{"title":"Projection-iterative modification of the method of local variations for problems with a quadratic functional","authors":"E.L. Hart, V.S. Hudramovich","doi":"10.1016/j.jappmathmech.2016.06.005","DOIUrl":null,"url":null,"abstract":"<div><p>A projection-iterative scheme of realization of the method of local variations for solving variational problems<span> with a quadratic functional is proposed. The convergence of the proposed scheme to the use of functional analysis is investigated. For the case of solving problems of the local stability of a spherical shell, the practical effectiveness of the proposed modification of the method of local variations is shown.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 2","pages":"Pages 156-163"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.06.005","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892816300788","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: 12
Abstract
A projection-iterative scheme of realization of the method of local variations for solving variational problems with a quadratic functional is proposed. The convergence of the proposed scheme to the use of functional analysis is investigated. For the case of solving problems of the local stability of a spherical shell, the practical effectiveness of the proposed modification of the method of local variations is shown.
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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