Thermal Post-Buckling of Porous Thin Plates Following a Power and Sigmoid Distribution Law Based on an Elastic Foundation

In this study, a new analytical model based on an nth-order shear deformation theory formulation is used to analyse the post buckling of porous FGM plates resting on an elastic Winkler–Pasternak type foundation. The model presented contains a smaller number of variables than other higher-order theories in the literature. In addition, with this model, the effective properties of the structure are calculated as a function of the even and odd distributions of the porosity, and these distributions follow the power and sigmoid laws. The behaviour of the elastic foundation is governed by the constant Winkler parameter, which represents the reaction of the elastic springs, and the Pasternak parameter in the form of a shear layer of the foundation. The non-linear equilibrium equations are based on Von Karman’s theorem, the principle of virtual work and the equilibrium criterion. To solve these equations, approximate solutions and boundary conditions are considered. The accuracy of the nth-order HSDT model used takes into account the uniform, linear and non-linear variation of temperature across the thickness. We obtained several results for the evolution of the critical temperature: as a function of the amplitude/height ratio, as a function of the porosity and as a function of the foundations. The relative error between our results and those in the literature is generally less than 5%.