Mohamed Fahmy | Umm Al-Qura University, Makkah, Saudi Arabia (original) (raw)

Papers by Mohamed Fahmy

Materials, Feb 28, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Computers, Materials & Continua, 2021

The main objective of this paper is to introduce a new theory called size-dependent thermopiezoel... more The main objective of this paper is to introduce a new theory called size-dependent thermopiezoelectricity for smart nanostructures. The proposed theory includes the combination of thermoelastic and piezoelectric influences which enable us to describe the deformation and mechanical behaviors of smart nanostructures subjected to thermal, and piezoelectric loadings. Because of difficulty of experimental research problems associated with the proposed theory. Therefore, we propose a new boundary element method (BEM) formulation and algorithm for the solution of such problems, which involve temperatures, normal heat fluxes, displacements, couple-tractions, rotations, force-tractions, electric displacement, and normal electric displacement as primary variables within the BEM formulation. The computational performance of the proposed methodology has been demonstrated by using the generalized modified shift-splitting (GMSS) iteration method to solve the linear systems resulting from the BEM discretization. GMSS advantages are investigated and compared with other iterative methods. The numerical results are depicted graphically to show the size-dependent effects of thermopiezoelectricity, thermoelasticity, piezoelectricity, and elasticity theories of nanostructures. The numerical results also show the effects of the sizedependent and piezoelectric on the displacement components. The validity, efficiency and accuracy of the proposed BEM formulation and algorithm have been demonstrated. The findings of the current study contribute to the further development of technological and industrial applications of smart nanostructures.

Fractal and Fractional

This paper proposes a three–dimensional (3D) local boundary element model based on meshless movin... more This paper proposes a three–dimensional (3D) local boundary element model based on meshless moving least squares (MLS) method for ultrasonic wave propagation fractional order boundary value problems of functionally graded anisotropic (FGA) fiber-reinforced plates. The problem domain is split into several circular sub-domains. The nodal points are randomly distributed across the examined region. Each node is the focal point of a circular sub-domain that encircles it. The Laplace-transform approach is used to solve dynamic issues. In the local weak form of the governing equations for the converted quantities, a unit test function is utilized. The Gauss divergence theorem to the weak-form is used to produce local boundary-domain integral equations. A meshless approximation is achieved using the MLS method. To find time-dependent solutions, an inverse Laplace-transform approach is used. The effects of the fractional order parameter, functionally graded material, anisotropy, and the time...

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Physical Mesomechanics, Apr 1, 2023

Results in physics, Jun 1, 2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Many challenges in different applied fields of research, such as materials science, viscoelastici... more Many challenges in different applied fields of research, such as materials science, viscoelasticity, biological sciences, physics, and mechanical engineering, require the study of derivative operators using single singular or nonsingular kernels. Atangana and Baleanu (AB) constructed a novel fractional derivative without a singular kernel based on the extended Mittag–Leffler function to overcome the singular kernel problem seen in previous definitions of fractional‐order derivatives. In this article, we provide a novel mathematical thermoelastic heat conduction model that includes the fractional AB derivative operators. In addition, the Moore–Gibson–Thompson (MGT) equation has been incorporated into the proposed heat transport model. The proposed model has been applied to study an infinite orthotropic material with a cylindrical aperture, and the thermal conductivity coefficient of the body depends on the temperature change. The Laplace transform approach has been used to solve the ...

AIMS mathematics, 2022

In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational bas... more In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.

Fractal and Fractional

The primary goal of this paper is to create a new fractional boundary element method (BEM) model ... more 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.

