 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13205 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8140
|
| In English (Mech. Solids): | | 5065 |
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| Nikita Karde, Dilip Kamdi, Vinod Varghese, and Nitin Chandel, "Eringen’s Non-Locality and Unified Exponential Operators Induce Thermoelasticity in a Cylindrical Cavity under Thermal Loads," Mech. Solids. 60 (2), 1404-1426 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
2 |
Pages |
1404-1426 |
| DOI |
10.1134/S0025654424607250 |
| Title |
Eringen’s Non-Locality and Unified Exponential Operators Induce Thermoelasticity in a Cylindrical Cavity under Thermal Loads |
| Author(s) |
Nikita Karde (Department of Mathematics, Rashtrapita Mahatma Gandhi Art’s, Comm and Sci College, Saoli, Chandrapur, India, nikitakarde30061997@gmail.com)
Dilip Kamdi (Department of Mathematics, Rashtrapita Mahatma Gandhi Art’s, Comm and Sci College, Saoli, Chandrapur, India, dilip.kamdi@rediffmail.com)
Vinod Varghese (Department of Mathematics, M.G. College, Armori, Gadchiroli, India, vino7997@gmail.com)
Nitin Chandel (Department of Mathematics, M.G. College, Armori, Gadchiroli, India, nitinsinghchandel9@gmail.com) |
| Abstract |
This paper develops a mathematical model for modified heat conduction by applying exponential operators and Eringen’s non-locality stress theory within an infinite-length cylindrical cavity
subjected to various time-dependent sectional heat supplies. The study employs both the Caputo-Fabrizio and Rabotnov fractional differential operators, which, despite both utilizing exponential functions, differ significantly in their definitions. The Caputo-Fabrizio operator is widely used in fractional
calculus due to its nonsingular kernel and broad applicability. In contrast, the Rabotnov operator is
particularly effective for modeling complex physical processes and real-life phenomena. The study
material is homogeneous and isotropic with uniform surface pressure across boundaries; the model
derives exact solutions to the modified heat conduction equations using the integral transformation
technique. Solutions in the Laplace transform domain are inverted back to the time domain via the
Gaver-Stehfest algorithm. This research highlights the importance of temperature distribution in predicting the behavior of non-local thermoelastic displacement and stress functions with fractional
exponential operators. The model, grounded in Eringen’s non-local continuum theory, provides numerical solutions illustrated graphically. The special case analyzed involves various sectional heat
supplies affecting the inner curved surface, emphasizing the non-Fourier thermal behavior and the
influence of non-local parameters on transient thermoelastic responses. These findings are crucial for accurate predictions in the design and processing of micro-and nanostructures. |
| Keywords |
three phase-lag, Caputo-Fabrizio kernel, Rabotnov fractional kernel, heat conduction, thermal stresses, non-local stress, cylindrical cavity, thermal load |
| Received |
29 December 2024 | Revised |
18 March 2025 | Accepted |
19 March 2025 |
| Link to Fulltext |
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