A new boundary element sensitivity analysis for generalized thermoelastic three-phase-lag model of anisotropic materials

This article presents a novel formulation of the boundary element method (BEM) for sensitivity analysis of the generalized thermoelastic three-phase-lag (TPL) model with directional dependence for anisotropic materials. It deals with closed-form transient fundamental solutions for two special cases in the Laplace transform domain based on advanced transform techniques. These fundamental solutions serve as the foundation for the proposed direct BEM formulation, which constructs the boundary integral equations by invoking the Maxwell–Betti reciprocal work theorem, adapted to the extended TPL theory in anisotropic media. The resulting boundary integral equations are numerically discretized, reducing the problem to solving a system of linear algebraic equations in the Laplace domain. Final time-domain solutions are subsequently retrieved through numerical Laplace inversion techniques. A significant number of numerical computations is performed to investigate the time history of thermal stress sensitivity for various thermoelastic models, namely the three-phase-lag (TPL), dual-phase-lag (DPL), and Lord–Shulman (L-S) theories. Furthermore, material anisotropy is investigated through comparison of sensitivity results for anisotropic, transversely isotropic, and isotropic material models. The findings are evidence of the validity, stability, and usability of the suggested BEM method to the simulation and assessment of thermal stress behavior of multifaceted anisotropic thermoelastic media, expanding computational technique in generalized thermoelasticity.