Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity
In nonlocal elasticity, the constitutive equation for the stress tensor is written in an integral form, with the weight function, referred to as the nonlocality kernel, often being the Green’s function for the partial differential equation. In this paper, we obtain solutions to elasticity problems f...
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MDPI AG
2025-02-01
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| author | Yuriy Povstenko Tamara Kyrylych Bożena Woźna-Szcześniak Ireneusz Szcześniak Andrzej Yatsko |
| author_facet | Yuriy Povstenko Tamara Kyrylych Bożena Woźna-Szcześniak Ireneusz Szcześniak Andrzej Yatsko |
| author_sort | Yuriy Povstenko |
| collection | DOAJ |
| description | In nonlocal elasticity, the constitutive equation for the stress tensor is written in an integral form, with the weight function, referred to as the nonlocality kernel, often being the Green’s function for the partial differential equation. In this paper, we obtain solutions to elasticity problems for a concentrated couple in a plane and on the boundary of a half-plane within framework of a new theory of nonlocal elasticity, where the nonlocal kernel is the Green’s function of the Cauchy problem for the fractional diffusion equation. The obtained solutions are free from nonphysical singularities that appear in the classical local elasticity solutions. |
| format | Article |
| id | doaj-art-1134ef802bce43d680ff0843153ec6b4 |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-1134ef802bce43d680ff0843153ec6b42025-08-20T03:12:08ZengMDPI AGApplied Sciences2076-34172025-02-01154204810.3390/app15042048Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal ElasticityYuriy Povstenko0Tamara Kyrylych1Bożena Woźna-Szcześniak2Ireneusz Szcześniak3Andrzej Yatsko4Department of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Al. Armii Krajowej 13/15, 42-200 Czestochowa, PolandDepartment of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Al. Armii Krajowej 13/15, 42-200 Czestochowa, PolandDepartment of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Al. Armii Krajowej 13/15, 42-200 Czestochowa, PolandDepartment of Computer Science, Czestochowa University of Technology, Dabrowskiego 73, 42-200 Czestochowa, PolandDepartment of Mathematics, Faculty of Civil Engineering, Environmental and Geodesic Sciences, Koszalin University of Technology, Sniadeckich 2, 75-453 Koszalin, PolandIn nonlocal elasticity, the constitutive equation for the stress tensor is written in an integral form, with the weight function, referred to as the nonlocality kernel, often being the Green’s function for the partial differential equation. In this paper, we obtain solutions to elasticity problems for a concentrated couple in a plane and on the boundary of a half-plane within framework of a new theory of nonlocal elasticity, where the nonlocal kernel is the Green’s function of the Cauchy problem for the fractional diffusion equation. The obtained solutions are free from nonphysical singularities that appear in the classical local elasticity solutions.https://www.mdpi.com/2076-3417/15/4/2048fractional calculusnonlocal elasticityconcentrated coupleCaputo fractional derivativefractional diffusion equationMittag-Leffler function |
| spellingShingle | Yuriy Povstenko Tamara Kyrylych Bożena Woźna-Szcześniak Ireneusz Szcześniak Andrzej Yatsko Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity Applied Sciences fractional calculus nonlocal elasticity concentrated couple Caputo fractional derivative fractional diffusion equation Mittag-Leffler function |
| title | Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity |
| title_full | Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity |
| title_fullStr | Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity |
| title_full_unstemmed | Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity |
| title_short | Concentrated Couple in a Plane and in a Half-Plane in the Framework of Fractional Nonlocal Elasticity |
| title_sort | concentrated couple in a plane and in a half plane in the framework of fractional nonlocal elasticity |
| topic | fractional calculus nonlocal elasticity concentrated couple Caputo fractional derivative fractional diffusion equation Mittag-Leffler function |
| url | https://www.mdpi.com/2076-3417/15/4/2048 |
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