Adaptive methods with C1 splines for multi-patch surfaces and shells

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2024_cmame_vazquez_adaptative.pdf (5.61 MB)
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URI: https://hdl.handle.net/10347/40749
ISSN: 0045-7825
DOI: 10.1016/j.cma.2024.117287

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2024

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Elsevier
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We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.

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Isogeometric analysis| Adaptivity| Hierarchical splines| C1 continuity| Multi-patch surfaces| Biharmonic problem| Kirchhoff–Love shells

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Bracco, C., Farahat, A., Giannelli, C., Kapl, M., & Vázquez, R. (2024). Adaptive methods with C1 splines for multi-patch surfaces and shells. Computer Methods in Applied Mechanics and Engineering, 431. https://doi.org/10.1016/J.CMA.2024.117287

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The authors would like to thank Giuliano Guarino for sharing his implementation of Nitsche’s method for shells. Andrea Farahat and Mario Kapl have been supported by the Austrian Science Fund (FWF) through the project P 33023-N. These supports are gratefully acknowledged. Cesare Bracco, and Carlotta Giannelli are members of INdAM research group GNCS, Italy. The INdAM-GNCS support through the SUNRISE Project and Progetti di Ricerca GNCS 2023 “ Tecniche spline innovative per metodi di approssimazione e isogeometrici adattivi” is gratefully acknowledged. In addition, Cesare Bracco and Carlotta Giannelli acknowledge the contribution of the National Recovery and Resilience Plan, Mission 4 Component 2 – Investment 1.4 – National Center for HPC, Big Data and Quantum Computing – funded by the European Union – NextGenerationEU – CUP (B83C22002830001). The partial support of the Italian Ministry of University and Research (MUR) through the PRIN projects COSMIC (No. 2022A79M75) and NOTES (No. P2022NC97R), funded by the European Union - NextGenerationEU , is also acknowledged.

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© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license. Attribution 4.0 International

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Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)