On the buckling analysis of functionally graded sandwich beams using a unified beam theory

In this paper, a unified beam theory is developed and applied to study the buckling response of two types of functionally graded sandwich beams. In the first type (Type A), the sandwich beam has a hardcore whereas in the second type (Type B), the sandwich beam has a softcore. In both the type of beams, face sheets are made up of functionally graded material. The material properties of face sheets are varied through the thickness according to the power-law distribution. A unified beam theory developed in the present study uses polynomial and non-polynomial type shape functions in-terms of thickness coordinate to account for the effect of shear deformation. The present theory is built upon classical beam theory and shows a realistic variation of transverse shear stresses through the thickness of the beam. The governing equations are deduced based on the principle of virtual work. Analytical solutions for simply supported sandwich beams subjected to axial force are presented. The critical buckling load factors of two types of FG sandwich beams are investigated. The numerical results are obtained for various power law coefficients and face-core-face thickness ratios. The validity of the present theory is proved by comparing the present results with various available solutions in the literature.