The Effects of Variable Thermal Conductivity in Thermoelastic Interactions in an Infinite Material with and without Kirchhoff's Transformation

In this paper, the problem of an unbonded material under variable thermal conductivity with and without Kirchhoff's transformations is investigated. The context of the problem is the generalized thermoelasticity model. The boundary plane of the medium is exposed to a thermal shock that is time-dependent and considered to be traction-free. Because nonlinear formulations are difficult, the finite element method is applied to solve the problem without Kirchhoff's transformations. In a linear case, when using Kirchhoff's transformations, the problem's solution is derived using the Laplace transforms and the eigenvalue approach. The effect of variable thermal conductivity is discussed and compared with and without Kirchhoff's transformations. The graphical representations of numerical results are shown for the distributions of temperature, displacement and stress.

Automated summary

This paper investigates the problem of an unbonded material with variable thermal conductivity, with and without the use of Kirchhoff's transformations. The study utilizes the finite element method to solve the problem and discusses the effects of variable thermal conductivity on the solution. The numerical results are presented graphically for temperature, displacement, and stress distributions.