A PEM-based topology optimization for structures subjected to stationary random excitations. (15th February 2021) - Zhao, Xuqi; Wu, Baisheng; Lai, Siu-Kai; Li, Zhengguang; Zhong, Huixiang
Highlights: A new PEM-based method is proposed for the topological optimization of structures. The method allows to investigate structures under stationary random excitations. Unknown higher-order modes can be approximated by a constructed convergent series. The sensitivity analysis of the objective function is carried out by a combined method. The proposed scheme enables trade-offs between computational effort and accuracy. Abstract: 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.