Thermal Stresses in Functionally Graded Beams

Abstract

Thermoelastic equilibrium equations for a functionally graded beam are solved in closed-form to obtain the axial stress distribution. The thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness. The Poisson ratio was held constant. The exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations. A simple Euler ‐ Bernoulli-type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis. The stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution. When both elastic constants and temperature increasethrough the thickness in the samedirection, they causea signie cant raise in thermal stresses. For the case of nearly uniform temperature along the length of the beam, beam theory is adequate in predicting thermal residual stresses.