International Journal of Thermophysics, Jan 13, 2021

The main objective of the present paper is to propose a new boundary element modeling technique f... more The main objective of the present paper is to propose a new boundary element modeling technique for simulation and optimization of three-temperature micropolar magneto-thermoviscoelastic problems in anisotropic porous smart structures, where we implemented the genetic algorithm (GA), as a method of optimization based on the free form deformation (FFD) methodology to improve the performance of our proposed technique. Two numerical examples are presented herein, in order to prove that the proposed technique is able to optimize the shape of the domains with minimum computational effort. A nonuniform rational B-spline curve (NURBS) has been introduced to define the optimum boundary where it decreases the number of control points and offers a new degree of versatility in the design of various different shapes. The profiles of the items considered shall be represented by the FFD methodology. The location vectors of the FFD control points are known to be the genes, and then the chromosomes for the profiles are determined by the gene sequence. The population is made up of several chromosomes individuals, where the fitness functions of individuals are assessed using BEM. The numerical results are depicted graphical forms to show the effects of viscosity and magnetic fields on the three temperatures, displacement components, microrotation components, pore pressure, electric potential, and thermal stress components. The validity, accuracy, and computational efficiency of the proposed BEM technique were demonstrated by comparing our BEM-obtained results with the corresponding results of normal mode analysis method (NMAM), finite difference method (FDM), and finite element method (FEM).

Polymers

A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fracti... more A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fractional-order thermo-elastoplastic ultrasonic wave propagation problems based on the meshless moving least squares (MLS) method. The temperature problem domain was divided into a number of circular sub-domains. Each node was the center of the circular sub-domain surrounding it. The Laplace transform method was used to solve the temperature problem. A unit test function was used in the local weak-form formulation to generate the local boundary integral equations, and the inverse Laplace transformation method was used to find the transient temperature solutions. Then, the three-dimensional elastoplastic problems could be solved using the boundary element method (BEM). Initial stress and strain formulations are adopted, and their distributions are interpolated using boundary integral equations. The effects of the fractional-order parameter and anisotropy are investigated. The proposed method’s...

COUPLED VI : proceedings of the VI International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2015

The mechanics of the piezoelectric functionally graded material (FGM) has received considerable r... more The mechanics of the piezoelectric functionally graded material (FGM) has received considerable research effort with their increasing usage in various applications including sensors and actuators, piezoelectric motors, reduction of vibrations and noise, infertility treatment and photovoltaics. It is hard to find the analytical solution of a problem in a general case, therefore, an important number of engineering and mathematical papers devoted to the numerical solution have studied the overall behavior of such materials. The time-stepping dual reciprocity boundary element method was proposed to solve the 2D coupled problem in anisotropic piezoelectric FGM plates. The accuracy of the proposed method was examined and confirmed by comparing the obtained results with those known previously.

14th WCCM-ECCOMAS Congress, 2021

The main objective of this paper is to develop a novel boundary element technique for describing ... more The main objective of this paper is to develop a novel boundary element technique for describing the three-dimensional (3D) biothermomechanical behavior of anisotropic biological tissues. The governing equations are studied on the basis of the dual phase lag bioheat transfer and Biot's theory for one-and two-temperature models. Because of the benefits of CQBEM, such as not being restricted by the complex shape of biological tissues and not requiring discretization of the interior of the treated region, it can cope with complex bioheat models and has low use of RAM and CPU. CQBEM is therefore a flexible and efficient tool for modeling the distribution of bioheat in anisotropic biological tissues and associated deformation. The resulting linear equations arising from CQBEM are solved by the generalized modified shift-splitting (GMSS) iterative method which reduces the number of iterations and the total time of the CPU. Numerical findings show the validity, efficacy and consistency of the proposed technique.

Journal of Advances in Mathematics and Computer Science, 2017

Aims: A shape optimization technique is developed, using the boundary element method, for twodime... more Aims: A shape optimization technique is developed, using the boundary element method, for twodimensional anisotropic structures to study the effects of anisotropy on the displacements and stresses, then minimize weight while satisfying certain constraints upon stresses and geometry.

World Journal of Mechanics, 2011

The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses i... more The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses in a non-homogeneous anisotropic solid under initial stress. The system of fundamental equations is solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are presented graphically to show the effects of initial stress and inhomogeneity on the displacement components and thermal stress components.

