Large Deflections of Functionally Graded Non-Linearly Elastic Cantilever Beams

Abstract

Uses of functionally graded materials (FGMs) is increasing owing to recent development in manufacturing technologies. Large deflection of beams that made of nonlinearly elastic, Ludwick's type of material and also FGMs has received considerable critical attention during recent years. However, the precise effect of number of laminae on both vertical and horizontal deflection of the beam in the finite element analysis (FEA) are unknown. Here, we examined the large deflections of a cantilever beam that subjected various loading conditions and made of nonlinearly elastic, modified Ludwick's type of material using FEA. The direction dependent material properties in the functionally graded material and non-linearity from modified Ludwick law are combined in the analysis by using Marlow's material model. Our results show that gradient function and number of laminae have significant effect on stress distribution through the thickness and the both vertical and horizontal deflection of the beam.