Page 6 - Finite Element Modeling and Simulations with ANSYS Workbench

Contents

Preface ..............................................................................................................................................xi
Authors ......................................................................................................................................... xiii

1. Introduction .............................................................................................................................1
1.1 Some Basic Concepts ....................................................................................................1
1.1.1 Why FEA? .........................................................................................................1
1.1.2 Finite Element Applications in Engineering ................................................1
1.1.3 FEA with ANSYS Workbench ..........................................................................3
1.1.4 A Brief History of FEA ....................................................................................3
1.1.5 A General Procedure for FEA ........................................................................4
1.2 An Example in FEA: Spring System ...........................................................................4
1.2.1 One Spring Element .........................................................................................5
1.2.2 A Spring System ...............................................................................................6
1.2.2.1 Assembly of Element Equations: Direct Approach .....................6
1.2.2.2 Assembly of Element Equations: Energy Approach ...................8
1.2.3 Boundary and Load Conditions ....................................................................9
1.2.4 Solution Verification ...................................................................................... 10
1.2.5 Example Problems ......................................................................................... 10
1.3 Overview of ANSYS Workbench ................................................................................13
1.3.1 The User Interface ..........................................................................................13
1.3.2 The Toolbox ..................................................................................................... 14
1.3.3 The Project Schematic ................................................................................... 14
1.3.4 Working with Cells ........................................................................................ 16
1.3.5 The Menu Bar ................................................................................................. 16
1.4 Summary ......................................................................................................................17
Problems ..................................................................................................................................18

2. Bars and Trusses ...................................................................................................................21
2.1 Introduction .................................................................................................................21
2.2 Review of the 1-D Elasticity Theory .........................................................................21
2.3 Modeling of Trusses ...................................................................................................22
2.4 Formulation of the Bar Element ................................................................................23
2.4.1 Stiffness Matrix: Direct Method ..................................................................23
2.4.2 Stiffness Matrix: Energy Approach .............................................................25
2.4.3 Treatment of Distributed Load ....................................................................27
2.4.4 Bar Element in 2-D and 3-D ..........................................................................28
2.4.4.1 2-D Case ...........................................................................................28
2.4.4.2 3-D Case ...........................................................................................31
2.4.5 Element Stress ................................................................................................31
2.5 Examples with Bar Elements .....................................................................................32
2.6 Case Study with ANSYS Workbench .........................................................................40
2.7 Summary ......................................................................................................................59
2.8 Review of Learning Objectives .................................................................................59
Problems ..................................................................................................................................59

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