OPTIMAL-DESIGN FOR MINIMUM WEIGHT AND COMPLIANCE IN PLANE-STRESS USING EXTREMAL MICROSTRUCTURES

We study the shape optimization of a two-dimensional elastic body load ed in plane stress. The design criteria are compliance and weight. A r elaxed 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. A simi lar method has recently been explored by Bendsoe, Kikuchi, and Suzuki, with the goal of ''topology optimization''. Our work differs from the irs in two important respects: we emphasize the use of optimal microst ructures, and we use a formulation based on stresses. While our numeri cal work is two dimensional, the method could in principle also be app lied to three dimensional structures.