Multiscale Stochastic Stress Analysis of Unidirectional FRP Considering Random Fiber Location Variation by an Improved Successive Local Approximation

Herein, a multiscale stochastic stress analysis of a unidirectional fiber reinforced composite material considering random fiber location variation in microscale is discussed. Since a microscopic quantity has an influence on the apparent material properties of heterogeneous materials, and a microscopic geometrical feature has a significant influence on microscopic stresses in composites. When microscopic randomness or uncertainty is observed, an apparent material property such as strength will become a random response, and therefore the uncertainty propagation through the different scales should be investigated for more reliable design of composite structures. For this problem, the Monte Carlo simulation-based approach will be effective but expensive because many fibers should be considered for more accurate analysis, and the successive local approximation-based approach has been proposed. However, accuracy of this approach depends on the local surrogate of the stresses for random variables, and an improved approach is proposed herein. In the proposed approach, a numerical condition for constructing a lower order surrogate is adjusted to minimize the estimation error to a reference solution obtained from a higher-order surrogate. Herein, the problem settings and outline of the methods are introduced. Then, numerical results are provided for discussing effectiveness of the proposed approach.