Large Deflections of Functionally Graded Nonlinearly Elastic Cantilever Beams

Uses of functionally graded materials (FGMs) are 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 a number of laminae on both vertical and horizontal deflection of the beam in the finite element analysis (FEA) is unknown. Here, we examined the large deflections of a cantilever beam that was subjected to 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 nonlinearity from modified Ludwick’s law are combined in the analysis using Marlow’s material model. Our results show that the gradient function and the number of laminae have significant effects on normal stress distribution along the horizontal axis and both vertical and horizontal deflection of the beam.