 11, 2005 Plan for Today Hand Calculations Aero Æ Structures FEM Lecture (ca. 45 min)

### Introduction to the Finite Element Method (FEM)

Introduction to the Finite Element Method (FEM) Lecture 1 The Direct Stiffness Method and the Global StiffnessMatrix Dr. J. Dean 1 Introduction The finite element method (FEM) is a numerical technique

### MAE4700/5700: Finite Element Analysis for Mechanical and Aerospace Design

MAE4700/5700: Finite Element Analysis for Mechanical and Aerospace Design Cornell University, Fall 2009 Lectures: PHL 403, TTh, 10:10-11:25 am Recitations (ANSYS instruction) Rhodes 471, Fr 1:25-2:15 pm

### Home Browse Search My settings My alerts Shopping cart

Home Browse Search My settings My alerts Shopping cart Articles All fields Author Images Journal/Book title Volume Issue Page Se Thumbnails Full-Size images View View Page 2 of 11 2. Formulation of the

### Modeling solids: Finite Element Methods

Chapter 9 Modeling solids: Finite Element Methods NOTE: I found errors in some of the equations for the shear stress. I will correct them later. The static and time-dependent modeling of solids is different

### ES240 Solid Mechanics Fall 2007. Stress field and momentum balance. Imagine the three-dimensional body again. At time t, the material particle ( x, y,

S40 Solid Mechanics Fall 007 Stress field and momentum balance. Imagine the three-dimensional bod again. At time t, the material particle,, ) is under a state of stress ij,,, force per unit volume b b,,,.

### On the Free Vibration Behavior of Cylindrical Shell Structures. Burak Ustundag

On the Free Vibration Behavior of Cylindrical Shell Structures by Burak Ustundag B.S., Mechanical Engineering Turkish Naval Academy, 2006 Submitted to the Department of Mechanical Engineering in Partial

### ANALYSIS OF STRUCTURAL MEMBER SYSTEMS JEROME J. CONNOR NEW YORK : ':,:':,;:::::,,:

ANALYSIS OF JEROME J. CONNOR, Sc.D., Massachusetts Institute of Technology, is Professor of Civil Engineering at Massachusetts Institute of Technology. He has been active in STRUCTURAL MEMBER teaching

### Interaction between plate and column buckling

Delft, University of Technology Engineering office of Public works Rotterdam Interaction between plate and column buckling Master Thesis Name: Alex van Ham Student number: 1306138 Email: vanham.alex@gmail.com

### Finite Element Analysis

Finite Element Analysis (MCEN 4173/5173) Instructor: Dr. H. Jerry Qi Fall, 2006 What is Finite Element Analysis (FEA)? -- A numerical method. -- Traditionally, a branch of Solid Mechanics. -- Nowadays,

### 3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM

3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM Fabian Krome, Hauke Gravenkamp BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, 12205 Berlin, Germany email: Fabian.Krome@BAM.de

### Volumetric locking in finite elements

Volumetric locking in finite elements on the relation between constraint ratio and locking behavior Bachelor Final Project Bart Vossen MT 08.31 July 31, 2008 Supervisors: H. R. Javani Joni, MSc dr. ir.

### 820446 - ACMSM - Computer Applications in Solids Mechanics

Coordinating unit: 820 - EUETIB - Barcelona College of Industrial Engineering Teaching unit: 737 - RMEE - Department of Strength of Materials and Structural Engineering Academic year: Degree: 2015 BACHELOR'S

### Finite Element Method

16.810 (16.682) Engineering Design and Rapid Prototyping Finite Element Method Instructor(s) Prof. Olivier de Weck deweck@mit.edu Dr. Il Yong Kim kiy@mit.edu January 12, 2004 Plan for Today FEM Lecture

### Pre-requisites 2012-2013

Pre-requisites 2012-2013 Engineering Computation The student should be familiar with basic tools in Mathematics and Physics as learned at the High School level and in the first year of Engineering Schools.

