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

authored by: Wei Long Fan, Xiao Wei Gao, Yong Tong Zheng, Bing Bing Xu, Hai Feng Peng
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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
Nanchang University
Type: Article
Journal: Engineering with computers
No. of pages: 19
ISSN: 0177-0667
Publication date: 09.04.2024
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Modelling and Simulation, Engineering(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1007/s00366-024-01963-7 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{e6e5abebd7a8488e8791854082208326,
title = "Element differential method for contact problems with non-conforming contact discretization",
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.",
keywords = "Contact problems, Element differential method, Non-conforming contact discretization, Point collocation method, Strong-form formulation",
author = "Fan, {Wei Long} and Gao, {Xiao Wei} and Zheng, {Yong Tong} and Xu, {Bing Bing} and Peng, {Hai Feng}",
note = "Funding Information: This work was supported by the National Natural Science Foundation of China (12072064,12272081) and the Natural Science Foundation of Liaoning Province, China (2022-MS-138).",
year = "2024",
month = apr,
day = "9",
doi = "10.1007/s00366-024-01963-7",
language = "English",
journal = "Engineering with computers",
issn = "0177-0667",
publisher = "Springer London",
}