Bracco, CesareFarahat, AndreaGiannelli, CarlottaKapl, MarioVázquez Hernández, Rafael2025-04-102025-04-102024Bracco, 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.2024.1172870045-7825https://hdl.handle.net/10347/40749We 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.eng© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license. Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Isogeometric analysisAdaptivityHierarchical splinesC1 continuityMulti-patch surfacesBiharmonic problemKirchhoff–Love shellsjournal article10.1016/j.cma.2024.117287open access