Efficient uncertainty propagation for stochastic multiscale linear elasticity

This article develops an efficient uncertainty propagation framework for stochastic multiscale linear elasticity. Stochastic microscale problems are solved on the RVE with random material properties and random geometries. A stochastic homogenization approach is then used to calculate equivalent macroscale random material properties. According to different spatial correlations at the macroscale, random variables, random fields and high-dimensional random inputs are generated to model macroscale randomness. Stochastic finite element equations at both micro and macro scales are solved by using a unified and efficient numerical algorithm, which relies on a unified stochastic solution construction and an efficient iterative algorithm. It is efficient and accurate even for very high-dimensional problems due to its insensitivity to stochastic dimensions. Numerical results demonstrate the promising performance of the proposed framework, especially its high efficiency without loss of accuracy.