Static analysis of an exponentially varying functionally graded beam using trigonometric shear deformation theory

Abstract

The present study investigates the bending behavior of a functionally graded beam under transverse loads (sinusoidal and uniform) using trigonometric shear deformation theory (TSDT). Boundary value problem are derive using principle of virtual work. The Navier-type closed-form solution is obtained under simply supported boundary conditions. The material properties across the thickness directions vary according to the exponential law of distribution. The present theory does not need a problem-dependent shear correction factor since it accurately accounts for the distribution of transverse shear stress across the beam thickness. Results from higher-order shear and normal deformation theory (HOSNT), exact elasticity theory, and other theories are compared with the current approach to ensure its accuracy and efficacy. The results of present theory is in excellent agreement with the exact elasticity theory.