Page 8 - Finite Element Modeling and Simulations with ANSYS Workbench

Contents vii

5.2 Symmetry ................................................................................................................... 161
5.2.1 An Example .................................................................................................. 162
5.3 Substructures (Superelements) ............................................................................... 163
5.4 Equation Solving .......................................................................................................164
5.4.1 Direct Methods (Gauss Elimination) ........................................................164
5.4.2 Iterative Methods .........................................................................................164
5.4.3 An Example: Gauss Elimination ................................................................164
5.4.4 An Example: Iterative Method ................................................................... 165
5.5 Nature of Finite Element Solutions ........................................................................ 166
5.6 Convergence of FEA Solutions ................................................................................ 167
5.7 Adaptivity (h-, p-, and hp-Methods) ........................................................................ 167
5.8 Case Study with ANSYS Workbench ....................................................................... 168
5.9 Summary .................................................................................................................... 182
5.10 Review of Learning Objectives ...............................................................................183
Problems ................................................................................................................................183

6. Plate and Shell Analyses ................................................................................................... 187
6.1 Introduction ............................................................................................................... 187
6.2 Review of Plate Theory ............................................................................................ 187
6.2.1 Force and Stress Relations in Plates .......................................................... 187
6.2.2 Thin Plate Theory (Kirchhoff Plate Theory) ............................................ 189
6.2.2.1 Example: A Thin Plate ................................................................. 191
6.2.3 Thick Plate Theory (Mindlin Plate Theory) ............................................. 192
6.2.4 Shell Theory .................................................................................................. 193
6.2.4.1 Shell Example: A Cylindrical Container ................................... 193
6.3 Modeling of Plates and Shells ................................................................................. 194
6.4 Formulation of the Plate and Shell Elements ........................................................ 195
6.4.1 Kirchhoff Plate Elements ............................................................................ 195
6.4.2 Mindlin Plate Elements ............................................................................... 196
6.4.3 Discrete Kirchhoff Elements ...................................................................... 197
6.4.4 Flat Shell Elements ....................................................................................... 197
6.4.5 Curved Shell Elements ................................................................................ 198
6.5 Case Studies with ANSYS Workbench .....................................................................199
6.6 Summary .................................................................................................................... 214
6.7 Review of Learning Objectives ............................................................................... 214
Problems ................................................................................................................................ 214

7. Three-Dimensional Elasticity .......................................................................................... 219
7.1 Introduction ............................................................................................................... 219
7.2 Review of Theory of Elasticity ................................................................................ 219
7.2.1 Stress–Strain Relation .................................................................................220
7.2.2 Displacement ................................................................................................221
7.2.3 Strain–Displacement Relation ....................................................................221
7.2.4 Equilibrium Equations ................................................................................221
7.2.5 Boundary Conditions ..................................................................................222
7.2.6 Stress Analysis .............................................................................................222
7.3 Modeling of 3-D Elastic Structures ........................................................................222
7.3.1 Mesh Discretization .....................................................................................223
7.3.2 Boundary Conditions: Supports ................................................................223