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Spline‐ and hp ‐basis functions of higher differentiability in the finite cell method
Author(s) -
Kollmannsberger Stefan,
D'Angella Davide,
Rank Ernst,
Garhuom Wadhah,
Hubrich Simeon,
Düster Alexander,
Stolfo Paolo Di,
Schröder Andreas
Publication year - 2020
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.202000004
Subject(s) - basis function , differentiable function , basis (linear algebra) , mathematics , hyperelastic material , discretization , spline (mechanical) , nonlinear system , context (archaeology) , gravitational singularity , finite element method , polynomial , mathematical analysis , geometry , physics , paleontology , quantum mechanics , biology , thermodynamics
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, C k hp ‐basis functions based on classical B‐splines and a new approach for the construction of C 1 hp ‐basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C 1 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 C k hp ‐basis functions based on B‐splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.