Microstructure/geometric imperfection sensitivity on the thermo-mechanical nonlinear stability behavior of functionally graded plates using four variable refined structural kinematics

Abstract

The present work deals with the nonlinear stability characteristics of geometrically imperfect shear deformable functionally graded plates (FGP) subjected to thermo-mechanical loads. The equilibrium, stability, and compatibility equations are derived using trigonometric shear-strain function based refined shear deformation plate theory. The displacement field used in the present study has been employed for FGP for the first time. The in-plane and transverse displacements consist of bending and shear components, whereas the displacement field contains only four unknowns. Geometric nonlinearity has been incorporated in the formulation in a von-Karman sense. A generalized porosity model has also been developed to accommodate both even and uneven porosity distribution reported in the literature. Various models of geometric imperfection have been modeled using imperfection function. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGPs for various loading conditions have been developed. After ensuring the excellent accuracy of the developed expression, the influence of geometric imperfection, porosity inclusion, and geometric configuration on the nonlinear stability of FGPs has been discussed extensively. The results presented in this paper will be used as a benchmark for future research.