In the present paper, thermo‐mechanical stability analysis of geometrically imperfect porous functionally graded plates (FGP) with geometric nonlinearity is presented. The equilibrium, stability, and compatibility equations are derived using Logarithmic structural kinematics in conjunction with the von‐Karman type of geometric nonlinearity. A logarithmic‐based shear‐strain function has been used for the first time for the buckling response of functionally graded material (FGM) plates. Generic imperfection function has been implemented to incorporate the various imperfection modes like sin‐type or global type in the formulation. The effective materials properties of the plates with porosity inclusion have been computed using modified power law. The plate is subjected to uniaxial and biaxial compression as well as combined compression and tension along with thermal loading. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGM plate for each loading case has been developed. After confirming the excellent accuracy of the current exact solutions, the effect of geometric imperfection, porosity inclusion, and geometric configurations on the nonlinear stability of the FGM plate have been discussed extensively. The results presented in this paper will be used as a benchmark for future research.

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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.