Static Analysis | p. 1 |
Linear Analysis of Framed Structures | p. 3 |
Linear Analysis of Continuum Structures | p. 6 |
Solution of the Linear Equilibrium Equations | p. 13 |
Matrix Factorization | p. 13 |
Iterative Solution Procedures | p. 15 |
Nonlinear Analysis | p. 20 |
Geometric Nonlinearity | p. 21 |
Material Nonlinearity | p. 26 |
Time Varying Loads | p. 29 |
Buckling Analysis | p. 30 |
Solution of the Nonlinear Equations | p. 32 |
References | p. 35 |
Vibration Analysis | p. 37 |
Free Vibration | p. 37 |
Properties of the Eigenproblem | p. 39 |
The Standard Eigenproblem and the Rayleigh Quotient | p. 40 |
Solution of the Eigenproblem | p. 42 |
Static Condensation | p. 42 |
Solution Methods | p. 43 |
Vector Iteration Methods | p. 45 |
Inverse Vector Iteration | p. 45 |
Vector Iteration with Shifts | p. 48 |
Matrix Deflation and Gram-Schmidt Orthogonalization | p. 50 |
Transformation Methods | p. 51 |
Polynomial Iterations | p. 52 |
Rayleigh-Ritz Analysis | p. 54 |
Approximate Eigenproblem Solution | p. 54 |
Load-Dependent Ritz Vectors | p. 55 |
The Lanczos Method | p. 58 |
Subspace Iteration | p. 60 |
References | p. 63 |
Dynamic Analysis | p. 65 |
Linear Dynamic Analysis | p. 65 |
Direct Integration | p. 66 |
Mode Superposition | p. 72 |
Special Analysis Procedures | p. 78 |
Reduced Basis | p. 81 |
Static Analysis | p. 82 |
Dynamic Analysis | p. 84 |
Nonlinear Dynamic Analysis | p. 86 |
Implicit Integration | p. 86 |
Mode Superposition | p. 87 |
References | p. 91 |
Reanalysis of Structures | p. 93 |
Design Variables | p. 95 |
Formulation of Static Reanalysis | p. 97 |
Linear Static Reanalysis | p. 97 |
Nonlinear Static Reanalysis | p. 99 |
Formulation of Vibration Reanalysis | p. 102 |
Eigenproblem Reanalysis | p. 102 |
Iterative Procedures | p. 103 |
Formulation of Dynamic Reanalysis | p. 105 |
Linear Dynamic Reanalysis | p. 105 |
Nonlinear Dynamic Reanalysis | p. 107 |
Reanalysis Methods | p. 109 |
Direct Methods | p. 110 |
Approximate Methods | p. 110 |
The Combined Approximations Approach | p. 112 |
References | p. 116 |
Static Reanalysis | p. 121 |
Determination of the Basis Vectors | p. 122 |
The Binomial Series | p. 122 |
Calculation of the Basis Vectors | p. 123 |
Convergence of the Series | p. 125 |
Linear Reanalysis | p. 125 |
Coupled Basis Vectors | p. 125 |
Uncoupled Basis Vectors | p. 131 |
Topological Changes | p. 139 |
Number of DOF is Decreased | p. 139 |
Number of DOF is Increased | p. 142 |
Nonlinear Analysis and Reanalysis | p. 146 |
Problem Formulation | p. 146 |
Solution by Combined Approximations | p. 148 |
Procedures for Analysis and Reanalysis | p. 151 |
References | p. 158 |
Vibration Reanalysis | p. 159 |
The Reduced Eigenproblem | p. 160 |
Problem Formulation | p. 160 |
Determination of the Basis Vectors | p. 161 |
Improved Basis Vectors | p. 163 |
Gram-Schmidt Orthogonalizations of the Modes | p. 163 |
Shifts of the Basis Vectors | p. 164 |
Gram-Schmidt Orthogonalizations of the Basis Vectors | p. 166 |
General Solution Procedure | p. 166 |
Numerical Examples | p. 168 |
Reanalysis by Iterative Procedures | p. 175 |
References | p. 183 |
Dynamic Reanalysis | p. 185 |
Linear Dynamic Reanalysis | p. 185 |
Solution by Direct Integration | p. 186 |
Solution by Mode Superposition | p. 190 |
Nonlinear Dynamic Reanalysis | p. 197 |
Solution by Implicit Integration | p. 197 |
Solution by Mode Superposition | p. 197 |
References | p. 204 |
Direct Reanalysis | p. 207 |
Direct Methods | p. 208 |
A Single Rank-One Change | p. 208 |
Multiple Rank-One Changes | p. 209 |
General Procedure | p. 212 |
Direct Solutions by Combined Approximations | p. 215 |
Multiple Rank-One Changes | p. 216 |
Solution Procedure | p. 217 |
Topological and Geometrical Changes | p. 221 |
Topological Changes | p. 221 |
Geometrical Changes | p. 223 |
References | p. 224 |
Repeated Sensitivity Analysis | p. 227 |
Finite-Difference Derivatives | p. 228 |
Static Problems | p. 230 |
Analytical Derivatives | p. 230 |
Semi-Analytical Derivatives | p. 231 |
Repeated Analytical Derivatives | p. 233 |
Repeated Finite-Difference Derivatives | p. 237 |
Errors Due to Rigid Body Motions | p. 240 |
Vibration Problems | p. 243 |
Analytical Derivatives | p. 243 |
Repeated Finite-Difference Derivatives | p. 244 |
Improved Basis Vectors using Central-Differences | p. 247 |
Linear Dynamic Problems | p. 249 |
Modal Analysis Equations | p. 249 |
Analytical Derivatives | p. 250 |
Reducing the Number of Differential Equations | p. 251 |
Nonlinear Dynamic Problems | p. 255 |
Modal Analysis Equations | p. 255 |
Nonlinear-Dynamic Sensitivity Analysis | p. 256 |
Efficient Solution Procedures | p. 258 |
References | p. 262 |
Computational Considerations | p. 265 |
Efficiency of the Calculations | p. 266 |
Static Reanalysis | p. 266 |
Dynamic Reanalysis | p. 269 |
Dynamic Sensitivity Analysis | p. 270 |
Accuracy Considerations | p. 273 |
Linearly Dependent Basis Vectors | p. 273 |
Scaled and Nearly Scaled Designs | p. 276 |
Equivalence of the PCG and CA Methods | p. 278 |
Error Evaluation | p. 281 |
Static Reanalysis | p. 281 |
Vibration Reanalysis | p. 284 |
Accuracy of Forces and Stresses | p. 289 |
References | p. 291 |
Index | p. 293 |
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