2D stress analysis of functionally graded beam under static loading condition

Abstract

Two dimensional (2D) stress analysis is performed in this paper for functionally graded (FG) beam under the plane stress condition of elasticity by using semi analytical approach developed by Kant et al. [6]. Modulus of elasticity is assumed to be varied exponentially through the thickness of beam. The mathematical model consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) in the beam thickness direction. Elasticity solutions presented by Sankar [9] is used to show the accuracy, simplicity and effectiveness of present semi analytical solution. It is observed from the numerical investigation that the present mixed semi analytical model predicts structural response as good as the one given by the elasticity solution, which in turn proves the robustness of the presented formulation.