 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| L.A. Alexeyeva and M.M. Akhmetzhanova, "Spatially One-Dimensional Boundary Value Problems of Coupled Thermoelasticity: Generalized Functions Method," Mech. Solids. 57 (8), 2151-2165 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
2151-2165 |
| DOI |
10.3103/S0025654422080325 |
| Title |
Spatially One-Dimensional Boundary Value Problems of Coupled Thermoelasticity: Generalized Functions Method |
| Author(s) |
L.A. Alexeyeva (Institute of Mathematics and Mathematical Modeling, Almaty, 050010 Kazakhstan, alexeeva@math.kz)
M.M. Akhmetzhanova (Institute of Mathematics and Mathematical Modeling, Almaty, 050010 Kazakhstan, mariella80@mail.ru) |
| Abstract |
Problems of determining the thermostressed state of a thermoelastic rod using the coupled
thermoelasticity model are considered. In this case, the heat conductivity equation includes divergence of the speed of material points of the medium; the elasticity equations include the temperature
gradient. The generalized functions method is used to construct generalized solutions to nonstationary
and stationary direct and semi-inverse boundary value problems under the action of power and thermal sources of various types, including those described by singular generalized functions under different boundary conditions at the ends of rod. Thermal shock waves arising in such structures under the
action of impact loads and heat fluxes are considered, and the conditions at their fronts are obtained.
The uniqueness of the solutions to the posed boundary value problems, including those with allowance
for shock waves, has been proved. Regular integral representations of the generalized solutions are presented, which yield an analytical solution to the posed boundary value problems. |
| Keywords |
coupled thermoelasticity, thermoelastic rod, boundary value problems, fundamental and generalized solution, Laplace transform, stationary oscillations |
| Received |
20 October 2019 | Revised |
25 February 2020 | Accepted |
29 November 2022 |
| Link to Fulltext |
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