A New Fractional Boundary Element Model for the 3D Thermal Stress Wave Propagation Problems in Anisotropic Materials

Abstract

The primary purpose of this work is to provide a new fractional boundary element method (BEM) formulation to solve thermal stress wave propagation problems in anisotropic materials. In the Laplace domain, the fundamental solutions to the governing equations can be identified. Then, the boundary integral equations are constructed. The Caputo fractional time derivative was used in the formulation of the considered heat conduction equation. The three-block splitting (TBS) iteration approach was used to solve the resulting BEM linear systems, resulting in fewer iterations and less CPU time. The new TBS iteration method converges rapidly and does not involve complicated computations; it performs better than the two-dimensional double successive projection method (2D-DSPM) and modified symmetric successive overrelaxation (MSSOR) for solving the resultant BEM linear system. We only studied a special case of our model to compare our findings to those of other articles in the literature. Because the BEM results are so consistent with the finite element method (FEM) findings, the numerical results demonstrate the validity, accuracy, and efficiency of our proposed BEM formulation for solving three-dimensional thermal stress wave propagation problems in anisotropic materials.