Free vibration and bending analysis of porous bi-directional FGM sandwich shell using a TSDT p-version finite element method

Abstract

Compared to the first-order shear deformation theory and other classical shell theories, the higher-order shear theory is deemed more accurate due to its superior ability to capture transverse shear effects, especially vital for precision in modeling thicker, doubly curved shell panels. Additionally, the third-order shear deformation theory (TSDT) is acknowledged for its computational efficiency compared to the 3D solution striking a balance between result precision and computational efficiency. This paper explores the static bending and free vibration analysis of a porous bi-directional functionally graded doubly curved sandwich shell. For the first time, a combination of TSDT theory with the p-version finite element method is applied, demonstrated for the analysis of bi-directional functionally graded doubly curved sandwich shell. In the initial phase, the mathematical formulation has been meticulously derived. Four models of sandwich FGM distributions, taking into account the porosity effect and comprising a blend of two ceramic materials and a metallic material, have been thoroughly explored. Subsequently, the study evaluates the effectiveness and accuracy of the formulation implemented in FORTRAN CODE through benchmark results, showcasing its adaptability for different shell panel geometries by adjusting the values of the radius of curvature. The latter part of the research delves into new findings related to bi-directional functionally graded porous sandwich FGM shell panels, investigating the effects of gradient indexes and porosity distribution on their behavior.