Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model

Tareq Saeed
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Tareq Saeed: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-13

Abstract: In this work, the effect of the fractional time derivative on the piezo-thermo-elastic medium is studied, using the hybrid Laplace transform and finite element methods (LFEM). The generalized fractional piezoelectric–thermoelastic basic equations for piezo-thermo-elastic medium are formulated. The Laplace transforms are used for the time derivatives, and the finite element method is used to discretize for the space derivatives. The inversions process is performed using the Stehfest numerical technique. The finite element approach is used to obtain the solutions of complex coupled formulations of this problem. The effects of fractional time derivative and thermal relaxation time on piezoelectric–thermoelastic mediums are studied. It can be seen from the distribution that the thermal-induced displacement, the temperature and the stress of the medium increase at a high fractional parameter.

Keywords: fractional time parameter; finite element approach; Laplace transforms; piezo-thermo-elastic medium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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