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Frictionless Contact (frictionless + contact)

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Engineering100%

Selected Abstracts

A dual mortar approach for 3D finite deformation contact with consistent linearization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010
Alexander Popp
Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source]

A modified node-to-segment algorithm passing the contact patch test

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
Giorgio Zavarise
Abstract Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Symmetry preserving algorithm for large displacement frictionless contact by the pre-discretization penalty method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
D. Gabriel
Abstract A three-dimensional contact algorithm based on the pre-discretization penalty method is presented. Using the pre-discretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation of the problem and allows an easy incorporation of higher-order elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. The proposed algorithm utilizes the BFGS method modified for constrained non-linear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Non-linear dynamic contact of thin-walled structures

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
Thomas Cichosz
In many areas of mechanical engineering contact problems of thin,walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment,rotation characteristics of a bolted beam,column joint, contact occurs. Effective simulation of these and other contact problems, especially in three,dimensional non,linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin,walled character and dynamic effects into account. We use a segment,to,segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized-, Method and the Generalized Energy,Momentum Method. Using the "Velocity,Update" Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

The p-version of the FEM for computational contact mechanics

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
David Franke
Contact analyses are being performed in various engineering applications. Here, like in most other fields, FE codes are based on low order elements using linear or quadratic shape functions. The intention of this paper is to show that finite elements with shape functions of high polynomial degree (p -FEM) are a very attractive alternative to low order elements, even for computational contact mechanics. One of the advantages is the possibility to enhance the element formulation with the blending function method in order to accurately discretize the given geometry, which leads in combination with high convergence rates to very efficient computations. In order to solve the problem of frictionless contact, a penalty formulation is applied in this work. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]