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On a saddle-point theorem in minimum compliance design. (English) Zbl 0992.90076

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. [R. Lipton, 81, 549-568 (1994; Zbl 0810.73041)] 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.

MSC:

90C46 Optimality conditions and duality in mathematical programming
49N90 Applications of optimal control and differential games
74P99 Optimization problems in solid mechanics
49N15 Duality theory (optimization)

Citations:

Zbl 0810.73041
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References:

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