Elasticity solution for a functionally graded two-layer beam with simple supported edges

An analytical solution for a functionally graded two-layer beam subjected to transverse loading is handled based on the theory of elasticity. The upper and lower layers are fully bonded to each other and simply supported at the edges. Poisson's ratios are taken as constant and Young's moduli are assumed to vary exponentially through the thickness of the layers. Numerical results for the normal stresses and shear stress are given as a solution and the effect of grading on the stress distributions is investigated. In the functionally graded beam solution it is required that one side of the beam is stiffer while the other side is softer when Young's modulus is assumed to vary exponentially through the thickness. The exponential variation of the elasticity modulus may be symmetrical about the mid-plane when the beam is designated as layered.