Novel finite element modeling for free vibration and buckling analysis of non-uniform thickness 2D-FG sandwich porous plates using refined Quasi 3D theory

Abstract

A novel four-node quadrilateral element with eleven degrees of freedom per node is approximated using the C1 -order non-conforming Hermite and Lagrange functions and the novel refined Quasi-3D plate hypothesis for buckling and free vibration analysis of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) plates resting on variable elastic foundations (VEF) in a hygro-thermal environment. Material and mechanical properties that change in both the length and thickness directions with three different laws of porosity, which are made up of a fully ceramic core layer and two bi-directional functionally graded (2D-FG) material ones, may be used a lot in the aerospace engineering and military industries. In order to analyze the buckling and free oscillation behaviors shown by the plate with arbitrary boundary conditions, a series of mathematical methods created in Matlab’s software are used. The computation program’s correctness is verified by comparing numerical findings to dependable assertions. In addition, a comprehensive analysis of the impact of factors on the buckling and free oscillation responses is conducted. The findings reveal that the novel porosity patterns, the hygro-thermal environment, the elastic medium characteristics, and the boundary conditions have a substantial impact on the mechanical behaviors of the non-uniform thickness 2D-FG sandwich porous plates. The results of this article can be used as a useful reference for engineers when calculating and designing structures of this type in engineering practice.