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Alternative integration algorithms for three-dimensional mortar contact

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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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Acknowledgments

The authors would like to gratefully acknowledge the financial support of this work by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under Grant number BI 722/7-1. Moreover, the fruitful discussions with Anton Tkachuk and his helpful suggestions are highly appreciated.

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  1. Institute for Structural Mechanics, University of Stuttgart, Pfaffenwaldring 7, 70550, Stuttgart, Germany

    C. Wilking & M. Bischoff

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  1. C. Wilking
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Correspondence to C. Wilking.

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Wilking, C., Bischoff, M. Alternative integration algorithms for three-dimensional mortar contact. Comput Mech 59, 203–218 (2017). https://doi.org/10.1007/s00466-016-1345-4

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