{"title":"Internal Stresses in an Elastic Half-space under Discrete Contact Conditions","authors":"I. G. Goryacheva, A. A. Yakovenko","doi":"10.1134/s0081543823040089","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the contact interaction of a periodic system of axisymmetric rigid indenters with two height levels with an elastic half-space in the absence of friction forces. To construct a solution of the problem, we use the localization method. We obtain analytical expressions for the characteristics of the contact interaction (the radius of contact spots and the distribution of contact pressure) as well as for the components of the internal stress tensor on the symmetry axes of indenters of both levels. We analyze the effect of the shape of the contact surface of indenters, which is described by a power function (with arbitrary integer exponent), and the spatial arrangement of indenters on the contact characteristics and the stressed state of the elastic half-space. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"70 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823040089","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the contact interaction of a periodic system of axisymmetric rigid indenters with two height levels with an elastic half-space in the absence of friction forces. To construct a solution of the problem, we use the localization method. We obtain analytical expressions for the characteristics of the contact interaction (the radius of contact spots and the distribution of contact pressure) as well as for the components of the internal stress tensor on the symmetry axes of indenters of both levels. We analyze the effect of the shape of the contact surface of indenters, which is described by a power function (with arbitrary integer exponent), and the spatial arrangement of indenters on the contact characteristics and the stressed state of the elastic half-space.
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
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