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A New BEM Modeling Algorithm for Size-Dependent Thermopiezoelectric Problems in Smart Nanostructures

Mohamed Abdelsabour Fahmy1,2,*

1 Department of Mathematics, Jamoum University College, Umm Al-Qura University, Alshohdaa, 25371, Jamoum, Makkah, 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: email

Computers, Materials & Continua 2021, 69(1), 931-944.


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 size-dependent 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.


Cite This Article

M. Abdelsabour Fahmy, "A new bem modeling algorithm for size-dependent thermopiezoelectric problems in smart nanostructures," Computers, Materials & Continua, vol. 69, no.1, pp. 931–944, 2021.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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