{"title":"The Moment-Membrane Theory of Elastic Flexible Plates as a Continual Geometrically Nonlinear Theory of a Graphene Sheet","authors":"S. H. Sargsyan","doi":"10.1134/S1028335823040055","DOIUrl":null,"url":null,"abstract":"<p>A geometrically nonlinear moment-membrane theory of elastic plates has been built as a continual theory of deformations of flexible graphene under the assumption of smallness of deformations, bending-torsional characteristics, and angles of rotation (including a free one) of plate elements on the basis of the 3D geometrically nonlinear moment theory of elasticity with preservation of only the nonlinear terms that come from normal displacement (deflection) and its derivatives. For this nonlinear theory of elastic plates, the resolving equations are presented also in mixed form by introducing stress functions: this is a system of equilibrium equations for the transverse bending deformation compiled in the deformed state of the plate and the deformation continuity equations expressed by the stress and deflection functions. The Lagrangian-type variational principle for the geometrically nonlinear moment-membrane theory of elastic plates has been established.</p>","PeriodicalId":533,"journal":{"name":"Doklady Physics","volume":"68 4","pages":"125 - 130"},"PeriodicalIF":0.6000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1028335823040055","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
A geometrically nonlinear moment-membrane theory of elastic plates has been built as a continual theory of deformations of flexible graphene under the assumption of smallness of deformations, bending-torsional characteristics, and angles of rotation (including a free one) of plate elements on the basis of the 3D geometrically nonlinear moment theory of elasticity with preservation of only the nonlinear terms that come from normal displacement (deflection) and its derivatives. For this nonlinear theory of elastic plates, the resolving equations are presented also in mixed form by introducing stress functions: this is a system of equilibrium equations for the transverse bending deformation compiled in the deformed state of the plate and the deformation continuity equations expressed by the stress and deflection functions. The Lagrangian-type variational principle for the geometrically nonlinear moment-membrane theory of elastic plates has been established.
期刊介绍：
Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.
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