Analysis-Suitable T-splines are Dual-Compatible

Veiga, L. Beirão da; Buffa, Annalisa; Cho, D.; Sangalli, Giancarlo

doi:10.1016/j.cma.2012.02.025

Cited by 85 publications

(76 citation statements)

References 37 publications

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“…The standard tensor-product B-spline spaces do not allow for local changes in spatial resolution and thus different generalizations providing adaptive refinement were proposed in the last 25 years. Forsey and Bartels (1988) introduced the hierarchical splines, later studied by Kraft (1997) and more recently by Giannelli et al (2012) and Mokriš et al (2014), Sederberg et al (2003Sederberg et al ( , 2004 introduced T-splines of which an Analysis Suitable subset (AST) was described by Beirão da Veiga et al (2012), Deng et al (2008) introduced PHT-splines and Dokken et al (2013) introduced LR-splines whose local linear independence was studied by Bressan (2013). Each of ✩ This paper has been recommended for acceptance by Thomas Sederberg. these approaches has their own strengths and weaknesses determined by the focus with which they were developed.…”

Section: Introductionmentioning

confidence: 98%

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A hierarchical construction of LR meshes in 2D

Bressan

Jüttler

2015

Computer Aided Geometric Design

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Section: Introductionmentioning

confidence: 98%

“…In the context of T-splines this property is called overlap (Beirão daVeiga et al, 2012). We prefer the name compatible because two separate knot vectors with θ n < ξ 1 or ξ m < θ 1 are compatible, but it would be counter-intuitive to call them overlapping.…”

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confidence: 96%

A hierarchical construction of LR meshes in 2D

Bressan

Jüttler

2015

Computer Aided Geometric Design

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“…With similar properties, one may also cite the development of LRB-splines [18] and multigrids-based NURBS [19]. Alternatively, another technology seems to have gathered an important momentum from both the computational geometry and analysis communities: the so-called T-splines [20][21][22]. In addition to be efficient for local mesh refinement, the T-splines also appear suitable to address trimmed multi-patch geometries.…”

Section: Introductionmentioning

confidence: 99%

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Bouclier

Passieux

Salaün

2017

Computer Methods in Applied Mechanics and Engineering

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of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. (2017) Highlights• We develop a new mortar method for NURBS that keeps the benefit of using more regular functions.• We propose to match the tractions in addition to the displacements at the coupling interface.• We apply the methodology to perform the non-intrusive local enrichment of NURBS patches.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we develop a mortar method for the coupling of non-conforming NURBS subdomains within a NURBS patch that keeps the benefit of using more regular functions. The idea is to use two Lagrange multipliers to match, across the coupling interface, the tractions coming from the discrete displacements in addition to the discrete displacements. It results in a strategy that is suitable with the continuity of the physical solution: when the physical solution is sufficiently smooth, the strategy enables to represent a C 1 behavior; but, when only a C 0 displacement is expected, no additional errors are introduced since only the traction force is continuous and not the whole derivative fields. Lower stress jumps at the coupling interface can then be observed which allows for a better transition of the information. As an application, a non-intrusive algorithm is also built to solve the proposed coupling method, which enables simple and flexible local enrichments of NURBS patches without losing the interest of using more regular functions. A range of numerical examples in two-dimensional linear elasticity are carried out along with comparisons with other published NURBS coupling techniques to demonstrate the performance of the proposed coupling and its interest when combined to a non-intrusive strategy.

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“…T-splines [9,10] were introduced in the CAD community as a generalization and extension of NURBS allowing for local refinement and coarsening, and representation of geometry of arbitrary topological genus. T-splines have been applied successfully in the context of IGA [11][12][13][14][15][16] and have been further improved to meet the demands of analysis [17][18][19][20]. Recent attempts to construct trivariate solid T-splines can be found in [21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

An interactive geometry modeling and parametric design platform for isogeometric analysis

Hsu

Wang

Herrema

et al. 2015

Computers & Mathematics with Applications

102

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In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. KeywordsIsogeometric analysis, NURBS and T-splines, Parametric design, Rhino and Grasshopper, Visual programming, Graphical generative algorithms RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. Authors Ming-Chen

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Analysis-Suitable T-splines are Dual-Compatible

Cited by 85 publications

References 37 publications

A hierarchical construction of LR meshes in 2D

A hierarchical construction of LR meshes in 2D

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

An interactive geometry modeling and parametric design platform for isogeometric analysis

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