Elasticity-based analysis of bigraded FGM beams subjected to shear loading

This paper explores the plane stress problem for a cantilever beam under shear loading that causes bending, specifically focusing on functionally graded materials (FGMs). These materials exhibit a gradual change in mechanical properties, promoting enhanced performance over traditional homogeneous materials. The authors introduce a new formulation for the elastic modulus of FGM, incorporating two graduation parameters: one for material composition variation along the beam and another for the longitudinal elastic modulus ratio, which characterizes stiffness variation. The study formulates the static equilibrium equations that relate external forces, stresses, and internal deformations. Analytical expressions derived from these equations predict stress and displacement distributions within the beam, particularly under a tangential load at the free end, which induces shear and bending deformations. The analysis reveals how the gradation parameters influence the beam's structural response, demonstrating the effect of elastic modulus variation on stress distribution and deflection behavior. The study culminates in an analytical framework for assessing FGM cantilever beams under shear loading, enhancing understanding of material gradation impacts on structural behavior and aiding in the design and optimization of advanced engineering structures utilizing FGMs.