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

Author

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  • Tareq Saeed

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

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.

Suggested Citation

  • Tareq Saeed, 2022. "Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model," Mathematics, MDPI, vol. 10(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:650-:d:753423
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    References listed on IDEAS

    as
    1. Mahmoud Ragab & S. M. Abo-Dahab & Ahmed E. Abouelregal & A. A. Kilany & Dan Selisteanu, 2021. "A Thermoelastic Piezoelectric Fixed Rod Exposed to an Axial Moving Heat Source via a Dual-Phase-Lag Model," Complexity, Hindawi, vol. 2021, pages 1-11, July.
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    Cited by:

    1. Ahmed E. Abouelregal & Marin Marin & Sahar M. Abusalim, 2023. "An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    2. Tareq Saeed, 2022. "Generalized Thermoelastic Interactions in an Infinite Viscothermoelastic Medium under the Nonlocal Thermoelastic Model," Mathematics, MDPI, vol. 10(23), pages 1-11, November.

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