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A solution approach for contact problems based on the dual interpolation boundary face method

Zhang, Jianming; Shu, Xiaomin; Trevelyan, Jon; Lin, Weicheng; Chai, Pengfei


Jianming Zhang

Xiaomin Shu

Weicheng Lin

Pengfei Chai


The recently proposed dual interpolation boundary face method (DiBFM) has been shown to have a much higher accuracy and improved convergence rates compared with the traditional boundary element method. In addition, the DiBFM has the ability to approximate both continuous and discontinuous fields, and this provides a way to approximate the discontinuous pressure at a contact boundary. This paper presents a solution approach for two dimensional frictionless and frictional contact problems based on the DiBFM. The solution approach is divided into outer and inner iterations. In the outer iteration, the size of the contact zone is determined. Then the elements near the contact boundary are updated to approximate the discontinuous pressure. The inner iteration is used to determine the contact state (sticking or sliding), and is only performed for frictional contact problems. To make the system of equations solvable, the contact constraints and some supplementary equations are also given. Several numerical examples demonstrate the validity and high accuracy of the proposed approach. Furthermore, due to the continuity of elements in DiBFM and the detection of the contact boundary, the pressure oscillations near the contact boundary can be treated.


Zhang, J., Shu, X., Trevelyan, J., Lin, W., & Chai, P. (2019). A solution approach for contact problems based on the dual interpolation boundary face method. Applied Mathematical Modelling, 70, 643-658.

Journal Article Type Article
Acceptance Date Feb 6, 2019
Online Publication Date Feb 13, 2019
Publication Date Jun 30, 2019
Deposit Date Feb 14, 2019
Journal Applied Mathematical Modelling
Print ISSN 0307-904X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 70
Pages 643-658