Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method

Xu, Gang; Mourrain, Bernard; Duvigneau, Régis; Galligo, André

doi:10.1016/j.jcp.2013.06.029

Cited by 105 publications

(47 citation statements)

References 37 publications

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“…However, most work known to us primarily focuses on 2D problems, which are inconsequential for practical engineering applications. Indeed, the generation of analysis-suitable 3D volume parametrization for complex geometries is still an open question [80][81][82].…”

Section: Dealing With Component Complexitymentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

202

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Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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Section: Dealing With Component Complexitymentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

202

View full text Add to dashboard Cite

show abstract

“…The approach is capable of generating good-quality volumetric models, but for a specific object, or a family of objects. Although modeling of solid geometry to this day presents a big research challenge in IGA, some innovative solutions are currently emerging that can handle geometries of greater generality [24][25][26][27][103][104][105][106][107]140].…”

Section: Example 2: Integrally Bladed Rotormentioning

confidence: 99%

“…This enhanced accuracy is in part attributable to the higher-order smoothness of the basis functions employed. Recent research directions in IGA include collocation [85][86][87][88][89][90][91][92], quadrature rules [93][94][95][96], trimmed geometries and patch coupling [97][98][99][100][101][102], analysis-suitable trivariate model [25][26][27][28][103][104][105][106][107], and standardized file formats for data exchange between geometry modeling and computational analysis software [108][109][110][111][112]. For more details of mathematical developments, basis function research, geometry modeling, model quality assessment, and early applications, the reader is referred to [2] and references therein.…”

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 construction of conformal solid T-spline from boundary T-spline representation is studied by using octree structure and boundary offset [34]. In [32], variational harmonic method is proposed to construct analysis-suitable parameterization of computational domain from given CAD boundary information. Wang and Qian proposed an efficient method by combining divide-and-conquer, constraint aggregation and the hierarchical optimization technique to obtain valid trivariate Bspline solids from six boundary B-spline surfaces [28].…”

Section: Introductionmentioning

confidence: 99%

“…Previous work mainly focus on the construction of inner control points [28,[31][32][33][34]. To our best knowledge, the effect of the boundary parameterization on the interior volumetric parameterization has not been studied before.…”

Section: Introductionmentioning

confidence: 99%

High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods

Mourrain

Galligo

et al. 2014

Comput Mech

Self Cite

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International audienceHigh-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbius transformation to improve the quality of the isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods

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Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method

Cited by 105 publications

References 37 publications

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

An interactive geometry modeling and parametric design platform for isogeometric analysis

High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods

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