Large deflection response of functionally graded porous structures considering geometrical nonlinearity using an improved FSDT

Abstract

This study’s objective is to propose a full 3D finite element modeling for examining the geometrically nonlinear (NL) response of functionally graded (FG) porous materials with plates, ring, and cylindrical shapes. An improved first-order shear deformation theory (IFSDT) is utilized in order to develop the 3D solid-shell element. The governing equations are developed in a way that offers a parabolic distribution of the transverse shear strains through the FG porous shell thickness and a zero condition of the transverse shear stresses on the top and bottom surfaces. The given IFSDT solid-shell element has the ability to model any kind of shell structures and incorporates a 3D material law. In this study, two types of porosity distribution functions are considered. The effectiveness of the present IFSDT solid-shell element is demonstrated through linear (L) and NL numerical examples. The effect of the porosity distribution, porosity coefficient, power-law index, geometrical design parameters, and boundary conditions on the geometrically NL response of FG porous shells structures is evaluated.