Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method

SUMMARYEnforcing essential boundary conditions plays a central role in immersed boundary methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints. We formulate an extension of Nitsche's method for elasticity problems in the framework...

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Vydáno v:	International journal for numerical methods in engineering Ročník 95; číslo 10; s. 811 - 846
Hlavní autoři:	Ruess, M., Schillinger, D., Bazilevs, Y., Varduhn, V., Rank, E.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Chichester Blackwell Publishing Ltd 07.09.2013 Wiley Wiley Subscription Services, Inc
Témata:	Boundaries Boundary conditions Computational methods in fluid dynamics Exact sciences and technology fictitious domain Fluid dynamics Fundamental areas of phenomenology (including applications) high order approximation immersed boundary isogeometric analysis Mathematical analysis Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical approximation NURBS Physics Reproduction Sciences and techniques of general use Solid mechanics Splines Static elasticity (thermoelasticity...) Structural and continuum mechanics Three dimensional trimmed geometry weak boundary conditions Isogeometric analysis B spline Constraint fictitious domain Fluid structure interaction Finite Cell Method Boundary condition Flexibility Modeling Spline approximation NURBS high order approximation Numerical approximation Finite element method immersed boundary Discretization Non uniform rational B spline weak boundary conditions trimmed geometry Computer aided design Numerical integration Computational fluid dynamics Continuous function Immersed boundary method Fictitious domain method Non linear effect
ISSN:	0029-5981, 1097-0207
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Shrnutí:	SUMMARYEnforcing essential boundary conditions plays a central role in immersed boundary methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints. We formulate an extension of Nitsche's method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the B‐spline and non‐uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries. Furthermore, we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3D geometries. With several benchmark problems, we demonstrate the overall good convergence behavior of the proposed method and its good accuracy. We provide extensive studies on the stability of the method, its influence parameters and numerical properties, and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two. A newly composed boundary integration concept further enhances the modeling process and allows a flexible, discretization‐independent introduction of boundary conditions. Finally, we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non‐uniform rational basis spline geometries. Copyright © 2013 John Wiley & Sons, Ltd.
Bibliografie:	German Research Foundation - No. Ra624/15-2 ARO - No. W911NF-11-1-0083 istex:838CBB9FE5A70629CDF9CA362E75FFA3C09139BB ArticleID:NME4522 ark:/67375/WNG-2V1VW1RK-9 ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0029-5981 1097-0207
DOI:	10.1002/nme.4522