Isogeometric finite element data structures based on Bézier extraction of T‐splines

Scott, Michael A.; Borden, Michael J.; Verhoosel, Clemens V.; Sederberg, Thomas W.; Hughes, Thomas J.R.

doi:10.1002/nme.3167

Cited by 309 publications

(205 citation statements)

References 49 publications

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“…We can see the separation of the boundary from the domain in equation (11). The boundary is defined by the formalism of the boundary integrals (13) and (14). In our further considerations, integral (14) is used to describe the transformationũñ m (ξ ) on the boundary .…”

Section: A Fourier Transformation Of the Somigliana Identitymentioning

confidence: 99%

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Zieniuk

Szerszeń

2017

Numerical Methods Partial

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In this article, we present a strategy of using rectangular and triangular Bézier surface patches for nonelement representation of 3D boundary geometries for problems of linear elasticity. The boundary generated in this way is directly incorporated in the parametric integral equation system (PIES), which has been developed by the authors. The boundary values on each surface patch are approximated by Lagrange polynomials. Three illustrative examples are presented to confirm the effectiveness of the proposed boundary representation in connection with PIES and to show good accuracy of numerical results.

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Section: A Fourier Transformation Of the Somigliana Identitymentioning

confidence: 99%

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Zieniuk

Szerszeń

2017

Numerical Methods Partial

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“…(19) ∂x e ∂ξ is the Jacobian determinant of the geometrical mapping, N is the number of elements. For more details about the calculation of the Jacobian and the tangential derivatives, the reader is referred to [57,77]. Hereinafter, we drop the upper index e i and for convenience we keep the subindex i to refer to the source point.…”

Section: Isogeometric Bemmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

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“…This is at variance with the finite element method where numerical integration is done on a single parent element. In order to blend isogeometric analysis into existing finite element computer programs, Bézier elements and Bézier extraction operators are used to provide a finite element structure for B-splines, NURBS [19], and T-splines [20]. In general, a degree p Bézier curve is defined by a linear combination of p + 1 Bernstein basis functions B(ξ) [21].…”

Section: Bézier Extractionmentioning

confidence: 99%

An isogeometric continuum shell element for non-linear analysis

Hosseini

Remmers

Verhoosel

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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Isogeometric finite element data structures based on Bézier extraction of T‐splines

Cited by 309 publications

References 49 publications

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

An isogeometric continuum shell element for non-linear analysis

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