Numerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams

Abstract

Abstract—In this paper, thermo-mechanical stress distribution has been determined for a three layered composite beam having a middle layer of functionally graded material (FGM), by analytical and numerical methods. Beam is subjected to uniformly transverse distributed loading whereas the uniform temperature gradient arises in it. FGM beams with continuous and smooth grading of metal and ceramics based on power law index are considered for study, whereas Poisson ratio is to be held constant through FGM layer. Analytical solution is based on simple Euler-Bernoulli type beam theory for long, slender beam. Also, the principle of stationary potential function is used to obtain the static finite element equations for the FGM composite beam. By comparing the deduced results with FEM calculations in ANSYS, good agreement has been indicated between them. Index Terms — composite beam, Euler-Bernoulli beam theory, functionally graded material, neutral axis, thermo-mechanical stress. I.