Skew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact

A simple skew-symmetric Nitsche’s formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as...

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Veröffentlicht in:Computer methods in applied mechanics and engineering 2018-11, Vol.341, p.188-220
Hauptverfasser: Hu, Qingyuan, Chouly, Franz, Hu, Ping, Cheng, Gengdong, Bordas, Stéphane P.A.
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Sprache:eng
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Zusammenfassung:A simple skew-symmetric Nitsche’s formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free. For contact conditions, it remains stable and accurate for a wide range of the stabilization parameter. Several numerical tests are performed to illustrate its accuracy, stability and convergence performance. We investigate particularly the effects introduced by Nitsche’s coupling, including the convergence performance and condition numbers in statics as well as the extra “outlier” frequencies and corresponding eigenmodes in structural dynamics. We present the Hertz test, the block test, and a 3D self-contact example showing that the skew-symmetric Nitsche’s formulation is a suitable approach to simulate contact problems in IGA. •A simple skew-symmetric Nitsche’s formulation is introduced into IGA.•For linear boundary and interface conditions, the formulation is parameter-free.•For contact conditions, the formulation is stable for the stabilization parameter.•Robustness and accuracy of the method is studied numerically for various problems.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2018.05.024