Bi-directional Evolutionary Structural Optimization of Continuum Structures with Multiple Constraints

Abstract

Most of the structural topology optimization problems involved in practical engineering applications are problems with many constraints. Thus, this paper presented an improved bi-directional evolutionary structural optimization (BESO) method for problems with many constraints. Slack variables were introduced to transform the inequality constraints into equality constraints. Then the Lagrange multiplier method converted the multi-constrained optimization problem to an unconstrained optimization problem and an advanced multiplier calculation was proposed. Elemental sensitivity numbers were derived according to the obtained multipliers. The design variables were updated by the BESO method. One numerical example that aimed to minimizing the structural mean compliance and involved volume, fundamental frequency and displacement constraints was used to validate the proposed method. The new method extends the BESO method to topology optimization that has a number of constraints, such as volume, displacement and frequency constraints.