This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology.

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.

This article provides a novel three-dimensional fractional Boundary Element Method (BEM) for effective knowledge of thermo-elastoplastic stress sensitivity of anisotropic materials with temperature-dependent material properties. The approach incorporates nonlocality and memory effects caused by the intercoupled thermal and mechanical loadings through the coupling of BEM with fractional calculus. For efficient representation of material response, the model formulation is made in terms of a temperature-dependent constitutive law and a fractional yield function. For enabling higher computational efficiency, a mixed-type splitting (TMS) iterative scheme is employed that significantly reduces the number of iterations and the overall computation time. Domain integrals are handled by the very high precision Cartesian Transformation Method (CTM). Numerical computation confirms the practicability and the utility of the process in the simulation of complex stress behaviors, and findings underscore the significance of temperature variation and anisotropy. The process provides a robust and reliable means for advanced materials’ analysis engineering.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.