## 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. |

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### Contents

Preliminaries | 1 |

Abstract setting of optimal shape design problem and | 28 |

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

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algorithm Appendix applied approach approximation associated assume assumptions Banach space body boundary bounded called Chapter closed compute Consequently consider constant constraints contains continuous convex corresponding cost functional defined definition denote depend derivative differentiable direction discrete displacement domain elastic element equivalent Example exist a subsequence exists field Figure Finally Find fixed follows formula function give given hand holds initial ITERATION Lemma linear mapping material matrix means method minimize Moreover moving nodes nonlinear numerical Numerical results obtain optimal shape design parameter positive presented programming Proof prove reads refer relation Remark respect results for Example satisfying sensitivity analysis sequence shape design problems solution solves space Step stress structural sufficiently suppose Table term Theorem triangulation unique vector write