Static and vibration analyses of functionally graded porous shell structures by using an averaged edge/node-based smoothed MITC3 element

Abstract

In this paper, a combined scheme of edge/node-based smoothed finite element method (ENS-FEM) and the mixed interpolation of the tensorial components for the three-node triangular element (MITC3) named aENS-MITC3 is developed to investigate the static and free vibration for functionally graded (FG) porous shells. The effective material properties of FG porous shells are estimated using the rule of mixture, which incorporates an additional term for porosity in the through-thickness direction. The improved first-order shear deformation theory (FSDT) is used to accurately describe the shear stress distributing evenly throughout the thickness and is zero on the top and bottom surfaces of the doubly curved shell. Using Hamilton's principle, the governing equation of FG porous shells is established. The obtained numerical results of aENS-MITC3 are compared with other existing methods in the literature to show the effectiveness of the present method. Then, the effect of geometric parameters, porosity coefficients and power law indexes on the displacements and natural frequencies of FG porous curved shells are examined.