{"title":"Variational formulation of dynamic problems for a nonlinear Cosserat medium","authors":"E.V. Zdanchuk, V.V. Kuroyedov, V.V. Lalin, I.I. Lalina, E.A. Provatorova","doi":"10.1016/j.jappmathmech.2017.07.007","DOIUrl":null,"url":null,"abstract":"<div><p><span>A variational formulation of </span>dynamic problems<span><span> for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity<span> vectors are calculated. The equivalence of the Euler equations with </span></span>natural boundary conditions<span> to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 66-70"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.007","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892817300436","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
A variational formulation of dynamic problems for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity vectors are calculated. The equivalence of the Euler equations with natural boundary conditions to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.
期刊介绍：
This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.
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