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Analysis and Application of the Rational B‐Spline Finite Element Method in 2D
Author(s) -
Klassen Markus,
Müller Ralf,
Mergheim Julia,
Fischer Paul,
Steinmann Paul
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010273
Subject(s) - isogeometric analysis , finite element method , basis function , cad , elasticity (physics) , b spline , mathematics , spline (mechanical) , basis (linear algebra) , computer science , context (archaeology) , mathematical analysis , geometry , structural engineering , engineering drawing , engineering , physics , paleontology , biology , thermodynamics
Non‐Uniform Rational B‐Splines (NURBS) are basis functions used in CAD software to describe exact geometric models. The implementation of these basis functions in the context of the Finite Element Analysis (FEA) is known as isogeometric analysis. The concept and definition of NURBS is briefly presented here. Since these functions are implemented as shape functions for the isogeometric analysis, the refinement strategies are discussed. The example of an infinite plate with circular hole serves as a benchmark. Finally, isogeometric analysis is applied to gradient elasticity since NURBS functions are of higher continuity and this is required in gradient elasticity. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)