Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement - Archive ouverte HAL Access content directly
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2005

Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

(1) , (1) , (1)
1

Abstract

The concept of isogeometric analysis is proposed. Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element hand p-refinement schemes are presented and a new, more efficient, higher-order concept, k-refinement, is introduced. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description. In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions. A k-refinement strategy is shown to converge toward monotone solutions for advection–diffusion processes with sharp internal and boundary layers , a very surprising result. It is argued that isogeometric analysis is a viable alternative to standard, polynomial-based, finite element analysis and possesses several advantages.
Fichier principal
Vignette du fichier
HCBO.pdf (3.36 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01513346 , version 1 (25-04-2017)

Licence

Attribution - CC BY 4.0

Identifiers

Cite

T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194 (39-41), pp.4135-4195. ⟨10.1016/j.cma.2004.10.008⟩. ⟨hal-01513346⟩
1009 View
4069 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More