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Mathematical Problems in Engineering
Volume 2014, Article ID 465935, 10 pages
Research Article

Mixed Finite Element Method for Static and Dynamic Contact Problems with Friction and Initial Gaps

College of Water Conservancy and Hydropower, Hohai University, Xikang Road, Nanjing 210098, China

Received 27 February 2014; Accepted 28 July 2014; Published 26 August 2014

Academic Editor: Delfim Soares Jr.

Copyright © 2014 Lanhao Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel mixed finite element method is proposed for static and dynamic contact problems with friction and initial gaps. Based on the characteristic of local nonlinearity for the problem, the system of forces acting on the contactor is divided into two parts: external forces and contact forces. The displacement of structure is chosen as the basic variable and the nodal contact force in contact region under local coordinate system is selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. In this way, the sophisticated contact nonlinearity is revealed by the variety of the contact forces which are determined by the external load and the contact state stick, slip, or separation. Moreover, in the case of multibody contact problem, the flexibility matrix is symmetric and sparse; thus, the iterative procedure becomes easily carried out and much more economical. In the paper, both the finite element formulations and the iteration process are given in detail for static and dynamic contact problems. Four examples are included to demonstrate the accuracy and applicability of the presented method.