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Spline- and hp-basis functions of higher differentiability in the finite cell method
Citation Link: https://doi.org/10.15480/882.2673
Publikationstyp
Journal Article
Date Issued
2020-03-01
Sprache
English
TORE-DOI
TORE-URI
Journal
Volume
43
Issue
1
Start Page
1
End Page
17
Citation
GAMM Mitteilungen, Special Issue: Reliable Simulation Techniques in Solid Mechanics – Part I: 1 (43) (2020-03-01)
Publisher DOI
Scopus ID
Publisher
Wiley-VCH
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.
Subjects
continuity
finite cell method
finite strain elastoplasticity
hierarchical B-splines
hp-basis
local refinement
DDC Class
600: Technik
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.
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