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Development of a quadratic element formulation based on the X‐FEM and NURBS surfaces
Author(s) -
Haasemann Georg,
Kästner Markus,
Prüger Stefan,
Ulbricht Volker
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910321
Subject(s) - finite element method , boundary element method , quadratic equation , mixed finite element method , extended finite element method , stiffness matrix , computation , polygon mesh , element (criminal law) , smoothed finite element method , mathematical analysis , geometry , mathematics , computer science , boundary knot method , structural engineering , algorithm , engineering , political science , law
The FE‐simulation of inhomogeneous structures such as composite materials, biological tissues or foams requires the generation of respective finite element meshes. The Extended Finite Element Method (X‐FEM) allows for an efficient modelling technique where the element boundary needs not to be aligned to the interfaces. In this paper, a new plane element based on the X‐FEM and quadratic shape functions will be presented. This element allows for the description of curved material interfaces inside the element domain. The computation of the element stiffness matrix requires a numerical integration process which accounts for the discontinuous fields. In the case of a curved interface, the triangulation of the element domain as applied for linear element formulations is inappropriate. Hence, Non‐Uniform Rational B‐Spline (NURBS) surfaces are used to evaluate the integrals numerically. Finally, the results of different examples will show the properties and the quality of this element formulation. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)