Ionel-Dumitrel Ghiba, Mircea Bîrsan, Patrizio Neff
{"title":"一个包含至多\\(O(h^{5})\\项的线性各向同性Cosserat壳层模型。存在与唯一","authors":"Ionel-Dumitrel Ghiba, Mircea Bîrsan, Patrizio Neff","doi":"10.1007/s10659-022-09981-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we derive the linear elastic Cosserat shell model incorporating in the variational problem effects up to order <span>\\(O(h^{5})\\)</span> in the shell thickness <span>\\(h\\)</span> as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The existence and uniqueness of the solution is proven in suitable admissible sets. To this end, inequalities of Korn-type for shells are established which allow to show coercivity in the Lax-Milgram theorem. We are also showing an existence and uniqueness result for a truncated <span>\\(O(h^{3})\\)</span> model. Main issue is the suitable treatment of the curved reference configuration of the shell. Some connections to the classical Koiter membrane-bending model are highlighted.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A Linear Isotropic Cosserat Shell Model Including Terms up to \\\\(O(h^{5})\\\\). Existence and Uniqueness\",\"authors\":\"Ionel-Dumitrel Ghiba, Mircea Bîrsan, Patrizio Neff\",\"doi\":\"10.1007/s10659-022-09981-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we derive the linear elastic Cosserat shell model incorporating in the variational problem effects up to order <span>\\\\(O(h^{5})\\\\)</span> in the shell thickness <span>\\\\(h\\\\)</span> as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The existence and uniqueness of the solution is proven in suitable admissible sets. To this end, inequalities of Korn-type for shells are established which allow to show coercivity in the Lax-Milgram theorem. We are also showing an existence and uniqueness result for a truncated <span>\\\\(O(h^{3})\\\\)</span> model. Main issue is the suitable treatment of the curved reference configuration of the shell. Some connections to the classical Koiter membrane-bending model are highlighted.</p></div>\",\"PeriodicalId\":624,\"journal\":{\"name\":\"Journal of Elasticity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Elasticity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10659-022-09981-6\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-022-09981-6","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
A Linear Isotropic Cosserat Shell Model Including Terms up to \(O(h^{5})\). Existence and Uniqueness
In this paper we derive the linear elastic Cosserat shell model incorporating in the variational problem effects up to order \(O(h^{5})\) in the shell thickness \(h\) as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The existence and uniqueness of the solution is proven in suitable admissible sets. To this end, inequalities of Korn-type for shells are established which allow to show coercivity in the Lax-Milgram theorem. We are also showing an existence and uniqueness result for a truncated \(O(h^{3})\) model. Main issue is the suitable treatment of the curved reference configuration of the shell. Some connections to the classical Koiter membrane-bending model are highlighted.
期刊介绍:
The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.