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Isogeometric dual mortar methods for computational contact mechanics.pdf

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Isogeometric dual mortar methods for computational contact mechanics.pdf

Available online at ScienceDirect Comput. Methods Appl. Mech. Engrg. 301 (2016) 259–280 /locate/cma Isogeometric dual mortar methods for computational contact mechanics Alexander Seitza, Philipp Faraha, Johannes Kremhellera, Barbara I. Wohlmuthb, Wolfgang A. Walla, Alexander Poppa,? a Institute for Computational Mechanics, Technische Universita¨t Mu¨nchen, Boltzmannstrasse 15, D-85748 Garching b. Mu¨nchen, Germany b Institute for Numerical Mathematics, Technische Universita¨t Mu¨nchen, Boltzmannstrasse 3, D-85748 Garching b. Mu¨nchen, Germany Received 25 August 2015; received in revised form 17 December 2015; accepted 18 December 2015 Available online 7 January 2016 Highlights ? A dual mortar method for NURBS-based isogeometric analysis is developed. ? Spatial convergence orders are analyzed for mesh tying and contact mechanics. ? A lack of reproduction properties limits the convergence in mesh tying applications. ? Optimal convergence results are achieved for contact applications. ? The higher smoothness of NURBS delivers smoother results for contact forces. Abstract In recent years, isogeometric analysis (IGA) has received great attention in many fields of computational mechanics research. Especially for computational contact mechanics, an exact and smooth surface representation is highly desirable. As a consequence, many well-known finite element methods and algorithms for contact mechanics have been transferred to IGA. In the present contribution, the so-called dual mortar method is investigated for both contact mechanics and classical domain decomposition using NURBS basis functions. In contrast to standard mortar methods, the use of dual basis functions for the Lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional Lagrange multiplier degrees of freedom from the global system. This condensed system is smaller in size, and no longer of saddle point type but positive definite. A very simple and com