{"title":"The effect of surface stresses on the stress–strain state of shells","authors":"N.N. Rogacheva","doi":"10.1016/j.jappmathmech.2016.06.011","DOIUrl":null,"url":null,"abstract":"<div><p><span>The effect of surface stresses on the stress–strain state (SSS) of an elastic shell is investigated. The surface stresses are represented as a static pre-loading localized in ultra-thin layers of the shell close to its surface. It is assumed that the mechanical properties of the surface layers differ from the properties of the material far from the surface. The three-dimensional elasticity equations are analysed by an </span>asymptotic method<span> using several asymptotic parameters. Equations are obtained by the method of reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of shell theory in which surface stresses have to be taken into account for a sufficiently small shell thickness. Asymptotic estimates<span> of the effect of surface stresses on the SSS are obtained as a function of the ratio of the elastic moduli of the shell material and of the layer close to the surface, the ratio of the shell thickness to the thickness of the surface layer and the type of SSS and its variability with respect to the coordinates.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 2","pages":"Pages 173-181"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.06.011","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892816300855","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: 7
Abstract
The effect of surface stresses on the stress–strain state (SSS) of an elastic shell is investigated. The surface stresses are represented as a static pre-loading localized in ultra-thin layers of the shell close to its surface. It is assumed that the mechanical properties of the surface layers differ from the properties of the material far from the surface. The three-dimensional elasticity equations are analysed by an asymptotic method using several asymptotic parameters. Equations are obtained by the method of reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of shell theory in which surface stresses have to be taken into account for a sufficiently small shell thickness. Asymptotic estimates of the effect of surface stresses on the SSS are obtained as a function of the ratio of the elastic moduli of the shell material and of the layer close to the surface, the ratio of the shell thickness to the thickness of the surface layer and the type of SSS and its variability with respect to the coordinates.
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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