Robust structural optimization subjected to stochastic excitation using operation norm theory

Due to the uncertain nature of dynamic environment in which real structure operates, it has been well recognized that structural optimization should take the effects of stochastic loads into consideration to obtain a more efficient and safe structure design. To this end, in the present study a robust structural optimization method is proposed for linear structural system subjected to stationary stochastic excitation. The propagation of input uncertainties to dynamic response of interest is achieved using operator norm theory, such that the worst-case dynamic structural response under stochastic excitation can be effectively derived. Perturbation method and interval analysis are used to model the epistemic uncertainty on structural side, and the corresponding sensitivity of eigenvalues and eigenvectors with respect to design variables are also conducted for gradient-based optimization algorithm. The effectiveness of the proposed method is verified by using a two-dimensional frame structure, and the result shows that a reasonable robust structural design can be efficiently obtained against both stochastic excitation and structural uncertainty.