Analytic Technique for Determining Fundamental Solutions in Static Thermoelasticity

Static thermoelasticity, with an internal heat source involves analyzing the equilibrium state of a solid body in which both mechanical deformations and temperature distributions are influenced by an internal heat generation mechanism. The governing equations couple the static (time-independent) balance of momentum with the steady-state heat conduction equation, incorporating the effects of thermal expansion and source terms. This paper presents a rigorous derivation and analytical discussion of fundamental solutions for a line heat source in static coupled thermoelastic systems. The problem formulation considers an isotropic and homogeneous thermoelastic solid having an internal line heat source. Using Green’s function techniques and potential theory, the study formulates fundamental solutions. The general representation of displacements, stress tensors, and temperature fields is obtained from the governing partial differential equations. The findings offer new insights into heat–stress coupling for advanced materials, including semiconductors, porous composites, and micro-structured solids, where localized heating and steady deformation coexist. The study concludes that accurate fundamental representation offers predictive efficiency for coupled-field simulations across theoretical and engineering domains.