Thermal Stress in an Elastic Half-Space and Its Application in Partial Differential Equation

The article deals with the response of an infinite thermoelastic half-space model. An internal heat source of constant magnitude is acting in the half-space. This study sought to improve the comprehension of wave propagation in thermoelastic materials according to Classical theory of elasticity (CT) by developing precise wave solutions for the governing equations that take into consideration temperature-dependent material features. The analytical expressions of displacement and temperature field are obtained by Lame’s potential method and normal mode analysis technique. The work includes detailed graphical representations of crucial discoveries such as temperature distributions, stress components, and displacement components which provide amazing visual insights into the complex interactions that occur within thermo-elastic systems.