On a Saddle-Point Theorem in Minimum Compliance Design

This note deals with the displacement-based relaxed formulation of the minimum compliance layout problem of the optimal distribution of two isotropic materials within a given three-dimensional domain. In 1994, Lipton (Ref. 1) proved that minimization over elasticity tensors can be interchanged with...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2000-08, Vol.106 (2), p.441-450
Main Authors: Telega, J J, Lewinski, T
Format: Article
Language:English
Subjects:
Compliance
Lagrange multiplier
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Summary:This note deals with the displacement-based relaxed formulation of the minimum compliance layout problem of the optimal distribution of two isotropic materials within a given three-dimensional domain. In 1994, Lipton (Ref. 1) proved that minimization over elasticity tensors can be interchanged with maximization over displacements. This proof was based on the theory of Young measures. The aim of this contribution is to provide a new and straightforward proof of the Lipton saddle-point theorem by using a duality technique, thus bypassing the Young measure theory.
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1004667901231