Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method

Abstract

The purpose of this study is to investigate the buckling characteristics of a sandwich beam consisting of a porous ceramic core (Alumina), two bottom and upper layers which are gradually changed from ceramic (Alumina) to metal (Aluminum) through the thickness direction. A core with three kinds of porosity patterns is considered. Shear deformation effects are taken into account based on third-order shear deformation theory (TSDT) and a two-variable refined shear deformation theory. Based on the physical neutral axis of the beam, the governing equilibrium equations for buckling are obtained using the principle of virtual work and are solved for different end conditions using the differential transform method (DTM). A parametric study on buckling behavior is conducted to focus on the influences of length-to-thickness ratio, volume fraction of FGM in two FG layers, and three porosity patterns, namely, uniform, asymmetric and symmetric distribution of porosity in a ceramic core for clamped-clamped, pinned-pinned and cantilever beams. The convergence and comparison studies are carried out. It is demonstrated that the critical buckling load for an FG three-layer-beam, with an asymmetric pattern in a porous ceramic core, is higher than the two other ones. In addition, as demonstrated, DTM is an efficient and reliable method to be employed in this area of solid mechanics.