Numerical assessment of bending and buckling analysis of sigmoid functionally graded (S-FGM) porous plates in framework of secant hyperbolic shear deformation theory: A finite element study

This study aims to investigate the static deformation characteristics and buckling response of functionally graded (FG) porous plates for various combinations of boundary conditions in the framework of finite element (FE) formulation. The variation of properties in FG material is supposed to be along the thickness direction according to the power-law (P-FGM) and sigmoid-law (S-FGM). The porosity occurs in material during manufacturing process of sintering. Therefore, it is important to study the porosity effect in modeling the FG plates. A novel higher-order shear deformation theory which involves secant hyperbolic based strain function is utilized to approximate the displacement field of FG plate. The theory considers the nonlinear variation of transverse shear strains to satisfy the zero stress boundary conditions on the upper and lower surfaces of the plate. A suitable C0 continuous isoparametric eight noded FE with 7 degrees of freedom (DOF) per node combined with biquadratic serendipity shape functions is employed to examine the desired mechanical responses of FG plates. The numerical assessments of bending deflections and buckling loads for P-FGM and S-FGM porous plate are presented. Moreover, the influences of parameters like porosity, span-thickness ratio, boundary conditions, material exponent, etc., on the dimensionless deflection, and buckling load are discussed in detail. To demonstrate the accuracy of proposed theory, the comparison study is made between present and previously published results in literature and well agreement is achieved. Additionally, several numerical illustrations with new generated results are provided to serve as benchmarks for further study of porous FG plates.