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Hierarchically refined isogeometric analysis of trimmed shells

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Abstract

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff–Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of “small” trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales. In this contribution we focus our effort on the analysis of single-patch geometries, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

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Acknowledgements

The author L. Coradello gratefully acknowledges the support of the European Research Council, via the ERC AdG project CHANGE (No. 694515). A. Reali has been partially supported by the MIUR-PRIN project XFAST-SIMS (No. 20173C478N). The authors D. D’Angella and A. Reali acknowledge the support of the TUM Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under Grant agreement number 291763. D. D’Angella acknowledges the support of the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” under the project RA624/27-2.

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Authors and Affiliations

  1. Chair of Numerical Modelling and Simulation, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Luca Coradello

  2. Chair of Computational Modeling and Simulation, Technische Universität München, Munich, Germany

    Davide D’Angella, Massimo Carraturo, Stefan Kollmannsberger & Ernst Rank

  3. Institute for Advanced Study, Technische Universität München, Munich, Germany

    Davide D’Angella, Ernst Rank & Alessandro Reali

  4. Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Pavia, Pavia, Italy

    Massimo Carraturo & Alessandro Reali

  5. Institute of Engineering Mechanics and Structural Analysis, Bundeswehr University Munich, Munich, Germany

    Josef Kiendl

  6. Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway

    Josef Kiendl

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  1. Luca Coradello
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  2. Davide D’Angella
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Correspondence to Luca Coradello.

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Luca Coradello and Davide D’Angella contributed equally to this work.

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Coradello, L., D’Angella, D., Carraturo, M. et al. Hierarchically refined isogeometric analysis of trimmed shells. Comput Mech 66, 431–447 (2020). https://doi.org/10.1007/s00466-020-01858-6

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