An efficient algorithm to obtain the optimal topology of industrial structural design problems

Abstract

The purpose of the adaptive volume constraint algorithm (AVC) proposed in this paper is to obtain a topology of structure, which is capable of satisfying both stress and displacement constraints. The final topology thus obtained becomes a feasible design in a realistic working environment considering constraints, or alternatively serves as the ideal base design in subsequent shape optimization, seeking precise agreements with all design constraints. The AVC algorithm is developed from the material distribution method or the homogenization method, in which the compliance of the structure is minimized with a fixed volume constraint (FVC). The traditional material distribution method considers neither stress nor displacement conditions. The AVC algorithm can iteratively adjust its upper volume limit by comparing the difference of the maximum stress or displacement with the pre‐specified stress/displacement constraints. The final topology becomes an optimum topology satisfying stress/displacement constraints. In this paper, the AVC algorithm is successfully applied to two industrial design problems simultaneously with stress and displacement constraints, including a bicycle frame and a machine tool frame.