Applied Sciences

The principal objective of this work was to develop a semi-implicit hybrid boundary element metho... more The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlin...

Scientific Reports

The primary goal of this article is to propose a new fractional boundary element technique for so... more 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.

Recent Developments in the Solution of Nonlinear Differential Equations, 2021

The main purpose of this chapter is to propose a novel boundary element modeling and simulation a... more The main purpose of this chapter is to propose a novel boundary element modeling and simulation algorithm for solving fractional bio-thermomechanical problems in anisotropic soft tissues. The governing equations are studied on the basis of the thermal wave model of bio-heat transfer (TWMBT) and Biot’s theory. These governing equations are solved using the boundary element method (BEM), which is a flexible and effective approach since it deals with more complex shapes of soft tissues and does not need the internal domain to be discretized, also, it has low RAM and CPU usage. The transpose-free quasi-minimal residual (TFQMR) solver are implemented with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner to solve the linear systems arising from BEM. Numerical findings are depicted graphically to illustrate the influence of fractional order parameter on the problem variables and confirm the validity, efficiency and accuracy of the proposed BEM technique.

Noise and Environment, 2021

The principal aim of this chapter is to introduce a new theory called acoustic wave propagation o... more The principal aim of this chapter is to introduce a new theory called acoustic wave propagation of three-temperature nonlinear generalized magneto-thermoelasticity, and we propose a new boundary element model for solving problems of initially stressed multilayered functionally graded anisotropic (ISMFGA) structures using laser ultrasonics, which connected with the proposed theory. Since there are no available analytical or numerical solutions for the considered nonlinear wave propagation problems in the literature, we propose a new boundary element modeling formulation for the solution of such problems. The numerical results are depicted graphically to show the propagation of three temperatures and displacement waves. The results also show the effects of initial stress and functionally graded material on the displacement waves and confirm the validity and accuracy of our proposed theory and solution technique.

Materials, Feb 28, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Computers, Materials & Continua, 2021

The main objective of this paper is to introduce a new theory called size-dependent thermopiezoel... more The main objective of this paper is to introduce a new theory called size-dependent thermopiezoelectricity for smart nanostructures. The proposed theory includes the combination of thermoelastic and piezoelectric influences which enable us to describe the deformation and mechanical behaviors of smart nanostructures subjected to thermal, and piezoelectric loadings. Because of difficulty of experimental research problems associated with the proposed theory. Therefore, we propose a new boundary element method (BEM) formulation and algorithm for the solution of such problems, which involve temperatures, normal heat fluxes, displacements, couple-tractions, rotations, force-tractions, electric displacement, and normal electric displacement as primary variables within the BEM formulation. The computational performance of the proposed methodology has been demonstrated by using the generalized modified shift-splitting (GMSS) iteration method to solve the linear systems resulting from the BEM discretization. GMSS advantages are investigated and compared with other iterative methods. The numerical results are depicted graphically to show the size-dependent effects of thermopiezoelectricity, thermoelasticity, piezoelectricity, and elasticity theories of nanostructures. The numerical results also show the effects of the sizedependent and piezoelectric on the displacement components. The validity, efficiency and accuracy of the proposed BEM formulation and algorithm have been demonstrated. The findings of the current study contribute to the further development of technological and industrial applications of smart nanostructures.

Fractal and Fractional

This paper proposes a three–dimensional (3D) local boundary element model based on meshless movin... more This paper proposes a three–dimensional (3D) local boundary element model based on meshless moving least squares (MLS) method for ultrasonic wave propagation fractional order boundary value problems of functionally graded anisotropic (FGA) fiber-reinforced plates. The problem domain is split into several circular sub-domains. The nodal points are randomly distributed across the examined region. Each node is the focal point of a circular sub-domain that encircles it. The Laplace-transform approach is used to solve dynamic issues. In the local weak form of the governing equations for the converted quantities, a unit test function is utilized. The Gauss divergence theorem to the weak-form is used to produce local boundary-domain integral equations. A meshless approximation is achieved using the MLS method. To find time-dependent solutions, an inverse Laplace-transform approach is used. The effects of the fractional order parameter, functionally graded material, anisotropy, and the time...

