接触问题的元素微分法与非符合接触离散化

IF 8.7 2区 工程技术 Q1 Mathematics
Wei-Long Fan, Xiao-Wei Gao, Yong-Tong Zheng, Bing-Bing Xu, Hai-Feng Peng
{"title":"接触问题的元素微分法与非符合接触离散化","authors":"Wei-Long Fan, Xiao-Wei Gao, Yong-Tong Zheng, Bing-Bing Xu, Hai-Feng Peng","doi":"10.1007/s00366-024-01963-7","DOIUrl":null,"url":null,"abstract":"<p>In this paper, a new strong-form numerical method, the element differential method (EDM) is employed to solve two- and three-dimensional contact problems without friction. When using EDM, one can obtain the system of equations by directly differentiating the shape functions of Lagrange isoparametric elements for characterizing physical variables and geometry without the variational principle or any integration. Non-uniform contact discretization is used to enhance contact conditions, which avoids performing identical discretization along the contact surfaces of two contact objects. Two methods for imposing contact constraints are proposed. One method imposes Neumann boundary conditions on the contact surface, whereas the other directly applies the contact constraints as collocation equations for the nodes within the contact zone. The accuracy of the two methods is similar, but the multi-point constraints method does not increase the degrees of freedom of the system equations during the iteration process. The results of four numerical examples have verified the accuracy of the proposed method.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Element differential method for contact problems with non-conforming contact discretization\",\"authors\":\"Wei-Long Fan, Xiao-Wei Gao, Yong-Tong Zheng, Bing-Bing Xu, Hai-Feng Peng\",\"doi\":\"10.1007/s00366-024-01963-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, a new strong-form numerical method, the element differential method (EDM) is employed to solve two- and three-dimensional contact problems without friction. When using EDM, one can obtain the system of equations by directly differentiating the shape functions of Lagrange isoparametric elements for characterizing physical variables and geometry without the variational principle or any integration. Non-uniform contact discretization is used to enhance contact conditions, which avoids performing identical discretization along the contact surfaces of two contact objects. Two methods for imposing contact constraints are proposed. One method imposes Neumann boundary conditions on the contact surface, whereas the other directly applies the contact constraints as collocation equations for the nodes within the contact zone. The accuracy of the two methods is similar, but the multi-point constraints method does not increase the degrees of freedom of the system equations during the iteration process. The results of four numerical examples have verified the accuracy of the proposed method.</p>\",\"PeriodicalId\":11696,\"journal\":{\"name\":\"Engineering with Computers\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.7000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering with Computers\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s00366-024-01963-7\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering with Computers","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00366-024-01963-7","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

本文采用了一种新的强形式数值方法--元素微分法(EDM)来求解无摩擦的二维和三维接触问题。使用 EDM 时,无需变分原理或任何积分,通过直接微分表征物理变量和几何形状的拉格朗日等参数元素的形状函数,即可获得方程系统。非均匀接触离散化用于增强接触条件,避免沿两个接触物体的接触面进行相同的离散化。提出了两种施加接触约束的方法。一种方法在接触面上施加 Neumann 边界条件,而另一种方法则直接将接触约束条件作为接触区域内节点的配位方程。两种方法的精度相似,但多点约束方法在迭代过程中不会增加系统方程的自由度。四个数值实例的结果验证了所提方法的准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Element differential method for contact problems with non-conforming contact discretization

Element differential method for contact problems with non-conforming contact discretization

In this paper, a new strong-form numerical method, the element differential method (EDM) is employed to solve two- and three-dimensional contact problems without friction. When using EDM, one can obtain the system of equations by directly differentiating the shape functions of Lagrange isoparametric elements for characterizing physical variables and geometry without the variational principle or any integration. Non-uniform contact discretization is used to enhance contact conditions, which avoids performing identical discretization along the contact surfaces of two contact objects. Two methods for imposing contact constraints are proposed. One method imposes Neumann boundary conditions on the contact surface, whereas the other directly applies the contact constraints as collocation equations for the nodes within the contact zone. The accuracy of the two methods is similar, but the multi-point constraints method does not increase the degrees of freedom of the system equations during the iteration process. The results of four numerical examples have verified the accuracy of the proposed method.

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
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信