Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model
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 L...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/4/650 |
| _version_ | 1797478310718996480 |
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| author | Tareq Saeed |
| author_facet | Tareq Saeed |
| author_sort | Tareq Saeed |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T21:30:10Z |
| format | Article |
| id | doaj.art-13b451c865da470cae41fa716054c1cc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:10Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-13b451c865da470cae41fa716054c1cc2023-11-23T20:58:03ZengMDPI AGMathematics2227-73902022-02-0110465010.3390/math10040650Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative ModelTareq Saeed0Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn 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.https://www.mdpi.com/2227-7390/10/4/650fractional time parameterfinite element approachLaplace transformspiezo-thermo-elastic medium |
| spellingShingle | Tareq Saeed Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model Mathematics fractional time parameter finite element approach Laplace transforms piezo-thermo-elastic medium |
| title | Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model |
| title_full | Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model |
| title_fullStr | Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model |
| title_full_unstemmed | Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model |
| title_short | Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model |
| title_sort | hybrid finite element method to thermo elastic interactions in a piezo thermo elastic medium under a fractional time derivative model |
| topic | fractional time parameter finite element approach Laplace transforms piezo-thermo-elastic medium |
| url | https://www.mdpi.com/2227-7390/10/4/650 |
| work_keys_str_mv | AT tareqsaeed hybridfiniteelementmethodtothermoelasticinteractionsinapiezothermoelasticmediumunderafractionaltimederivativemodel |