The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field.
Author(s): J. Haslinger, R. A. E. Mäkinen
Series: Advances in design and control
Publisher: Society for Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics
Year: 2003
Language: English
Pages: 292
City: Philadelphia
Introduction to Shape Optimization......Page 2
Advances in Design and Control......Page 3
ISBN 0-89871-536-9......Page 5
Contents......Page 6
Preface......Page 10
Notation......Page 14
Introduction......Page 18
Part I Mathematical Aspects of Sizing and Shape Optimization......Page 20
1 Why the Mathematical Analysis Is Important......Page 22
2 A Mathematical Introduction to Sizing and Shape Optimization......Page 32
Part II Computational Aspects of Sizing and Shape Optimization......Page 116
3 Sensitivity Analysis......Page 118
4 Numerical Minimization Methods......Page 148
5 On Automatic Differentiation of Computer Programs......Page 172
6 Fictitious Domain Methods in Shape Optimization......Page 188
Part III Applications......Page 218
7 Applications in Elasticity......Page 220
8 Fluid Mechanical and Multidisciplinary Applications......Page 242
Appendix A Weak Formulations and Approximations of Elliptic Equations and Inequalities......Page 264
Appendix B On Parametrizations of Shapes and Mesh Generation......Page 276
Bibliography......Page 282
Index......Page 290
