Thermo-elastic Stresses in Composite Beams with Functionally Graded Layer

Abstract

Analytical expressions have been derived for the thermo-elastic stresses in a three-layered composite beam system whose middle layer is a functionally graded material (FGM). Continuous gradation of the volume fraction in the FGM layer is modeled in the form of an mth power polynomial of the coordinate axis in thickness direction of the beam. Solutions for beams with linear, quadratic, or cubic distributions of continuous gradation in the FGM layer can be obtained from a single algorithm, just by changing the value of the exponent ‘m’. A numerical scheme of discretizing the continuous FGM layer (in sublayers) and treating the beam as a discretely graded structure has also been developed. Appropriate expressions for the solution have been derived for the case of continuous power law gradation (mth power) of the FGM layer. The discretized FGM layer scheme has been shown to yield results that practically match those predicted analytically by the closed-form model.