Page 9 - Finite Element Modeling and Simulations with ANSYS Workbench

viii Contents

7.3.3 Boundary Conditions: Loads .....................................................................224
7.3.4 Assembly Analysis: Contacts .....................................................................224
7.4 Formulation of Solid Elements ................................................................................225
7.4.1 General Formulation ...................................................................................225
7.4.2 Typical Solid Element Types ......................................................................226
7.4.3 Formulation of a Linear Hexahedral Element Type ...............................227
7.4.4 Treatment of Distributed Loads .................................................................230
7.5 Case Studies with ANSYS Workbench .....................................................................230
7.6 Summary ....................................................................................................................255
7.7 Review of Learning Objectives ...............................................................................255
Problems ................................................................................................................................255

8. Structural Vibration and Dynamics ............................................................................... 261
8.1 Introduction ............................................................................................................... 261
8.2 Review of Basic Equations ....................................................................................... 261
8.2.1 A Single DOF System ..................................................................................262
8.2.2 A Multi-DOF System ...................................................................................264
8.2.2.1 Mass Matrices ...............................................................................264
8.2.2.2 Damping ........................................................................................266
8.3 Formulation for Modal Analysis ............................................................................ 267
8.3.1 Modal Equations ..........................................................................................269
8.4 Formulation for Frequency Response Analysis ...................................................271
8.4.1 Modal Method ..............................................................................................271
8.4.2 Direct Method ..............................................................................................272
8.5 Formulation for Transient Response Analysis......................................................272
8.5.1 Direct Methods (Direct Integration Methods) .........................................273
8.5.2 Modal Method .............................................................................................. 274
8.6 Modeling Examples ..................................................................................................275
8.6.1 Modal Analysis ............................................................................................275
8.6.2 Frequency Response Analysis ................................................................... 276
8.6.3 Transient Response Analysis ..................................................................... 276
8.6.4 Cautions in Dynamic Analysis .................................................................. 276
8.7 Case Studies with ANSYS Workbench .....................................................................277
8.8 Summary ....................................................................................................................293
8.9 Review of Learning Objectives ...............................................................................294
Problems ................................................................................................................................294

9. Thermal Analysis ...............................................................................................................301
9.1 Introduction ...............................................................................................................301
9.2 Review of Basic Equations .......................................................................................301
9.2.1 Thermal Analysis .........................................................................................301
9.2.1.1 Finite Element Formulation for Heat Conduction ...................303
9.2.2 Thermal Stress Analysis .............................................................................303
9.2.2.1 1-D Case .........................................................................................304
9.2.2.2 2-D Cases .......................................................................................305
9.2.2.3 3-D Case .........................................................................................305
9.2.2.4 Notes on FEA for Thermal Stress Analysis ..............................305
9.3 Modeling of Thermal Problems ..............................................................................306
9.3.1 Thermal Analysis .........................................................................................306