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Nitsche’s method for two and three dimensional NURBS patch coupling

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Abstract

We present a Nitche’s method to couple non-conforming two and three-dimensional non uniform rational b-splines (NURBS) patches in the context of isogeometric analysis. We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications.

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Notes

  1. As we were preparing the paper for submission, we became aware of contemporary work had been presented the previous week at the US National Congress for Computational Mechanics [99] in the context of the finite cell method.

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Acknowledgments

The authors would like to acknowledge the financial support of the Framework Programme 7 Initial Training Network Funding under grant number 289361 “Integrating Numerical Simulation and Geometric Design Technology”. Stéphane Bordas also thanks partial funding for his time provided by (1) the EPSRC under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method and (2) the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578) entitled “Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery”. Marco Brino thanks Politecnico di Torino for the funding that supports his visit to iMAM at Cardiff University.

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Authors and Affiliations

  1. Cardiff University, Queen’s Buildings, The Parade, Cardiff, Wales, CF24 3AA, UK

    Vinh Phu Nguyen, Pierre Kerfriden & Stéphane P. A. Bordas

  2. Faculté des Sciences, de la Technologie et de la Communication, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 , Luxembourg City, Luxembourg

    Stéphane P. A. Bordas

  3. Politecnico di Torino - DIGEP, corso Duca degli Abruzzi 24, 10129 , Turin, Italy

    Marco Brino & Elvio Bonisoli

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  1. Vinh Phu Nguyen
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Correspondence to Stéphane P. A. Bordas.

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Nguyen, V.P., Kerfriden, P., Brino, M. et al. Nitsche’s method for two and three dimensional NURBS patch coupling. Comput Mech 53, 1163–1182 (2014). https://doi.org/10.1007/s00466-013-0955-3

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