 | | 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: | | 13217 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8152
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| In English (Mech. Solids): | | 5065 |
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| A.H. Sargsyan and S.H. Sargsyan, "Stability of the Plane Stressed State of the Graphene Sheet Based on the Moment-Membrane Theory of Elastic Plates," Mech. Solids. 60 (3), 1605-1624 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
3 |
Pages |
1605-1624 |
| DOI |
10.1134/S0025654424604853 |
| Title |
Stability of the Plane Stressed State of the Graphene Sheet Based on the Moment-Membrane Theory of Elastic Plates |
| Author(s) |
A.H. Sargsyan (Shirak State University after M. Nalbandyan, Gyumri, 3126 Armenia, armenuhis@gmail.com)
S.H. Sargsyan (Shirak State University after M. Nalbandyan, Gyumri, 3126 Armenia, s_sargsyan@yahoo.com) |
| Abstract |
Two-dimensional nanomaterials (graphene, carbon nanotube) are high-strength and ultra-light materials that have several promising areas of application. From theoretical and applied perspectives, it is relevant to study various problems of their statics, stability, vibrations, and calculations of the required mechanical characteristics based on the corresponding continuum theory of the deformation behavior of two-dimensional nanomaterials.
In this work, based on the moment-membrane theory of elastic plates, which is interpreted as the continuum theory of the deformation behavior of graphene, stability problems of a freely supported graphene sheet (rectangular plate) are studied. The sheet is uniformly compressed in one direction, compressed in two directions, and subjected to shear stresses in its plane. The stability problem of uniformly compressed graphene sheets, freely supported on two opposite sides and having different boundary conditions on the other two sides, is also considered.
When solving stability problems of the graphene sheet (rectangular plate), the Euler method is applied, considering a form of equilibrium that is slightly deviated from the initial (moment-free) position (buckled plate). Differential equilibrium equations and boundary conditions are formulated for this shape. The critical load value is determined from the solution of these boundary problems, i.e., the load value at which the initial flat form of the plate becomes unstable. All solutions are accompanied by numerical results: tables or diagrams providing the critical load values for each particular case. |
| Keywords |
graphene sheet, moment membrane theory of plates, stability of the initially compressed state, critical loads |
| Received |
29 July 2024 | Revised |
29 September 2024 | Accepted |
01 November 2024 |
| Link to Fulltext |
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