横向各向同性固体线性弹性力学中的两类精确解法

IF 1.1 4区数学 Q1 MATHEMATICS

Ricerche di Matematica Pub Date : 2024-01-13 DOI:10.1007/s11587-023-00845-2

Kumbakonam R. Rajagopal, Giuseppe Saccomandi, Luigi Vergori

{"title":"横向各向同性固体线性弹性力学中的两类精确解法","authors":"Kumbakonam R. Rajagopal, Giuseppe Saccomandi, Luigi Vergori","doi":"10.1007/s11587-023-00845-2","DOIUrl":null,"url":null,"abstract":"<p>Due to the formal resemblance of some models for the Cauchy stress tensor of elastic solids and viscous fluids, some classes of exact solutions for the equations governing the flows in Navier–Stokes fluids have been generalized to linear and nonlinear elastodynamics. In this paper, we study the conditions under which two special classes of generalized Beltrami flows, the vortices in lattice form and Kelvin’s cat’s eye solutions, are solutions of the equations governing the motions in a linearly elastic transversely isotropic solid.\n</p>","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids\",\"authors\":\"Kumbakonam R. Rajagopal, Giuseppe Saccomandi, Luigi Vergori\",\"doi\":\"10.1007/s11587-023-00845-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Due to the formal resemblance of some models for the Cauchy stress tensor of elastic solids and viscous fluids, some classes of exact solutions for the equations governing the flows in Navier–Stokes fluids have been generalized to linear and nonlinear elastodynamics. In this paper, we study the conditions under which two special classes of generalized Beltrami flows, the vortices in lattice form and Kelvin’s cat’s eye solutions, are solutions of the equations governing the motions in a linearly elastic transversely isotropic solid.\\n</p>\",\"PeriodicalId\":21373,\"journal\":{\"name\":\"Ricerche di Matematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ricerche di Matematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11587-023-00845-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ricerche di Matematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11587-023-00845-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

由于弹性固体和粘性流体的 Cauchy 应力张量的某些模型在形式上相似，纳维-斯托克斯流体流动方程的某些精确解类已被推广到线性和非线性弹性动力学中。在本文中，我们研究了两类特殊的广义贝尔特拉米流（晶格形式的涡流和开尔文猫眼解）是线性弹性横向各向同性固体运动方程的解的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids

查看原文本刊更多论文

Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids

Due to the formal resemblance of some models for the Cauchy stress tensor of elastic solids and viscous fluids, some classes of exact solutions for the equations governing the flows in Navier–Stokes fluids have been generalized to linear and nonlinear elastodynamics. In this paper, we study the conditions under which two special classes of generalized Beltrami flows, the vortices in lattice form and Kelvin’s cat’s eye solutions, are solutions of the equations governing the motions in a linearly elastic transversely isotropic solid.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Ricerche di Matematica Mathematics-Applied Mathematics

CiteScore

3.00

自引率

8.30%

发文量

期刊介绍： “Ricerche di Matematica” publishes high-quality research articles in any field of pure and applied mathematics. Articles must be original and written in English. Details about article submission can be found online.