### Lecture 12: Fundamental Concepts in Structural Plasticity

Lecture 12: Fundamental Concepts in Structural Plasticity Plastic properties of the material were already introduced briefly earlier in the present notes. The critical slenderness ratio of column is controlled

### Graduate Courses in Mechanical Engineering

Graduate Courses in Mechanical Engineering MEEG 501 ADVANCED MECHANICAL ENGINEERING ANALYSIS An advanced, unified approach to the solution of mechanical engineering problems, with emphasis on the formulation

### Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method

Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method Yun-gang Zhan School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang,

### Reliable FE-Modeling with ANSYS

Reliable FE-Modeling with ANSYS Thomas Nelson, Erke Wang CADFEM GmbH, Munich, Germany Abstract ANSYS is one of the leading commercial finite element programs in the world and can be applied to a large

### Burst Pressure Prediction of Pressure Vessel using FEA

Burst Pressure Prediction of Pressure Vessel using FEA Nidhi Dwivedi, Research Scholar (G.E.C, Jabalpur, M.P), Veerendra Kumar Principal (G.E.C, Jabalpur, M.P) Abstract The main objective of this paper

### A quadrilateral 2-D finite element based on mixed interpolation of tensorial

A quadrilateral 2-D finite element based on mixed interpolation of tensorial components Eduardo N. Dvorkin and Sara I. Vassolo* Instituto de Materiales y Estructuras, Facultad de Ingenieria, Universidad

### 8.2 Elastic Strain Energy

Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for

### SOME BASIC CONCEPTS OF ENGINEERING ANALYSIS

SOME BASIC CONCEPTS OF ENGINEERING ANALYSIS LECTURE 1 46 MINUTES I-I SolIe basic ccnacepls of eugideeridg ualysis LECTURE 1 Introduction to the course. objective of lectures Some basic concepts of engineering

### FINITE ELEMENT METHOD IM _1

COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FINITE ELEMENT METHOD IM0238 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 96 HOURS OF INDEPENDENT WORK NUMERICAL

### STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL

STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL Paulo Mendes, Instituto Superior de Engenharia de Lisboa, Portugal Sérgio Oliveira, Laboratório Nacional de Engenharia

### ENGI 8673 Subsea Pipeline Engineering Faculty of Engineering and Applied Science

GUIDANCE NOTE LECTURE 12 THERMAL EXPANSION ANALYSIS OVERVIEW The calculation procedure for determining the longitudinal pipeline response can be formulated on the basis of strain. The longitudinal strain

### FREE VIBRATION OF SPHERICAL SHELL USING FINITE ELEMENT APPROACH

Communication Science & technology N 4. January 04 COST FREE VIBRATION OF SPHERICAL SHELL USING FINITE ELEMENT APPROACH M. BOUAZZA,, A. LAIREDJ 3, D. OUINAS 4, and A. HAMOUINE Department of Civil Engineering,

### List of Problems Solved Introduction p. 1 Concept p. 1 Nodes p. 3 Elements p. 4 Direct Approach p. 5 Linear Spring p. 5 Heat Flow p.

Preface p. v List of Problems Solved p. xiii Introduction p. 1 Concept p. 1 Nodes p. 3 Elements p. 4 Direct Approach p. 5 Linear Spring p. 5 Heat Flow p. 6 Assembly of the Global System of Equations p.

