## 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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Page vii

In Chapter 7 we

dimensional elastic body unilaterally supported by a rigid foundation . The

problem is to redesign the contact surface in such a way that the total potential

energy ...

In Chapter 7 we

**consider**the shape optimization of the contact surface of a two -dimensional elastic body unilaterally supported by a rigid foundation . The

problem is to redesign the contact surface in such a way that the total potential

energy ...

Page 51

... problem formulation , the initial separation design function a is restricted to be

small and smooth . As a consequence of the restriction to small separations one

may

... problem formulation , the initial separation design function a is restricted to be

small and smooth . As a consequence of the restriction to small separations one

may

**consider**the stiffness of the bodies to be unchanged by the design process .Page 198

Now we shall present another kind of a state problem , namely the so - called free

boundary value problem with constraints given in the interior of N . We

the problem of controlling the shape of a coincidence set in connection with an ...

Now we shall present another kind of a state problem , namely the so - called free

boundary value problem with constraints given in the interior of N . We

**consider**the problem of controlling the shape of a coincidence set in connection with an ...

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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 |

Copyright | |

9 other sections not shown

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### Common terms and phrases

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