{"title":"两个弹性横向各向同性半空间接触相互作用的数学建模,其中一个半空间包含一个椭圆截面的近表面凹槽","authors":"V. Kirilyuk, O. Levchuk, V. Gavrilenko","doi":"10.20535/srit.2308-8893.2022.1.09","DOIUrl":null,"url":null,"abstract":"On the basis of a mathematical model, the problem of compression of two elastic transversely isotropic half-spaces, one of which contains a shallow near-surface groove of an elliptical section, is considered. The solution to the problem is obtained using the Elliott representation for a transversely isotropic body in terms of harmonic functions, classical harmonic potentials and reducing the boundary value problem to considering an integro-differential equation with an unknown domain of integration. As a special case, the obtained analytical expressions yield the basic parameters of the contact of transversely isotropic half-spaces in the presence of an axisymmetric groove in one of them, as well as the parameters of the contact interaction of two elastic isotropic half-spaces, one of which contains an elliptical cross-section groove. Numerical results are obtained, the influence of elastic properties of half-spaces, geometrical parameters of groove and loading on contact interaction and closing of the gap between bodies is studied.","PeriodicalId":330635,"journal":{"name":"System research and information technologies","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical modeling of the contact interaction of two elastic transversely isotropic half-spaces, one of which contains a near-surface groove of an elliptical section\",\"authors\":\"V. Kirilyuk, O. Levchuk, V. Gavrilenko\",\"doi\":\"10.20535/srit.2308-8893.2022.1.09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"On the basis of a mathematical model, the problem of compression of two elastic transversely isotropic half-spaces, one of which contains a shallow near-surface groove of an elliptical section, is considered. The solution to the problem is obtained using the Elliott representation for a transversely isotropic body in terms of harmonic functions, classical harmonic potentials and reducing the boundary value problem to considering an integro-differential equation with an unknown domain of integration. As a special case, the obtained analytical expressions yield the basic parameters of the contact of transversely isotropic half-spaces in the presence of an axisymmetric groove in one of them, as well as the parameters of the contact interaction of two elastic isotropic half-spaces, one of which contains an elliptical cross-section groove. Numerical results are obtained, the influence of elastic properties of half-spaces, geometrical parameters of groove and loading on contact interaction and closing of the gap between bodies is studied.\",\"PeriodicalId\":330635,\"journal\":{\"name\":\"System research and information technologies\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"System research and information technologies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.20535/srit.2308-8893.2022.1.09\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"System research and information technologies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20535/srit.2308-8893.2022.1.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mathematical modeling of the contact interaction of two elastic transversely isotropic half-spaces, one of which contains a near-surface groove of an elliptical section
On the basis of a mathematical model, the problem of compression of two elastic transversely isotropic half-spaces, one of which contains a shallow near-surface groove of an elliptical section, is considered. The solution to the problem is obtained using the Elliott representation for a transversely isotropic body in terms of harmonic functions, classical harmonic potentials and reducing the boundary value problem to considering an integro-differential equation with an unknown domain of integration. As a special case, the obtained analytical expressions yield the basic parameters of the contact of transversely isotropic half-spaces in the presence of an axisymmetric groove in one of them, as well as the parameters of the contact interaction of two elastic isotropic half-spaces, one of which contains an elliptical cross-section groove. Numerical results are obtained, the influence of elastic properties of half-spaces, geometrical parameters of groove and loading on contact interaction and closing of the gap between bodies is studied.