An adaptive method for topology optimization subjected to stationary stochastic forced excitations

Topology optimization subjected to stochastic excitations is usually computationally expensive. This work addresses this challenge by first transforming stochastic response and sensitivity analysis problems at each iteration into a series of frequency response analysis problems, and then an adaptive hybrid expansion method is employed to compute the displacement and adjoint vectors. The proposed method has two features: (1) the derivatives of the eigenpairs are not involved when computing the sensitivities of the responses, thus no special treatment is needed when repeated eigenfrequencies are present; (2) the numbers of lower-order eigenvectors and basis vectors that need to be computed can be determined adaptively according to the given accuracy. The accuracy and efficiency of the proposed method as well as the effect of the excitation frequency on the optimum designs are demonstrated by three numerical examples.