Stochastic nonlinear free vibration analysis of elastically supported functionally graded materials plate with system randomness in thermal environment

► Higher order shear deformation theory with von-Karman nonlinear strain kinematics. ► Direct iterative based stochastic finite element method is used for free vibration. ► Nonlinear fundamental frequency of FGM plates with system randomness are presented. ► Effects of plate geometry, support conditions, foundation parameter are shown. ► Results are validated with independent Monte Carlo simulation. This paper presents the stochastic nonlinear free vibration response of elastically supported functionally graded materials (FGMs) plate resting on two parameter Pasternak foundation having Winkler cubic nonlinearity with random system properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituent’s material, volume fraction index and foundation parameters are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C 0 continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) developed by last two authors for the composite plate is extended for FGM plate to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with those results available in the literature and independent Monte Carlo simulation (MCS).