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

chentao807 添加于 2010-3-13 14:51 | 3019 次阅读 | 0 个评论

作者
HUGHES T, COTTRELL J, BAZILEVS Y
摘要
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 h - and 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.
详细资料
- 文献种类: Journal Article
- 期刊名称: Computer Methods in Applied Mechanics and Engineering
- 期刊缩写: Computer Methods in Applied Mechanics and Engineering
- 期卷页: 2005年第194卷第39-41期 4135-4195页
- ISBN: 0045-7825
学科领域工程技术 » 航空航天科学
标签

Isogeometric Analysis
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