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Optimal design in elasticity and plasticity. (English) Zbl 0593.73091
Summary: A direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non-convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ”relaxed problems” with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.

MSC:
74P99 Optimization problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
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