Thermoelectromechanically induced stochastic post buckling response of piezoelectric functionally graded beam

This paper deals with the stochastic post buckling response the functionally graded material (FGMs) beam with surface bonded piezoelectric layers subjected to thermoelectromechanical loadings. A C-0 nonlinear finite element method using higher order shear deformation theory with von-Karman nonlinearity is used for basic formulation. The random system parameter such as material properties of FGM and piezoelectric layers and thermoelectromechanical loadings are modeled as uncorrelated random input variables. The first and second order perturbation method and Monte Carlo sampling (MCS) are proposed to examine the mean, coefficient of variation, probability distribution function and probability of failure of critical post buckling load. Typical numerical results are presented for volume fraction indexes, slenderness ratios, boundary conditions, piezoelectric layers and thermoelectromechanical loadings with random system properties. The present outlined approach is validated with the results available in the literature and by employing MCS.