AN ANALYTICAL SOLUTION OF INVERSE COUPLED THERMOELASTICITY IN INHOMOGENEOUS RECTANGULAR BEAMS

Abstract

In recent years, inhomogeneous materials have drawn a lot of attention in all branches of engineering because they have a specific capability to improve the performance and quality of structural components. Inhomogeneous materials, defined by physically varying properties in space, provide engineered responses to an external stimulus and are therefore suited to sophisticated engineering applications. In this research, we propose an analytical method to solve the inverse coupled thermoelasticity problem for an inhomogeneous material. Particularly, we consider a rectangular beam made of such material loaded with a temperature field in the presence of an ambient medium.

The emphasis of our study is on examining the temperature distribution over the rectangular cross-section of the beam, considering internal heat generation, spatial thermal conductivity variation, and heat exchange with the ambient environment. Thermal stress-free boundary conditions are assumed to enable a better observation of the thermal response without interference from existing stresses. Mathematical modeling is established for representing thermal conductivity and associated linear thermal expansion rate as a function of spatial coordinates along a beam. The representation serves as the basis for the description of heat transfer characteristics in non-uniform composition materials, especially under stress-free and zero internal heat generation conditions. In order to test our theoretical model, we develop a mathematical model of an inhomogeneous rectangular Copper-Zinc beam with different thermal properties. Numerical simulations are conducted to assess the thermal response of the beam in the specified conditions. The simulations are conducted using the Python programming language, and the results are represented in detail through graphical figures.