An enhanced aggregation method for topology optimization with local stress constraints

By introducing a new reduction parameter into the Kreisselmeier–Steihauser (K–S) function, this paper presents a general K–S formulation providing an approximation to the feasible region restricted by active constraints. The approximation is highly accurate even when the aggregation parameter takes a relatively small value. Numerical difficulties, such as high nonlinearity and serious violation of local constraints that may be exhibited by the original K–S function, are thus effectively alleviated. In the considered topology optimization problem, the material volume is to be minimized under local von Mises stress constraints imposed on all the finite elements. An enhanced aggregation algorithm based on the general K–S function, in conjunction with a “removal and re-generation” strategy for selecting the active constraints, is then proposed to treat the stress constraints of the optimization problem. Numerical examples are given to demonstrate the validity of the present algorithm. It is shown that the proposed method can achieve reasonable solutions with a high computational efficiency in handling large-scale stress constrained topology optimization problems.