{"title":"On the Dynamic Tension of a Thin Round Perfectly Rigid-Plastic Layer Made of Transversely Isotropic Material","authors":"I. M. Tsvetkov","doi":"10.1134/s0012266124030078","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a system of equations modeling the dynamic tension of a homogeneous round\nlayer of incompressible perfectly rigid-plastic transversely isotropic material obeying the\nMises–Hencky criterion. The upper and lower bases are stress-free, the radial velocity is set on the\nlateral boundary, and the possibility of thickening or thinning of the layer, simulating formation\nand further development of a neck, is taken into account. Using the method of asymptotic\nintegration, two characteristic tension modes are identified, that is, relations of dimensionless\nparameters are determined that necessitate taking into account inertial terms. An approximate\nsolution of the problem is constructed when considering the mode associated with the acceleration\non the lateral face reaching its critical values.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"49 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030078","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study a system of equations modeling the dynamic tension of a homogeneous round
layer of incompressible perfectly rigid-plastic transversely isotropic material obeying the
Mises–Hencky criterion. The upper and lower bases are stress-free, the radial velocity is set on the
lateral boundary, and the possibility of thickening or thinning of the layer, simulating formation
and further development of a neck, is taken into account. Using the method of asymptotic
integration, two characteristic tension modes are identified, that is, relations of dimensionless
parameters are determined that necessitate taking into account inertial terms. An approximate
solution of the problem is constructed when considering the mode associated with the acceleration
on the lateral face reaching its critical values.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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