## Finite element approximation for optimal shape design: theory and applications |

### From inside the book

Results 1-3 of 3

Page 35

We shall begin with a standard example also presented in Haug, Choi and

Komkov (1981), Hou (1982). Example 2.1. Maximization of the torsional rigidity of

an elastic shaft. Consider the torsion of the elastic shaft

We shall begin with a standard example also presented in Haug, Choi and

Komkov (1981), Hou (1982). Example 2.1. Maximization of the torsional rigidity of

an elastic shaft. Consider the torsion of the elastic shaft

**shown in Figure**2.2.Page 42

Let in

constant. Moreover, Qp denotes the ferrous, Qc the copper and £Ia the air

material. In

the ...

Let in

**Figure**2.11 D be the polar region where the magnetic field is desired to beconstant. Moreover, Qp denotes the ferrous, Qc the copper and £Ia the air

material. In

**Figure**2.11 half of the original magnet is**shown**after a cut throughthe ...

Page 240

... violate the state constraint. After 18 SQP-iterations the initial weight 1.00 was

reduced to 0.514. The optimal shape is

Numerical results for Example 10.2; n(h) = 31, a = 0.1, P = 1.0, 7 = 2.0, r = 0.01, e

= 10"4.

... violate the state constraint. After 18 SQP-iterations the initial weight 1.00 was

reduced to 0.514. The optimal shape is

**shown in Figure**10.5. Figure 10.5.Numerical results for Example 10.2; n(h) = 31, a = 0.1, P = 1.0, 7 = 2.0, r = 0.01, e

= 10"4.

### 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 | |

10 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint algorithm Appendix applied approximation boundary conditions boundary value problem Chapter constraints contact problems convergence convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic exist a subsequence fi(a Figure finite element fixed follows formula ft(a G K(a G R2 G U&d G V(a given gradient Green's formula Haslinger Haug Hilbert space Hlavacek initial iterations Komkov Lagrange multipliers least one solution Lemma liminf limsup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative method minimize Moreover Necas Neittaanmaki nodal nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal pair optimal shape design parameter Pironneau Proof prove respect results for Example satisfying sequence sequential quadratic programming shape design problems shape optimization Sokolowski solves P(a stresses subgradient sufficiently small Tc(a Theorem triangulation variational inequality vector Zolesio