Two-dimensional thermoelasticity solution for functionally graded thick beams

Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.