Static behavior of elastically supported transversely inhomogeneous porous functionally graded plate with different thickness variations under a variety of external loadings

Abstract

The static behavior of a porous functionally graded material plate (FGMP) with variable thickness placed on two parametric elastic foundations exposed to various boundary conditions is investigated in this study. Thickness variation in the plate is assumed to vary in uni-direction/bi-direction with linear and parabolic variations. The properties of the constituent of FGMs are expected to change in the direction of thickness following the power law. The plate is subjected to three types of external loadings: uniformly distributed load (UDL), linearly increasing load (LIL), and linearly increasing decreasing load (LIDL). To explore the static behavior, numerical parameters (NP) linked with the bending and normal stresses of the plate have been determined. Classical plate theory is used to derive the governing equation using the energy principle. The transverse displacement functions are indigenously developed in the form of simple algebraic polynomials (using Pascal’s triangle) to handle any set of mixed- boundary conditions. The Rayleigh–Ritz method along with the algebraic polynomial is employed in the numerical simulation for getting NP. This method is straightforward, precise, and computationally efficient as it can handle any set of boundary conditions and the solution converges with very few iterations. Following the convergence and validation analyses, new findings are presented. The influence of aspect ratios, power-law exponents, porosity volume fraction, taper ratios, and the Winkler and Pasternak modulus on the NP of the plate has been thoroughly examined. The effect of various types of external loading and boundary conditions on deformed shapes and co-ordinate of maximum deflection of elastically supported porous FGMP with different thickness variations have also been reported. One of the important findings is that the effect of homogeneous porosity distribution on NP is more pronounced than in situations with non-homogeneous distributions. Also, the change in thickness of the plate and the distribution of various types of porosity has a substantial effect on the deformed shape of the plate. One of the interesting observations of this study is that the deformation in the plate is more significant in the case of bi-linear thickness variation compared to the uni-linear case. The results reported in this article are accurate enough to consider for further research and experimentation.