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Physical Mesomechanics, Apr 1, 2023

Results in physics, Jun 1, 2023

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Many challenges in different applied fields of research, such as materials science, viscoelastici... more Many challenges in different applied fields of research, such as materials science, viscoelasticity, biological sciences, physics, and mechanical engineering, require the study of derivative operators using single singular or nonsingular kernels. Atangana and Baleanu (AB) constructed a novel fractional derivative without a singular kernel based on the extended Mittag–Leffler function to overcome the singular kernel problem seen in previous definitions of fractional‐order derivatives. In this article, we provide a novel mathematical thermoelastic heat conduction model that includes the fractional AB derivative operators. In addition, the Moore–Gibson–Thompson (MGT) equation has been incorporated into the proposed heat transport model. The proposed model has been applied to study an infinite orthotropic material with a cylindrical aperture, and the thermal conductivity coefficient of the body depends on the temperature change. The Laplace transform approach has been used to solve the ...

AIMS mathematics, 2022

In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational bas... more In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.

Fractal and Fractional

The primary goal of this paper is to create a new fractional boundary element method (BEM) model ... more 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.

International Journal of Thermophysics, Jan 13, 2021

The main objective of the present paper is to propose a new boundary element modeling technique f... more The main objective of the present paper is to propose a new boundary element modeling technique for simulation and optimization of three-temperature micropolar magneto-thermoviscoelastic problems in anisotropic porous smart structures, where we implemented the genetic algorithm (GA), as a method of optimization based on the free form deformation (FFD) methodology to improve the performance of our proposed technique. Two numerical examples are presented herein, in order to prove that the proposed technique is able to optimize the shape of the domains with minimum computational effort. A nonuniform rational B-spline curve (NURBS) has been introduced to define the optimum boundary where it decreases the number of control points and offers a new degree of versatility in the design of various different shapes. The profiles of the items considered shall be represented by the FFD methodology. The location vectors of the FFD control points are known to be the genes, and then the chromosomes for the profiles are determined by the gene sequence. The population is made up of several chromosomes individuals, where the fitness functions of individuals are assessed using BEM. The numerical results are depicted graphical forms to show the effects of viscosity and magnetic fields on the three temperatures, displacement components, microrotation components, pore pressure, electric potential, and thermal stress components. The validity, accuracy, and computational efficiency of the proposed BEM technique were demonstrated by comparing our BEM-obtained results with the corresponding results of normal mode analysis method (NMAM), finite difference method (FDM), and finite element method (FEM).

Polymers

A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fracti... more A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fractional-order thermo-elastoplastic ultrasonic wave propagation problems based on the meshless moving least squares (MLS) method. The temperature problem domain was divided into a number of circular sub-domains. Each node was the center of the circular sub-domain surrounding it. The Laplace transform method was used to solve the temperature problem. A unit test function was used in the local weak-form formulation to generate the local boundary integral equations, and the inverse Laplace transformation method was used to find the transient temperature solutions. Then, the three-dimensional elastoplastic problems could be solved using the boundary element method (BEM). Initial stress and strain formulations are adopted, and their distributions are interpolated using boundary integral equations. The effects of the fractional-order parameter and anisotropy are investigated. The proposed method’s...

