A PEM-based topology optimization for structures subjected to stationary random excitations

This paper focuses on the topological optimization of structures subjected to stationary random excitations. A new topology optimization scheme based on the pseudo excitation method (PEM) for calculating structural random responses in a frequency domain is proposed. In this method, the Sturm sequence is applied to adaptively determine the number of lower-order modes used for mode superposition analysis. The contribution of unknown higher-order modes is approximated by the partial sum of a constructed convergent series. Since the method can offer an approximate expression of structural response solutions, not only it can enhance the flexibility of implementation and also improve the computational effort and accuracy. In addition, derivatives of the objective function are derived by means of the adjoint method. They can be achieved by solving an adjoint problem that is similar to the original governing equation of the system. Two illustrative examples are presented to affirm the proposed scheme in terms of computational accuracy and efficiency.