{"title":"非增量法在基于张量矩阵的轴对称大应变有限元分析中的应用","authors":"V. V. Chekhov","doi":"10.1134/S002565442460377X","DOIUrl":null,"url":null,"abstract":"<p>For the tensor-matrix FEM system of equations describing the final state of large deformations of an incompressible elastic body, a development to solve axisymmetric problems is obtained. Also, analytical expressions for the components of the partial derivatives matrix of the system are obtained. Examples of calculating the everted state of a circular cylinder, as well as analysis of sealing rings are described.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 5","pages":"2763 - 2775"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of the Non-Incremental Approach to Axisymmetric FEM Analysis of Large Strain in Tensor-Based Matrix Form\",\"authors\":\"V. V. Chekhov\",\"doi\":\"10.1134/S002565442460377X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For the tensor-matrix FEM system of equations describing the final state of large deformations of an incompressible elastic body, a development to solve axisymmetric problems is obtained. Also, analytical expressions for the components of the partial derivatives matrix of the system are obtained. Examples of calculating the everted state of a circular cylinder, as well as analysis of sealing rings are described.</p>\",\"PeriodicalId\":697,\"journal\":{\"name\":\"Mechanics of Solids\",\"volume\":\"59 5\",\"pages\":\"2763 - 2775\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S002565442460377X\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S002565442460377X","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Application of the Non-Incremental Approach to Axisymmetric FEM Analysis of Large Strain in Tensor-Based Matrix Form
For the tensor-matrix FEM system of equations describing the final state of large deformations of an incompressible elastic body, a development to solve axisymmetric problems is obtained. Also, analytical expressions for the components of the partial derivatives matrix of the system are obtained. Examples of calculating the everted state of a circular cylinder, as well as analysis of sealing rings are described.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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