Evolutionary topology optimization of structures with multiple displacement and frequency constraints

Topological design with multiple constraints is of great importance in practical engineering design problems. The present work extends the bi-directional evolutionary structural optimization (BESO) method to multiple constraints of displacement and frequency in addition to the amount of material usage. Besides the binary design variables, the Lagrange multipliers for constraints are considered as additional continuous variables and determined by a search scheme. The enhanced approach can include a number of constraints besides the simple volume constraint. To demonstrate the effectiveness of the proposed BESO approach, several examples are presented for the maximization of structural overall stiffness subject to the material volume, displacement and frequency constraints