Optimal design for minimum weight and compliance in plane stress using extremal microstructures. (English) Zbl 0794.73044

Allaire, G.; Kohn, Robert V.

Eur. J. Mech., A 12, No. 6, 839-878 (1993).

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.

MSC:

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

Keywords:

shape optimization; relaxed formulation; topology; optimal microstructures