Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.
Author(s): Kyung K. Choi, Nam-Ho Kim
Edition: 1
Year: 2004
Language: English
Pages: 482
1: Linear Systems......Page 10
Preface......Page 7
PART I: Structural Design and Analysis......Page 17
1.1 Elements of Structural Design......Page 18
1.2 Structural Modeling and Design Parameterization......Page 24
1.3 Structural Analysis......Page 30
1.4 Finite Element Analysis......Page 31
1.5 Structural Design Sensitivity Analysis......Page 35
1.6 Second-Order Design Sensitivity Analysis......Page 45
1.7 Design Optimization......Page 46
2.1 Introduction......Page 52
2.2 Energy Method......Page 54
2.3 Variational Formulation and the Principle of Virtual Work......Page 60
2.4 Hamilton's Principle......Page 64
2.5 Eigenvalue Problem......Page 66
2.6 Frequency Response Problem......Page 69
2.7 Thermoelastic Problem......Page 75
3. Variational Equations and Finite Element Methods......Page 78
3.1 Energy Bilinear and Load Linear Forms of Static Problems......Page 79
3.2 Vibration and Buckling of Elastic Systems......Page 98
3.3 Finite Element Structural Equations......Page 103
3.4 Global Matrix Equations for the Finite Element Method......Page 118
PART II: Design Sensitivity Analysis of Linear Structural Systems......Page 132
4. Discrete Design Sensitivity Analysis......Page 133
4.1 Static Response Design Sensitivity......Page 135
4.2 Design Sensitivity of the Eigenvalue Problem......Page 156
4.3 Transient Dynamic Response Design Sensitivity......Page 176
5. Continuum Sizing Design Sensitivity Analysis......Page 185
5.1 Design Sensitivity Analysis of Static Response......Page 186
5.2 Eigenvalue Design Sensitivity......Page 213
5.3 Transient Dynamic Response Design Sensitivity......Page 223
5.4 Frequency Response Design Sensitivity......Page 231
5.5 Structural-Acoustic Design Sensitivity Analysis......Page 244
6.1 Material Derivatives for Shape Design Sensitivity Analysis......Page 256
6.2 Static Response Design Sensitivity Analysis......Page 269
6.3 Eigenvalue Shape Design Sensitivity Analysis......Page 314
6.4 Frequency Response Problem......Page 322
6.5 Thermoelastic Problem......Page 335
6.6 Second-Order Shape Design Sensitivity Analysis......Page 341
7. Configuration Design Sensitivity Analysis......Page 359
7.1 Material Derivatives for Configuration Design Sensitivity Analysis......Page 360
7.2 Configuration Design Sensitivity Analysis......Page 367
7.3 Numerical Methods in Configuration Design Sensitivity Analysis......Page 381
7.4 Structural-Acoustic Problem......Page 401
7.5 Configuration Design Theory for Curved Structure......Page 414
A.1 Matrix Calculus Notation......Page 427
A.2.1 R[sup(k)]; k-Dimensional Euclidean Space......Page 429
A.2.2 C[sup(m)](Ω); m-Times Continuously Differentiable Functions on Ω......Page 432
A.2.3 L[sup(2)](Ω); The Space of Lebesgue Square Integrable Functions......Page 434
A.2.5 H[sup(m)](Ω); Sobolev Space of Order m......Page 437
A.2.6 H[sup(m)][sub(0)](Ω); Sobolev m-Space with Compact Support......Page 438
A.2.7 The Sobolev Imbedding Theorem......Page 439
A.2.9 Product Spaces......Page 440
A.3.1 Mappings in Normed Spaces......Page 441
A.3.2 Variations and Directional Derivatives......Page 442
A.3.3 Fréchet Differential and Derivative......Page 443
A.3.4 Partial Derivatives and the Chain Rule of Differentiation......Page 444
References......Page 446
D......Page 452
E......Page 453
H......Page 454
S......Page 455
Y......Page 457