### Element Selection Criteria

Element Selection Criteria Element Selection Criteria Overview Elements in ABAQUS Structural Elements (Shells and Beams) vs. Continuum Elements Modeling Bending Using Continuum Elements Stress Concentrations

### STRUCTURAL AND THERMAL ANALYSIS OF A BOILER USING FINITE ELEMENT ANALYSIS

STRUCTURAL AND THERMAL ANALYSIS OF A BOILER USING FINITE ELEMENT ANALYSIS D.Kondayya Department of Mechanical Engineering, Author Correspondence: Department of Mechancal Engineering, Sreenidhi Institute

### LINEAR SYSTEMS. Consider the following example of a linear system:

LINEAR SYSTEMS Consider the following example of a linear system: Its unique solution is x +2x 2 +3x 3 = 5 x + x 3 = 3 3x + x 2 +3x 3 = 3 x =, x 2 =0, x 3 = 2 In general we want to solve n equations in

### Programming the Finite Element Method

Programming the Finite Element Method FOURTH EDITION I. M. Smith University of Manchester, UK D. V. Griffiths Colorado School of Mines, USA John Wiley & Sons, Ltd Contents Preface Acknowledgement xv xvii

### CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS

1 CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS Written by: Sophia Hassiotis, January, 2003 Last revision: February, 2015 Modern methods of structural analysis overcome some of the

### 2. A tutorial: Creating and analyzing a simple model

2. A tutorial: Creating and analyzing a simple model The following section leads you through the ABAQUS/CAE modeling process by visiting each of the modules and showing you the basic steps to create and

### Group Members: Blake Maloney, Khaled Alroumi, Robert Mitchell

ME 461: Finite Element Analysis Fall 2015 A Semester Report on: The Development and Analysis of a Nose Landing Gear Group Members: Blake Maloney, Khaled Alroumi, Robert Mitchell Department of Mechanical

### Module 1: Introduction to Finite Element Analysis Lecture 1: Introduction

Module : Introduction to Finite Element Analysis Lecture : Introduction.. Introduction Te Finite Element Metod (FEM) is a numerical tecnique to find approximate solutions of partial differential equations.

### Exercise 1: Three Point Bending Using ANSYS Workbench

Exercise 1: Three Point Bending Using ANSYS Workbench Contents Goals... 1 Beam under 3-Pt Bending... 2 Taking advantage of symmetries... 3 Starting and Configuring ANSYS Workbench... 4 A. Pre-Processing:

### Week 9 - Lecture Linear Structural Analysis. ME Introduction to CAD/CAE Tools

Week 9 - Lecture Linear Structural Analysis Lecture Topics Finite Element Analysis (FEA) Overview FEA Parameters FEA Best Practices FEA Software Introduction Linear Structure Analysis Product Lifecycle

### Introduction to Fluid Mechanics. Chapter 9 External Incompressible Viscous Flow. Pritchard

Introduction to Fluid Mechanics Chapter 9 External Incompressible Viscous Flow Main Topics The Boundary-Layer Concept Boundary-Layer Thicknesses Laminar Flat-Plate Boundary Layer: Exact Solution Momentum

### Learning Module 6 Linear Dynamic Analysis

Learning Module 6 Linear Dynamic Analysis What is a Learning Module? Title Page Guide A Learning Module (LM) is a structured, concise, and self-sufficient learning resource. An LM provides the learner

### OpenFOAM Optimization Tools

OpenFOAM Optimization Tools Henrik Rusche and Aleks Jemcov h.rusche@wikki-gmbh.de and a.jemcov@wikki.co.uk Wikki, Germany and United Kingdom OpenFOAM Optimization Tools p. 1 Agenda Objective Review optimisation

### Chapter 9 CONCRETE STRUCTURE DESIGN REQUIREMENTS

Chapter 9 CONCRETE STRUCTURE DESIGN REQUIREMENTS 9.1 GENERAL 9.1.1 Scope. The quality and testing of concrete and steel (reinforcing and anchoring) materials and the design and construction of concrete

### EFFICIENT NUMERICAL SIMULATION OF INDUSTRIAL SHEET METAL BENDING PROCESSES

ECCOMAS Congress 06 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5 0 June 06

### FINITE ELEMENT METHOD (FEM): AN OVERVIEW. Dr A Chawla

FINITE ELEMENT METHOD (FEM): AN OVERVIEW Dr A Chawla ANALYTICAL / MATHEMATICAL SOLUTIONS RESULTS AT INFINITE LOCATIONS CONTINUOUS SOLUTIONS FOR SIMPLIFIED SITUATIONS ONLY EXACT SOLUTION NUMERICAL (FEM)

### 1. a) Discuss how finite element is evolved in engineering field. (8) b) Explain the finite element idealization of structures with examples.

