Introduction to shape optimization. Theory, approximation, and computation.

*(English)*Zbl 1020.74001
Advances in Design and Control. 7. Philadelphia, PA: SIAM Society for Industrial and Applied Mathematics. xi, 273 p. (2003).

The book consists of three parts. Part 1 presents an elementary mathematical introduction to size and shape optimization. Topics such as the existence of solutions, appropriate discretization of problems, and convergence properties of discrete models are studied. Results are presented in abstract, unified way allowing their application not only in problems of solid mechanics, but also in other areas of mathematical physics. Part 2 deals with modern computational aspects in shape optimization. The results on sensitivity analysis and on gradient, evolutionary, and stochastic-type minimization methods, including methods of multiobjective optimization, can be found. All these methods are then used in part 3, where nontrivial applications in various areas of industry, such as contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape as optimization of a dividing tube, are presented.

The book is accessible to the novice and expert, and thus can be used by students, engineers and scientists working in aerospace, automotive, and mechanical and civil engineering.

The book is accessible to the novice and expert, and thus can be used by students, engineers and scientists working in aerospace, automotive, and mechanical and civil engineering.

Reviewer: Stefan Jendo (Warszawa)

##### MSC:

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |

74Pxx | Optimization problems in solid mechanics |

65K10 | Numerical optimization and variational techniques |