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

•A novel generalized probabilistic edge-based smoothed finite element method (GP_ES-FEM) is proposed.•The edge-based smoothing technique is applied for stochastic analysis of Reissner–Mindlin plate.•The approach improves the numerical accuracy of deterministic output quantities.•It overcomes the drawbacks of conventional 2nd order perturbation approach with small perturbations.•Numerical examples verified the advantages of higher order perturbations for large input variability. 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.