FEM model for stochastic mechanical and thermal postbuckling response of functionally graded material plates applied to panels with circular and square holes having material randomness

In this study, the second order statistics of postbuckling analysis of functionally graded materials (FGMs) plates subjected to mechanical and thermal loadings without and with square and circular holes at center having random material properties is presented. Material properties of each constituent's materials, volume fraction index, thermal expansion coefficients and thermal conductivities are modeled as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) using modified C0 continuity. A nonlinear finite element method (FEM) based on direct iterative technique combined with mean centered first order perturbation technique (FOPT) developed by the author for composite plate is extended for FGM plates to solve the random nonlinear eigenvalue problem. Typical numerical results are presented to examine the effect of volume fractions index, plate length to thickness ratios, plate aspect ratios, types of loadings, amplitude ratios, support conditions and various shaped and sized holes with random thermomechanical properties. The results obtained by the present solution approach are validated with those available in the literatures and independent Monte Carlo Simulation (MCS). It is observed that the plates with circular and square hole have a significant influence on the postbuckling response under mechanical and thermal loading conditions and some new results are presented to demonstrate the applications of present work.

► Higher order shear deformation theory with von-Karman nonlinear strain kinematics is used for basic formulation. ► Direct iterative based stochastic C0 nonlinear finite element method in conjunction with FOPT is used for random eigenvalue problem. ► Postbuckling load and temperature of FGM plates without and with circular and square holes are presented. ► Effects of plate geometry, support conditions, types of loading, hole size and shapes, volume fraction index with random material properties are examined. ► Results are presented in the form of tables which can suit as benchmark for future work.