{"title":"非格林弹性固体二维梁剪应力的近似测定","authors":"Roger Bustamante","doi":"10.1177/10812865231201623","DOIUrl":null,"url":null,"abstract":"Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"46 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid\",\"authors\":\"Roger Bustamante\",\"doi\":\"10.1177/10812865231201623\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.\",\"PeriodicalId\":49854,\"journal\":{\"name\":\"Mathematics and Mechanics of Solids\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics and Mechanics of Solids\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1177/10812865231201623\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Mechanics of Solids","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/10812865231201623","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid
Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.
期刊介绍：
Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science.
The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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