Comparison of thermal stresses for exponential and actual temperature gradient along the depth of E-FG plate

Abstract

This paper describes the comprehensive thermal stress analysis and solution of simply supported functionally graded plates. Here, heat conduction formulation has been analytically simplified to access the exact temperature profile and the plate's thickness. Mathematical manipulation within basic elasticity equations has formed a two-point boundary value problem directed along the plate thickness. Here 4th order Runge-Kutta-Gill method has been adopted for numerical integration during the analysis of a group of coupled first-order ordinary differential equations. Thermoelastic constants such as modulus of elasticity, heat conductivity, and thermal expansion were supposed to change exponentially in the direction of the plate's thickness. The ratio of lateral strain to linear strain remained unchanged. Stress analysis has also been carried out by considering the thermal field change along the plate's thickness direction as per simple exponential law. For identifying a variation in structural response, stress analysis results have been compared with stress analysis for the exact thermal field acquired from the equation of heat conduction solution.