Swept Volume Parameterization for Isogeometric Analysis

Aigner, Martin; Heinrich, Ch.; Jüttler, Bert; Pilgerstorfer, Elisabeth; Simeon, Bernd; Vuong, Anh-Vu

doi:10.1007/978-3-642-03596-8_2

Cited by 75 publications

(75 citation statements)

References 19 publications

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“…Parameterization of the domain is obtained by establishing bijective mapping, between original domain and the parameter domain (unit square or unit cube). A NURBS parameterization for swept volume is presented in Aigner et al [19], using a variational approach, based on the boundary conditions.…”

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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“…After remeshing the tetrahedral mesh to the hexahedral mesh, a trivariate B-spline for the solid model is generated by an iterative fitting method. The second is the paper by Aigner et al [1] where the authors proposed a parameterization method for swept volumes which cover many free-form shapes in CAD system like blades or propellers. In this method, a spline approximation for a solid model can be found by solving a minimization problem with several penalty terms corresponding to particular features of the shape.…”

Section: Related Workmentioning

confidence: 99%

Parameterization of Contractible Domains Using Sequences of Harmonic Maps

Nguyen

Jüttler

2012

Curves and Surfaces

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Abstract. In this paper, we propose a new method for parameterizing a contractible domain (called the computational domain) which is defined by its boundary. Using a sequence of harmonic maps, we first build a mapping from the computational domain to the parameter domain, i.e., the unit square or unit cube. Then we parameterize the original domain by spline approximation of the inverse mapping. Numerical simulations of our method were performed with several shapes in 2D and 3D to demonstrate that our method is suitable for various shapes. The method is particular useful for isogeometric analysis because it provides an extension from a boundary representation of a model to a volume representation.

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“…Indeed, it is about creating the mesh of the boundary of the domain from a description in terms of curves. Few articles that discuss the topic provide strategies to build these meshes [1,9,17,20].…”

Section: Domain Parametrization Using Splines/nurbs Curvesmentioning

confidence: 99%

An axisymmetric PIC code based on isogeometric analysis

et al. 2011

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Abstract. Isogeometric analysis has been developed recently to use basis functions resulting from the CAO description of the computational domain for the finite element spaces. The goal of this study is to develop an axisymmetric Finite Element PIC code in which specific spline Finite Elements are used to solve the Maxwell equations and the same spline functions serve as shape function for the particles. The computational domain itself is defined using splines or NURBS.

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Swept Volume Parameterization for Isogeometric Analysis

Cited by 75 publications

References 19 publications

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Parameterization of Contractible Domains Using Sequences of Harmonic Maps

An axisymmetric PIC code based on isogeometric analysis

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