 | | 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: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
|
| In English (Mech. Solids): | | 5249 |
|
| << Previous article | Volume 60, Issue 6 / 2025 | Next article >> |
| Alexandr Vatulyan, Victor Yurov, and Ivan Gusakov, "On the Applied Theory of Rectangle Stretching," Mech. Solids. 60 (6), 4424-4433 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
4424-4433 |
| DOI |
10.1134/S0025654425603052 |
| Title |
On the Applied Theory of Rectangle Stretching |
| Author(s) |
Alexandr Vatulyan (Southern Federal University, Rostov-on-Don, 344049 Russia, vyurov@sfedu.ru)
Victor Yurov (Southern Federal University, Rostov-on-Don, 344049 Russia; Southern Mathematical Institute – the Affiliate of Vladikavkaz Scientific Center of Russian Academy of Sciences, Vladikavkaz, 362027 Russia, aovatulyan@sfedu.ru)
Ivan Gusakov (Southern Federal University, Rostov-on-Don, 344049 Russia, igusakov@sfedu.ru) |
| Abstract |
The paper considers deformation of isotropic rectangular samples within the generalized
plane stress state. Approximate models of different orders for elongated samples are constructed by
representing the displacement field as an expansion in first-and second-order polynomials with
unknown coefficient functions. The Kantorovich method within the Lagrange variational principle
allows one to reduce the problem to a system of ordinary differential equations with constant coefficients and to form the corresponding boundary conditions. The models are verified by the finite element method (FEM) implemented in FlexPDE, the suitability of the obtained models is investigated
depending on the relative thickness parameter of the rectangle. The inverse problem of reconstructing
Poisson’s ratio and Young’s modulus from information on the displacement field on the lateral face is solved. |
| Keywords |
plane stress state, Kantorovich method, Lagrange variational principle, simplified model, Poisson’s ratio, Young’s modulus, inverse problem |
| Received |
17 June 2025 | Revised |
30 June 2025 | Accepted |
01 July 2025 |
| Link to Fulltext |
|
| << Previous article | Volume 60, Issue 6 / 2025 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English