Stress-constrained topology optimization using the constrained natural element method

Abstract

This paper presents a topology optimization framework to achieve volume minimization with Crossland fatigue constraints under proportional loading using the Constrained Natural Element Method. The local minimization problem is solved by means of the augmented Lagrangian method to deal with a large number of evaluation points. To suppress the numerical instabilities, a neighbor-based filter is proposed and compared to the widely used density filter. Furthermore, to circumvent the problem of stress singularity, several different relaxations of the constraints are also investigated. Compared with the topology optimization procedure based on the finite element method, the proposed method has the advantage of showing greater flexibility and convenience in discretization of complex design domains and the ability to maintain stable output under various discretization conditions.