A New Approach for Stochastic Analysis of Cyclically Symmetric Structures

One of the most important numerical methods for uncertainty quantification in computational mechanics, is stochastic finite element method (StFEM) which consists of severely large matrices with respect to the relevant deterministic counterparts. Thus, it is necessary to minimize the computational efforts of StFEM. In this paper, an efficient StFEM is developed for analysis of cyclically symmetric structures, in which a preconditioner is applied to decompose the matrices to Kronecker products of sub-matrices, and then some algebraic decompositions are utilized to solve the governing linear equation of equilibrium without inversing the final matrix, whereas only a small matrix is inversed instead. The present method provides significant improvement in the stochastic structural analysis.