Vol.68, No.1, 2021, pp.59-76, doi:10.32604/cmc.2021.015115
OPEN ACCESS
ARTICLE
A New BEM for Fractional Nonlinear Generalized Porothermoelastic Wave Propagation Problems
• Mohamed Abdelsabour Fahmy1,2,*
1 Department of Mathematics, Jamoum University College, Umm Al-Qura University, Alshohdaa, 25371, Jamoum, Saudi Arabia
2 Department of Basic Sciences, Faculty of Computers and Informatics, Suez Canal University, New Campus, Ismailia, 41522, Egypt
* Corresponding Author: Mohamed Abdelsabour Fahmy. Email:
Received 06 November 2020; Accepted 24 January 2021; Issue published 22 March 2021
Abstract
The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperature-dependent functionally graded anisotropic (FGA) structures. The system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity, fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous structures. Therefore, an efficient boundary element method (BEM) has been proposed to overcome this difficulty, where, the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the Cartesian transformation method (CTM). The generalized modified shift-splitting (GMSS) iteration method was used to solve the linear systems resulting from BEM, also, GMSS reduces the iterations number and CPU execution time of computations. The numerical findings show the effects of fractional order parameter, anisotropy and functionally graded material on the nonlinear porothermoelastic stress waves. The numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.
Keywords
Boundary element method; fractional-order; nonlinear generalized porothermoelasticity; wave propagation; functionally graded anisotropic structures; Cartesian transformation method