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A weighted point-based formulation for isogeometric contact.pdf
Available online at
ScienceDirect
Comput. Methods Appl. Mech. Engrg. 308 (2016) 73–95
/locate/cma
A weighted point-based formulation for isogeometric contact
M.E. Matzen?, M. Bischoff
Institute of Structural Mechanics, University of Stuttgart, Pfaffenwaldring 7, D-70550 Stuttgart, Germany Received 11 February 2016; received in revised form 7 April 2016; accepted 8 April 2016 Available online 21 May 2016
Abstract
In the context of isogeometric contact analysis, surfaces of objects can be described smoothly due to the high continuity of the involved shape functions. This facilitates construction of a continuous normal field which may be beneficial for modeling of contact problems. This property allows for stable collocation of the virtual contact work using considerable less evaluation points than numerical integration, while the approximation quality of the computational results is almost the same. In this context, a weighted point-based method (PTS+) is introduced as an extension of the Point-To-Segment method (PTS) proposed previously by Matzen et al. (2013). The weights enable transmission of contact stresses instead of contact forces along the contact surfaces. In normal direction the non-penetration condition is enforced by the Lagrange multiplier method, combined with the penalty method in tangential direction. Corresponding to the collocation weights, a constant or NURBS Lagrange multiplier field is introduced. A comparison between the collocation-based contact formulations PTS, PTS+ and a mortar method is drawn, showing that weighted collocation is able to achieve almost the same accuracy as the integration-based mortar formulation. ?c 2016 Elsevier B.V. All rights reserved.
Keywords: Isogeometric contact; Point-To-Segment; Weighted collocation; Friction
1. Introduction
Computational contact formulations, exploiting higher continuity and smoothness of the involved function spaces have been one of the first and most obvious applications of the isogeometric co
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