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https://doi.org/10.15480/882.2673
Publisher DOI: | 10.1002/gamm.202000004 | Title: | Spline- and hp-basis functions of higher differentiability in the finite cell method | Language: | English | Authors: | Kollmannsberger, Stefan D'Angella, Davide Rank, Ernst Garhuom, Wadhah ![]() Hubrich, Simeon Düster, Alexander Stolfo, Paolo Di Schröder, Andreas |
Keywords: | continuity; finite cell method; finite strain elastoplasticity; hierarchical B-splines; hp-basis; local refinement | Issue Date: | 1-Mar-2020 | Publisher: | Wiley-VCH | Source: | GAMM Mitteilungen, Special Issue: Reliable Simulation Techniques in Solid Mechanics – Part I: 1 (43) (2020-03-01) | Abstract (english): | In this paper, the use of hp-basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, Ck hp-basis functions based on classical B-splines and a new approach for the construction of C1 hp-basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C1 approach also includes varying polynomial degrees. The properties of the hp-basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the Ck hp-basis functions based on B-splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains. |
URI: | http://hdl.handle.net/11420/4852 | DOI: | 10.15480/882.2673 | ISSN: | 1522-2608 | Journal: | GAMM-Mitteilungen | Institute: | Konstruktion und Festigkeit von Schiffen M-10 | Document Type: | Article | Project: | SPP 1748: Teilprojekt "High-Order Immersed-Boundary-Methoden in der Festkörpermechanik für generativ gefertigte Strukturen" | More Funding information: | Support by 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 DU 405/8-2, SCHR 1244/4-2, and RA 624/27-2. | License: | ![]() |
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