M.TECH. DEGREE EXAMINATION Branch: Civil Engineering Specialization Geomechanics and structures Model Question Paper - I MCEGS 106-2 FINITE ELEMENT ANALYSIS Time: 3 hours Maximum: 100 Marks Answer ALL

### Section 3: Nonlinear Analysis

Autodesk Simulation Workshop Section 3: Nonlinear Analysis This section presents the theory and methods used to perform nonlinear analyses using Autodesk Simulation Multiphysics. Nonlinear phenomena can

### Types of Elements

chapter : Modeling and Simulation 439 142 20 600 Then from the first equation, P 1 = 140(0.0714) = 9.996 kn. 280 = MPa =, psi The structure pushes on the wall with a force of 9.996 kn. (Note: we could

### METHODS FOR ACHIEVEMENT UNIFORM STRESSES DISTRIBUTION UNDER THE FOUNDATION

International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 45-66, Article ID: IJCIET_07_02_004 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

### BEAM THEORIES The difference between Euler-Bernoulli and Timoschenko

BEAM THEORIES The difference between Euler-Bernoulli and Timoschenko Uemuet Goerguelue Two mathematical models, namely the shear-deformable (Timoshenko) model and the shearindeformable (Euler-Bernoulli)

### Finite Element Method (FEM) Introduction

Engineering manual No. 20 Updated: 06/2016 Finite Element Method (FEM) Introduction The objective of this engineering manual is to explain the basic terms of a particular field of problems and the practical

### SEISMIC ANALYSIS OF FRAMED STEEL STRUCTURE WITH SEMI- RIGID JOINTS

EUROSTEEL 214, September 1-12, 214, Naples, Italy SEISMIC ANALYSIS OF FRAMED STEEL STRUCTURE WITH SEMI- RIGID JOINTS INTRODUCTION Paulina Krolo, Mehmed Čaušević, Mladen Bulić University of Rijeka, Faculty

### Universal Format of Shape Function for Numerical Analysis using Multiple Element Forms

, pp.63-67 http://dx.doi.org/0.4257/astl.206. Universal Format of Shape Function for Numerical Analysis using Multiple Element Forms Yuting Zhang, Yujie Li, Xiuli Ding Yangtze River Scientific Research

### From Weighted Residual Methods to Finite Element Methods. Lars Erik Lindgren

From Weighted Residual Methods to Finite Element Methods Lars Erik Lindgren 2009 TABLE OF CONTENT 1 INTRODUCTION 3 2 SOME DEFINITIONS 3 3 SHORT FINITE ELEMENT COURSE 4 4 WEIGHTED RESIDUAL METHODS 6 4.1

### 3 Concepts of Stress Analysis

3 Concepts of Stress Analysis 3.1 Introduction Here the concepts of stress analysis will be stated in a finite element context. That means that the primary unknown will be the (generalized) displacements.

### Notes on Application of Finite Element Method to the Solution of the Poisson Equation

Notes on Application of Finite Element Method to the Solution of the Poisson Equation Consider the arbitrary two dimensional domain, shown in Figure 1. The Poisson equation for this domain can be written

### Part 1 : Modelling. Practical application of the MFE. Method of Finite Elements I. Institute of Structural Engineering Page 1

Institute of Structural Engineering Page 1 Practical application of the MFE Part 1 : Modelling Institute of Structural Engineering Page 2 Goals of this Lecture Demonstrating the importance of modelling

