Topological optimization design of structures under random excitations using SQP method

More and more stringent structural performance requirements are imposed in advanced engineering application, only a limited number of works have been devoted to the topology optimization of the structures with random vibration response requirements. In this study, the topology optimization problem with the objective function being the structural weight and the constraint functions being structural random vibration responses is investigated. An approximate topological optimization model for suppressing ‘localized modes’ of vibrating Cauchy solids is established in this paper. Based on moving asymptotes approximate functions, approximated–approximations expressions of the dynamic responses are constructed. In order to control the change quantity of topologic design variables, new dynamic response constraint limits are formed and introduced into the optimization model at the beginning of each sub-loop iteration. Then, an optimization sequential quadratic programming is introduced, and a set of iteration formulas for Lagrange multipliers is developed. Two examples are provided to demonstrate that the proposed method is feasible and effective for obtaining optimal topology.