List of Figures
1.1. Rayleigh Damping................................................. ................................................... .............................. 6
2.1. Diagram of Allen Wrench............................................... ................................................... .................... 22
3.1. Diagram of a Model Airplane Wing................................................ ................................................... ..... 51
4.1. Harmonic Systems............................................... ................................................... .............................. 77
4.2. Relationship Between Real/Imaginary Components and Amplitude/Phase Angle................................... 82
4.3. An Unbalanced Rotating Antenna............................................... ................................................... ....... 83
4.4. Two-Mass-Spring-System........................................ ................................................... ........................... 91
5.1. Examples of Load-Versus-Time Curves............................................... .................................................. 111
5.2. Effect of Integration Time Step on Period Elongation................................................ ........................... 131
5.3. Transient Input vs. Transient Response................................................ ................................................. 131
6.1. Single-Point and Multi-Point Response Spectra.............................................. ...................................... 136
6.2. Simply Supported Beam with Vertical Motion of Both Supports................................................ ........... 147
6.3. Three-Beam Frame................................................ ................................................... ........................... 177
7.1. Buckling Curves............................................... ................................................... ................................ 180
7.2. Adjusting Variable Loads to Find an Eigenvalue of 1.0.................................................. ........................ 183
7.3. Bar with Hinged Ends.................................................. ................................................... ..................... 187
8.1. Common Examples of Nonlinear Structural Behavior................................................ ........................... 193
8.2. A Fishing Rod Demonstrates Geometric Nonlinearity............................................... ............................ 194
8.3. Newton-Raphson Approach................................................ ................................................... ............. 195
8.4. Traditional Newton-Raphson Method vs. Arc-Length Method................................................ ............... 196
8.5. Load Steps, Substeps, and Time................................................ ................................................... ........ 197
8.6. Nonconservative (Path-Dependent) Behavior................................................ ...................................... 198
8.7. Load Directions Before and Aft er Deflection................................................ ........................................ 199
8.8. Stress-Stiffened Beams................................................. ................................................... .................... 201
8.9. Hyperelastic Structure.............................................. ................................................... ........................ 202
8.10. Stress Relaxation and Creep................................................ ................................................... ........... 211
8.11. Time Hardening Creep Analysis................................................ ................................................... ...... 212
8.12. Viscoplastic Behavior in a Rolling Operation............................................... ........................................ 214
8.13. Viscoelastic Behavior (Maxwell Model)................................................ ............................................... 215
8.14. Linear Interpolation of Nonlinear Results Can Introduce Some Error............................................... .... 252
8.15. Convergence Norms Displayed By the Graphical Solution Tracking (GST ) Feature............................... 269
8.16. Typical Nonlinear Output Listing.................................................. ................................................... ... 271
8.17. Cyclic Point Load History................................................ ................................................... ................ 274
9.1. Flowchart of Linear Perturbation Static Analysis................................................ ................................... 288
9.2. Flowchart of Linear Perturbation Modal Analysis................................................ .................................. 289
9.3. Flowchart of Linear Perturbation Eigenvalue Buckling Analysis................................................ ............ 290
9.4. Flowchart of Linear Perturbation Full Harmonic Analysis................................................ ...................... 291
10.1. Element Topology of a 3-D 8-Node Interface Element................................................ ......................... 319
10.2. Pressure vs. Closure Behavior of a Gasket Material.............................................. ................................ 321
10.3. Gasket Material Input: Linear Unloading Curves............................................... .................................. 323
10.4. Gasket Material Input: Nonlinear Unloading Curves............................................... ............................. 324
10.5. Gasket Compression and Unloading Curves at Two Temperatures............................................ .......... 327
10.6. Gasket Finite Element Model Geometry................................................ ............................................. 329
10.7. Whole Model Mesh with Brick Element................................................ .............................................. 330
10.8. Interface Layer Mesh................................................. ................................................... ..................... 330
10.9. Whole Model Tetrahedral Mesh................................................. ................................................... ..... 330
10.10. Interface Layer Mesh with Degenerated Wedge Elements................................................ ................ 331
11.1. Schematic of the Fracture Modes................................................ ................................................... .... 340
11.2. Schematic of a Crack Tip................................................ ................................................... ................. 342
11.3. Matrix with Inclusion.................................................. ................................................... .................... 344
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