A new approach to solid modeling with trivariate T-splines based on mesh optimization

Escobar, J. M.; Cascón, J.M.; Rodríguez, Eduardo; Montenegro, R.

doi:10.1016/j.cma.2011.07.004

Cited by 83 publications

(45 citation statements)

References 20 publications

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“…T-spline models are used for IGA, because of their ease and flexibility in geometric modelling in Escobar et al [13], where adaptive tetrahedral mesh of parametric domain and B-spline is modelled, using mesh untangling and smoothing algorithm. A mapping-based tri-variate T-spline solid construction method was developed in Zhang et al [14], for genus zero geometry, starting from a boundary surface triangulation.…”

Section: State Of the Art Reviewmentioning

confidence: 99%

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Gondegaon¹,

Voruganti²

2017

Journal of Theoretical and Applied Mechanics

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Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no selfintersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

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Section: State Of the Art Reviewmentioning

confidence: 99%

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Gondegaon¹,

Voruganti²

2017

Journal of Theoretical and Applied Mechanics

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show abstract

“…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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“…The method was firstly introduced for genus zero solid in [13]. Our procedure can be summarized in two stages.…”

Section: Introductionmentioning

confidence: 99%

The meccano method for isogeometric solid modeling and applications

Escobar

Montenegro

Rodríguez

et al. 2012

Engineering with Computers

Self Cite

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We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

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A new approach to solid modeling with trivariate T-splines based on mesh optimization

Cited by 83 publications

References 20 publications

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

An interactive geometry modeling and parametric design platform for isogeometric analysis

The meccano method for isogeometric solid modeling and applications

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