## Finite Element Approximation for Optimal Shape Design: Theory and ApplicationsExplains how to speed the optimal shape design process using a computer. Outlines the problems inherent in optimal shape design and discusses methods of their solution. Concentrates on finite element approximation and describes numerical realization of optimization techniques. Treats optimal design problems via the optimal control theory when the state systems are governed by variational inequalities. Provides useful background information, followed by numerous approaches to optimal shape design, all supported by illustrative examples. Appendices provide algorithms and numerous examples and their calculations are included. |

### From inside the book

Results 1-3 of 96

Page v

In spite of graphical work stations and modern software for structural analysis ,

finding the best shape for a structure is still a very tedious and time - consuming

task . The goal in

to ...

In spite of graphical work stations and modern software for structural analysis ,

finding the best shape for a structure is still a very tedious and time - consuming

task . The goal in

**optimal shape design**( structural optimization , or redesign ) isto ...

Page 261

Mathematical theory on

optimal control which is based on the calculus of variations . The techniques of

the optimal control of distributed systems have been applied since the beginning

...

Mathematical theory on

**optimal shape design**Shape optimization is a branch ofoptimal control which is based on the calculus of variations . The techniques of

the optimal control of distributed systems have been applied since the beginning

...

Page

The authors explain the mathematical basis of

examples of the calculations involved . In the first chapters they outline the

problems inherent in

problems ...

The authors explain the mathematical basis of

**optimal shape design**, and giveexamples of the calculations involved . In the first chapters they outline the

problems inherent in

**optimal shape design**and the ways in which theseproblems ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminaries | 1 |

Abstract setting of optimal shape design problem and | 28 |

Optimal shape design of systems governed by a unilateral | 53 |

Copyright | |

14 other sections not shown

### Other editions - View all

### Common terms and phrases

algorithm Appendix applied approach approximation associated assume body boundary bounded called Chapter closed compute Consequently consider constant constraints contains continuous convergence convex corresponding cost functional defined definition denote depend differentiable direction discrete displacement domain elasticity element equivalent Example exists field Figure Finally Find fixed follows force formula function give given hand Haslinger holds initial iterations Lemma linear mapping material derivative matrix means method minimize Moreover moving multipliers Neittaanmäki nodes nonlinear numerical Numerical results obtain optimal shape design parameters positive present programming Proof prove reads refer relation Remark respect results for Example satisfying sequence shape design problems smooth solution solving space Step stress structural subgradient subset sufficiently suppose Table term Theorem triangulation unilateral unique vector write Zolesio