{"title":"各向异性矩的定义方程线性弹性理论与二维约束旋转纯剪切问题","authors":"B. D. Annin, N. I. Ostrosablin, R. I. Ugryumov","doi":"10.1134/S1990478923010015","DOIUrl":null,"url":null,"abstract":"<p> The paper presents the equations of the linear moment theory of elasticity for the case of\narbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetric\ncomponents are distinguished in the defining relations. Some simplified versions of linear defining\nrelations are considered. The possibility of Cauchy elasticity is allowed when material tensors of\nthe fourth rank do not have the main symmetry. For material tensors that determine force and\ncouple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of an\nelastic moment medium. For the case of plane deformation and constrained rotation, an example\nof a complete solution of the two-dimensional problem is given when there are only shear stresses.\nThe solutions turn out to be significantly different for anisotropic and isotropic elastic media.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 1","pages":"1 - 14"},"PeriodicalIF":0.5800,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation\",\"authors\":\"B. D. Annin, N. I. Ostrosablin, R. I. Ugryumov\",\"doi\":\"10.1134/S1990478923010015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The paper presents the equations of the linear moment theory of elasticity for the case of\\narbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetric\\ncomponents are distinguished in the defining relations. Some simplified versions of linear defining\\nrelations are considered. The possibility of Cauchy elasticity is allowed when material tensors of\\nthe fourth rank do not have the main symmetry. For material tensors that determine force and\\ncouple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of an\\nelastic moment medium. For the case of plane deformation and constrained rotation, an example\\nof a complete solution of the two-dimensional problem is given when there are only shear stresses.\\nThe solutions turn out to be significantly different for anisotropic and isotropic elastic media.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"17 1\",\"pages\":\"1 - 14\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2023-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478923010015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923010015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation
The paper presents the equations of the linear moment theory of elasticity for the case of
arbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetric
components are distinguished in the defining relations. Some simplified versions of linear defining
relations are considered. The possibility of Cauchy elasticity is allowed when material tensors of
the fourth rank do not have the main symmetry. For material tensors that determine force and
couple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of an
elastic moment medium. For the case of plane deformation and constrained rotation, an example
of a complete solution of the two-dimensional problem is given when there are only shear stresses.
The solutions turn out to be significantly different for anisotropic and isotropic elastic media.
期刊介绍:
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.