Shear Correction Factor Effects on Functionally Graded Materials (FGMs) Beams using Discrete Shear Gap (DSG) Element

Abstract

Materials and computational methods are essential to support the development of infrastructure. Composite material has been used in many applications; in the laminated composite, failure due to excessive interlaminar stresses between two materials causes delamination. Thus, functionally graded materials (FGMs) have emerged. A numerical computation such as the finite element method (FEM) is widely used to support the analysis of FGMs in structural applications. The discrete shear gap DSG element is developed using Timoshenko beam theory, where the shear correction factor is used in their formulation. The shear correction factor is assumed to be constant in many applications; thus, it is valid for isotropic homogenous material. However, the effect of shear deformation significantly impacts the results of the FGMs beam, so the shear correction factor cannot be considered constant. Therefore, this paper presents the shear correction factor effect on static analysis of FGMs beam using DSG element. Various boundary conditions with length thickness ratio (L/h = 4) are evaluated. The DSG element yields good results in FGMs beam for different power-law index ratios. Furthermore, the DSG element result shows that the higher the modulus of elasticity ratio of the top-to-bottom material, the further the difference between k FGMs and k = 5/6 (constant). The DSG element can provide precise results without shear locking.