Topology optimization of linear structural system under stationary stochastic excitation Zhu, Mu; Yang, Yang; Shields, Michael D.; Guest, James K.
Topology optimization as a form-finding methodology for design has developed rapidly in recent years. Its applications can vary from small-scale material microstructures to large-scale building systems. While deterministic optimization of structural systems under static loading is well understood, optimization under dynamic loading is less studied, and the more challenging problem of finding optimal structural systems under stochastic dynamic loading has not yet been addressed. In this work, topology optimization is used to design the lateral load system of structures such that the expected system responses to stationary stochastic excitations are optimized. More specifically, we design the size and location of bracings for multi-story building to minimize the variance of relative deformations under stationary base excitations. To evaluate the variance, we first solve this problem in frequency domain by using the autospectral density function of the relative displacement for the covariant stationary situation. This is compared to analysis in time domain through use of the impulse response function. The resulting stochastic dynamic topology optimization problem is solved using the gradient-based optimizer Method of Moving Asymptotes (MMA), with sensitivities provided via the adjoint method. The popular Solid Isotropic Material with Penalization (SIMP) is used to prevent existence of low-area bracing members and provide clear indications of bracing patterns. Numerical results are presented and comparisons of time and frequency domain methods are given.
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