Generalized Thermoelastic Interaction in Orthotropic Media under Variable Thermal Conductivity Using the Finite Element Method

This article addresses a thermoelastic problem under varying thermal conductivity with and without Kirchhoff’s transforms. The temperature increment, displacement, and thermal stresses in an orthotropic material with spherical cavities are studied. The inner surface of the hole is constrained and heated by thermal shock. The numerical solutions are derived using the finite element technique in the setting of the generalized thermoelasticity model with one thermal delay time. The thermal conductivity of the material is supposed to be temperature-dependent without Kirchhoff’s transformation. Due to the difficulty of nonlinear formulations, the finite element approach is used to solve the problem without using Kirchhoff’s transformation. The solution is determined using the Laplace transform and the eigenvalues technique when employing Kirchhoff’s transformation in a linear example. Variable thermal conductivity is addressed and compared with and without Kirchhoff’s transformation. The numerical result for the investigated fields is graphically represented. According to the numerical analysis results, the varying thermal conductivity provides a limited speed for the propagations of both mechanical and thermal waves.