### Chapter 12 Elasticity

If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences

### The Application of ABAQUS for CATIA V5 for Analyses in the Pre-Design and Design Phase

The Application of ABAQUS for CATIA V5 for Analyses in the Pre-Design and Design Phase Fabien Debarle PSA Peugeot Citroën - 18 rue des Fauvelles - 92250 La Garenne Colombes - France Mathieu Durix Digital

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Introduction to Basics of FEA and

Introduction to Basics of FEA and Pro/MECHANICA 25.353 Lecture Series G. Gary Wang Department of Mechanical and Manufacturing Engineering The University of Manitoba What is Pro/MECHANICA Pro/MECHANICA

### THREE-DIMENSIONAL INSERT MOLDING SIMULATION IN INJECTION MOLDING

THREE-DIMENSIONAL INSERT MOLDING SIMULATION IN INJECTION MOLDING Rong-Yeu Chang* National Tsing-Hua University, HsinChu, Taiwan 30043, ROC Yi-Hui Peng, David C.Hsu and Wen-Hsien Yang CoreTech System Co.,Ltd.,

### Modeling of inflatable dams partially filled with fluid and gas considering large deformations and stability

Institute of Mechanics Modeling of inflatable dams partially filled with fluid and gas considering large deformations and stability October 2009 Anne Maurer Marc Hassler Karl Schweizerhof Institute of

### 10 Space Truss and Space Frame Analysis

10 Space Truss and Space Frame Analysis 10.1 Introduction One dimensional models can be very accurate and very cost effective in the proper applications. For example, a hollow tube may require many thousands

### 4.3 Results... 27 4.3.1 Drained Conditions... 27 4.3.2 Undrained Conditions... 28 4.4 References... 30 4.5 Data Files... 30 5 Undrained Analysis of

Table of Contents 1 One Dimensional Compression of a Finite Layer... 3 1.1 Problem Description... 3 1.1.1 Uniform Mesh... 3 1.1.2 Graded Mesh... 5 1.2 Analytical Solution... 6 1.3 Results... 6 1.3.1 Uniform

### Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 23 Bending of Beams- II

Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 23 Bending of Beams- II Welcome to the second lesson of the fifth module which is on Bending of Beams part

### A Comparative Study on Non-Linear Analysis of Frame with and without Structural Wall System

A Comparative Study on Non-Linear Analysis of Frame with and without Structural Wall System Dr.Binu Sukumar #1, A.Hemamathi *2, S.Kokila #3 C.Hanish #4 #1 Professor &Head, Department of Civil Engineering,

### Deflections. Question: What are Structural Deflections?

Question: What are Structural Deflections? Answer: The deformations or movements of a structure and its components, such as beams and trusses, from their original positions. It is as important for the

### Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams

MECH 466 Microelectromechanical Sstems Universit of Victoria Dept. of Mechanical Engineering Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams 1 Overview Compliant Mechanisms Basics of Mechanics

### DESIGN AND ANALYSIS OF A TYPICAL WING RIB FOR PASSENGER AIRCRAFT

DESIGN AND ANALYSIS OF A TYPICAL WING RIB FOR PASSENGER AIRCRAFT Bindu H.C 1,Muhammad Muhsin Ali.H 2 P.G. Student, Department of Mechanical Engineering, Ghousia college of Engineering, Ramanagaram, Karnataka,

### Mechanical Properties - Stresses & Strains

Mechanical Properties - Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =

### An Overview of the Finite Element Analysis

CHAPTER 1 An Overview of the Finite Element Analysis 1.1 Introduction Finite element analysis (FEA) involves solution of engineering problems using computers. Engineering structures that have complex geometry

### 1. Start the NX CAD software. From the start menu, select Start All Programs UGS NX 8.0 NX 8.0 or double click the icon on the desktop.

Lab Objectives Become familiar with Siemens NX finite element analysis using the NX Nastran solver. Perform deflection and stress analyses of planar truss structures. Use modeling and FEA tools to input