A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner-Mindlin plates

Probabilistic analysis is becoming more important in mechanical science and real-world engineering applications. In this work, a novel generalized stochastic edge-based smoothed finite element method is proposed for Reissner-Mindlin plate problems. The edge-based smoothing technique is applied in the standard FEM to soften the over-stiff behavior of Reissner-Mindlin plate system, aiming to improve the accuracy of predictions for deterministic response. Then, the generalized nth order stochastic perturbation technique is incorporated with the edge-based S-FEM to formulate a generalized probabilistic ES-FEM framework (GP_ES-FEM). Based upon a general order Taylor expansion with random variables of input, it is able to determine higher order probabilistic moments and characteristics of the response of Reissner-Mindlin plates. The significant feature of the proposed approach is that it not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also overcomes the inherent drawbacks of conventional second-order perturbation approach, which is satisfactory only for small coefficients of variation of the stochastic input field. Two numerical examples for static analysis of Reissner-Mindlin plates are presented and verified by Monte Carlo simulations to demonstrate the effectiveness of the present method.