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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.
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: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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