Determination of exact temperature distribution through the depth of functionally varied layered laminate by semi-analytical approach

This paper involves, development of a two-dimensional heat conduction equation, which has solved analytically to determine precisely through thickness variation of temperature in the FG beams and compared with exponentially assumed thermal filed. In this paper, an attempt has to made to solve the two-point boundary value problems (BVP) along with the depth of the beam, which is commanded by a set of first-order ordinary equations (ODE’s). This BVP has converted to initial value problems (IVPs) with the help of the shooting approach, and the 4th order Runge Kutta-Grill method had useful for numerical integration. Heat conductivity and coefficient of thermal expansion have varied as per exponential law along with the thickness of the domain. Poisson’s ratio has held constant. Parametric studies have reported various aspect ratios ranging from thick to slender beams.