The primary goal of this article is to propose a new fractional boundary element technique for solving nonlinear three-temperature (3 T) thermoelectric problems. Analytical solution of the current problem is extremely difficult to obtain. To overcome this difficulty, a new numerical technique must be developed to solve such problem. As a result, we propose a novel fractional boundary element method (BEM) to solve the governing equations of our considered problem. Because of the advantages of the BEM solution, such as the ability to treat problems with complicated geometries that were difficult to solve using previous numerical methods, and the fact that the internal domain does not need to be discretized. As a result, the BEM can be used in a wide variety of thermoelectric applications. The numerical results show the effects of the magnetic field and the graded parameter on thermal stresses. The numerical results also validate the validity and accuracy of the proposed technique.

The primary goal of this article is to implement a dual reciprocity boundary element method (DRBEM) to analyze problems of rotating functionally graded anisotropic fiber-reinforced magneto-thermoelastic composites. To solve the governing equations in the half-space deformation model, an implicit–implicit scheme was utilized in conjunction with the DRBEM because of its advantages, such as dealing with more complex shapes of fiber-reinforced composites and not requiring the discretization of the internal domain. So, DRBEM has low RAM and CPU usage. As a result, it is adaptable and effective for dealing with complex fiber-reinforced composite problems. For various generalized magneto-thermoelasticity theories, transient temperature, displacements, and thermal stresses have been computed numerically. The numerical results are represented graphically to demonstrate the effects of functionally graded parameters and rotation on magnetic thermal stresses in the fiber direction. To validate the proposed method, the obtained results were compared to those obtained using the normal mode method, the finite difference method, and the finite element method. The outcomes of these three methods are extremely consistent.

The primary goal of this paper is to create a new fractional boundary element method (BEM) model for bio-thermomechanical problems in functionally graded anisotropic (FGA) nonlinear viscoelastic soft tissues. The governing equations of bio-thermomechanical problems are briefly presented, including the fractional dual-phase-lag (DPL) bioheat model and Biot’s model. The more complex shapes of nonlinear viscoelastic soft tissues can be handled by the boundary element method, which also avoids the need for the interior domain to be discretized. The fractional dual-phase-lag bioheat equation was solved using the general boundary element method (GBEM) based on the local radial basis function collocation method (LRBFCM). The poroelastic fields are then calculated using the convolution quadrature boundary element method (CQBEM) The numerical findings show that our proposed numerical model is valid, efficient, and accurate.

The primary goal of this article is to propose a new fractional boundary element technique for solving nonlinear three-temperature (3T) thermoelectric problems. Analytical solution of the current problem is extremely difficult to obtain. To overcome this difficulty, a new numerical technique must be developed to solve such problem. As a result, we propose a novel fractional boundary element method (BEM) to solve the governing equations of our considered problem. Because of the advantages of the BEM solution, such as the ability to treat problems with complicated geometries that were difficult to solve using previous numerical methods, and the fact that the internal domain does not need to be discretized. As a result, the BEM can be used in a wide variety of thermoelectric applications. The numerical results show the effects of the magnetic field and the graded parameter on thermal stresses. The numerical results also validate the validity and accuracy of the proposed technique.