Topology optimization for linear stationary stochastic dynamics: Applications to frame structures

This work develops some foundations of topology optimization for the robust design of structural systems subjected to general stationary stochastic dynamic loads. Three methods are explored to evaluate the dynamic response - the time domain, frequency domain, and state space methods - and the associated design variable sensitivities are derived analytically. The resulting stochastic dynamic topology optimization problem is solved using the gradient-based optimizer Method of Moving Asymptotes (MMA). Sensitivities are computed using the adjoint method and the popular Solid Isotropic Material with Penalization (SIMP) is used to achieve clear existence of structural members. The approach is used to design the lateral load systems of structures that minimize the variance of the system response to stationary stochastic ground motion excitation. Numerical results are presented to illustrate the differences between topologies optimized for stochastic ground motion and topologies optimized for equivalent static loading.