An elasticity solution for functionally graded beams

An elasticity solution is obtained for a functionally graded beam subjected to transverse loads. The Young's modulus of the beam is assumed to vary ex ponentially through the thickness, and the Poisson ratio is held constant. The exponential variation of the elastic stiffness coefficients allow an ex act solution for the elasticity equations. A simple Euler-Bernoulli type be am theory is also developed on the basis of the assumption that plane secti ons remain plane and normal to the beam axis. The stresses and displacement s are found to depend on a single non-dimensional parameter for a given var iation of Young's modulus in the functionally graded direction. It is found that the beam theory is valid for long, slender beams with slowly varying transverse loading. Stress concentrations occur in short or thick beams. Th e stress concentrations are less than that in homogeneous beams when the so fter side of the functionally graded beam is loaded. The reverse is true wh en the stiffer side is loaded. (C) 2001 Elsevier Science Ltd. All rights re served.