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Optimal design for minimum weight and compliance in plane stress using extremal microstructures. (English) Zbl 0794.73044
We study the shape optimization of a two-dimensional elastic body loaded in plane stress. The design criteria are compliance and weight. A relaxed formulation is used, whereby perforated composite materials are admitted as structural components. This approach has the advantage of placing no implicit restriction on the topology of the design. We emphasize the use of optimal microstructures, and we use a formulation based on stresses. While our numerical work is two-dimensional, the method could in principle also be applied to three-dimensional structures.

74P99 Optimization problems in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids