2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase
ISSN: 2168-9873

# Journal of Applied Mechanical EngineeringOpen Access

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## 2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase

Kallel A* and Bouabdallah S

Pôle Universitaire Léonard De Vinci, De Vinci Reserach Center, Paris La Défense, France

Laboratoire Roberval UMR 7337, Université Technologique de Compiègne, 60205 Compiègne, France

*Corresponding Author:
Kallel A Pôle Universitaire Léonard de Vinci
De Vinci Reserach Center, Paris La Défense, France
Tel: +33 1 41 16 70 00
E-mail: [email protected]

Received Date: June 14, 2017; Accepted Date: June 30, 2017; Published Date: July 04, 2017

Citation: Kallel A, Bouabdallah S (2017) 2d Frictional B-Spline Smoothed Mortar Contact Problems Part II: Resolution Phase. J Appl Mech Eng 6:275. doi: 10.4172/2168-9873.1000275

Copyright: © 2017 Kallel A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

### Abstract

We detailed in this paper three formulations for the resolution of a contact problem by mortar method. The penalty method is a simple technique which does not introduce new unknowns which can increase the size of the system to be solved. But this formulation suffers of conditioning problems especially when the penalty coefficient becomes very high. The Lagrange multipliers method is more accurate than the penalty formulation. The multiplier λN represents in the contact surface the exact value of the normal contact effort. This approach requires additional variables which are the Lagrange multiplier in the contact interface nodes. The augmented Lagrange method is a combination between the penalty formulation and the Lagrange multipliers method. The contact constraints are applied by a Lagrange multiplier approached without increasing the problem size. The penalty coefficient in this method has less influence on the quality of the result and the robustness of the solution than in the penalty formulation.

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