A cutting plane approach to maximization of fundamental frequency in truss topology optimization

Abstract

This work introduces a cutting plane algorithm to solve the maximization of the minimum frequency of truss structures subject to volume and compliance constraints. Multiple load cases and multiple scenarios of non-structural mass distributions are considered. This problem is formulated as a nonconvex semi-definite programming problem with Bi-linear Matrix Inequality (BMI) constraints. The proposed algorithm consists of iteratively tightening a linear relaxation of that problem. A new family of linear constraints (cutting planes) is defined as a linearization of BMI constraints. It is proved that the algorithm can find a violated valid cut for any infeasible solution that could be found in any iteration. Implementation details of the algorithm are given. We show the robustness of the method with some numerical examples and compare its performance with other available solvers. The reported results indicate that the new method outperforms the previous ones when the number of load cases and non-structural masses scenarios is big.