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

Zhang, Jianming and Shu, Xiaomin and Trevelyan, Jon and Lin, Weicheng and Chai, Pengfei (2019) 'A solution approach for contact problems based on the dual interpolation boundary face method.', Applied mathematical modelling., 70 . pp. 643-658.


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.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
File format - PDF
Publisher Web site:
Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:06 February 2019
Date deposited:14 February 2019
Date of first online publication:13 February 2019
Date first made open access:13 February 2020

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