Skip to Main content Skip to Navigation
Journal articles

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

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [77 references]  Display  Hide  Download
Contributor : Mathias Legrand Connect in order to contact the contributor
Submitted on : Tuesday, April 25, 2017 - 6:11:15 AM
Last modification on : Tuesday, July 3, 2018 - 11:30:03 AM
Long-term archiving on: : Wednesday, July 26, 2017 - 12:41:59 PM


Files produced by the author(s)


Distributed under a Creative Commons Attribution 4.0 International License




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, Elsevier, 2005, 194 (39-41), pp.4135-4195. ⟨10.1016/j.cma.2004.10.008⟩. ⟨hal-01513346⟩



Record views


Files downloads