COUPLED VI : proceedings of the VI International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2015

The mechanics of the piezoelectric functionally graded material (FGM) has received considerable r... more The mechanics of the piezoelectric functionally graded material (FGM) has received considerable research effort with their increasing usage in various applications including sensors and actuators, piezoelectric motors, reduction of vibrations and noise, infertility treatment and photovoltaics. It is hard to find the analytical solution of a problem in a general case, therefore, an important number of engineering and mathematical papers devoted to the numerical solution have studied the overall behavior of such materials. The time-stepping dual reciprocity boundary element method was proposed to solve the 2D coupled problem in anisotropic piezoelectric FGM plates. The accuracy of the proposed method was examined and confirmed by comparing the obtained results with those known previously.

14th WCCM-ECCOMAS Congress, 2021

The main objective of this paper is to develop a novel boundary element technique for describing ... more The main objective of this paper is to develop a novel boundary element technique for describing the three-dimensional (3D) biothermomechanical behavior of anisotropic biological tissues. The governing equations are studied on the basis of the dual phase lag bioheat transfer and Biot's theory for one-and two-temperature models. Because of the benefits of CQBEM, such as not being restricted by the complex shape of biological tissues and not requiring discretization of the interior of the treated region, it can cope with complex bioheat models and has low use of RAM and CPU. CQBEM is therefore a flexible and efficient tool for modeling the distribution of bioheat in anisotropic biological tissues and associated deformation. The resulting linear equations arising from CQBEM are solved by the generalized modified shift-splitting (GMSS) iterative method which reduces the number of iterations and the total time of the CPU. Numerical findings show the validity, efficacy and consistency of the proposed technique.

Journal of Advances in Mathematics and Computer Science, 2017

Aims: A shape optimization technique is developed, using the boundary element method, for twodime... more Aims: A shape optimization technique is developed, using the boundary element method, for twodimensional anisotropic structures to study the effects of anisotropy on the displacements and stresses, then minimize weight while satisfying certain constraints upon stresses and geometry.

World Journal of Mechanics, 2011

The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses i... more The object of the present paper is to study the transient magneto-thermo-visco-elastic stresses in a non-homogeneous anisotropic solid under initial stress. The system of fundamental equations is solved by means of a dual reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are presented graphically to show the effects of initial stress and inhomogeneity on the displacement components and thermal stress components.

Applied Sciences

The principal objective of this work was to develop a semi-implicit hybrid boundary element metho... more The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlin...

Scientific Reports

The primary goal of this article is to propose a new fractional boundary element technique for so... more 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.

Recent Developments in the Solution of Nonlinear Differential Equations, 2021

The main purpose of this chapter is to propose a novel boundary element modeling and simulation a... more The main purpose of this chapter is to propose a novel boundary element modeling and simulation algorithm for solving fractional bio-thermomechanical problems in anisotropic soft tissues. The governing equations are studied on the basis of the thermal wave model of bio-heat transfer (TWMBT) and Biot’s theory. These governing equations are solved using the boundary element method (BEM), which is a flexible and effective approach since it deals with more complex shapes of soft tissues and does not need the internal domain to be discretized, also, it has low RAM and CPU usage. The transpose-free quasi-minimal residual (TFQMR) solver are implemented with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner to solve the linear systems arising from BEM. Numerical findings are depicted graphically to illustrate the influence of fractional order parameter on the problem variables and confirm the validity, efficiency and accuracy of the proposed BEM technique.

Noise and Environment, 2021

The principal aim of this chapter is to introduce a new theory called acoustic wave propagation o... more The principal aim of this chapter is to introduce a new theory called acoustic wave propagation of three-temperature nonlinear generalized magneto-thermoelasticity, and we propose a new boundary element model for solving problems of initially stressed multilayered functionally graded anisotropic (ISMFGA) structures using laser ultrasonics, which connected with the proposed theory. Since there are no available analytical or numerical solutions for the considered nonlinear wave propagation problems in the literature, we propose a new boundary element modeling formulation for the solution of such problems. The numerical results are depicted graphically to show the propagation of three temperatures and displacement waves. The results also show the effects of initial stress and functionally graded material on the displacement waves and confirm the validity and accuracy of our proposed theory and solution technique.