NON-LINEAR BENDING RESPONSE OF FUNCTIONALLY GRADED BEAMS UNDER TRANSVERSE LOADS

In this study, an analytical method is developed to analyze analytically displacements and stresses in a functionally graded composite beam subjected to transverse load. Assuming the functionally graded beam has nonhomogeneous mechanical properties in the thickness direction, the displacements and stresses of a beam are obtained based on a first-order shear deformation beam theory (FSDBT). The non-linear strain-displacement relations in the von Kármán sense are used to study the effect of geometric non-linearity. Equilibrium equations are obtained by using principle of minimum total potential energy and solved exactly. The results obtained from this method are compared with the finite element solution done by ANSYS. Numerical results of the linear and non-linear first-order theory are presented to show the effects of using FGMs instead of classical layered composites on the deflections and stresses.