article

Alternative integration algorithms for three-dimensional mortar contact

Authors:

M. BischoffAuthors Info & Claims

Computational Mechanics, Volume 59, Issue 2

Pages 203 - 218

https://doi.org/10.1007/s00466-016-1345-4

Published: 01 February 2017 Publication History

Abstract

In this paper, a new approach is proposed to improve efficiency of the integration procedure for mortar integrals within finite element mortar methods for contact. Appropriate approaches subdivide polygonal integration segments into triangular integration cells where well-established quadrature rules can be applied for numerical integration. Here, a subdivision of segments into quadrilateral integration cells is proposed and investigated in detail. By this procedure, the numerical effort is decreased because the number of integration cells is smaller and less quadrature points are needed. In all the aforementioned methods, necessary projections of integration points result in rational polynomials in the integrand. Thus, an exact numerical integration is impossible. Using quadrilateral integration cells additionally involves non-constant Jacobian determinants which further increases the polynomial degree of the integrand. Numerical experiments indicate, that the resulting increase in the error is small enough to be acceptable in consideration of the gained speed-up.

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Cited By

Mayr MPopp A(2023)Scalable computational kernels for mortar finite element methodsEngineering with Computers10.1007/s00366-022-01779-339:5(3691-3720)Online publication date: 25-Jan-2023
https://dl.acm.org/doi/10.1007/s00366-022-01779-3
Duong TLorenzis LSauer R(2019)A segmentation-free isogeometric extended mortar contact methodComputational Mechanics10.1007/s00466-018-1599-063:2(383-407)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s00466-018-1599-0
Song YYoun SPark K(2017)Virtual gap element approach for the treatment of non-matching interface using three-dimensional solid elementsComputational Mechanics10.5555/3158457.315848060:4(585-594)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.5555/3158457.3158480

Alternative integration algorithms for three-dimensional mortar contact
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Computational Mechanics

Computational Mechanics Volume 59, Issue 2

February 2017

168 pages

ISSN:0178-7675

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Copyright © Copyright © 2017 Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 February 2017

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Cited By

Mayr MPopp A(2023)Scalable computational kernels for mortar finite element methodsEngineering with Computers10.1007/s00366-022-01779-339:5(3691-3720)Online publication date: 25-Jan-2023
https://dl.acm.org/doi/10.1007/s00366-022-01779-3
Duong TLorenzis LSauer R(2019)A segmentation-free isogeometric extended mortar contact methodComputational Mechanics10.1007/s00466-018-1599-063:2(383-407)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s00466-018-1599-0
Song YYoun SPark K(2017)Virtual gap element approach for the treatment of non-matching interface using three-dimensional solid elementsComputational Mechanics10.5555/3158457.315848060:4(585-594)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.5555/3158457.3158480

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