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

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
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引用次数: 0

Abstract

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.

Abstract Image

接触问题的元素微分法与非符合接触离散化
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。
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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.
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