Spline- and hp-basis functions of higher differentiability in the finite cell method

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

Funding(s)

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.

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

Kollmannsberger_et_al-2019-GAMM-Mitteilungen-1.pdf

Size

2.64 MB

Format

Adobe PDF

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Spline- and hp-basis functions of higher differentiability in the finite cell method