On the optimal design of elastic shafts

Paz, R.B. Gonzalez de

doi:10.1051/m2an/1989230406151

Cited by 7 publications

(3 citation statements)

References 8 publications

(8 reference statements)

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“…where A 0 is the area of the region bounded by Γ 0 and c is an unknown quantity whose value can be determined using (46). Using a relaxed problem defined on a ball B R as before, the existence of an optimal domain Ω R has been proved in [14]. In [22], Lederman and in [30] R. Tahraoui prove that the domain Ω R is connected and, for a radius R large enough, it solves the original problem.…”

Section: The Exterior Boundary Casementioning

confidence: 99%

On a variational principle for shape optimization and elliptic free boundary problems

Paz

1999

RMTA

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A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality conditions, it is shown that the corresponding sets are domains bounded by free boundaries, so that the equivalence of the solution of the relaxed problem with the solution of several free boundary value problem is proved.

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Section: The Exterior Boundary Casementioning

confidence: 99%

On a variational principle for shape optimization and elliptic free boundary problems

Paz

1999

RMTA

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“…More recently R. B. Gonzales de Paz [8] studied this question using a different approach. However, it seems that some of the results in [8] are not complete. In the present paper we show an existence theorem and we give some qualitative information not contained in [8].…”

Section: Introductionmentioning

confidence: 99%

“…However, it seems that some of the results in [8] are not complete. In the present paper we show an existence theorem and we give some qualitative information not contained in [8]. We suppose that the beam is of a homogeneous and isotropic material.…”

Section: Introductionmentioning

confidence: 99%