Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness

Matt, Michael A.

doi:10.1007/978-3-8348-2384-7

Cited by 5 publications

(2 citation statements)

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“…Для получения сплайнов с первым, вторым, тре-тьим и четвертым порядками гладкости необходимо обеспечить условия склеивания (7), (12), (13), (14), (15), (18) …”

Section: результаты исследований и их обсуждениеunclassified

“…Работа является логическим продолжением иссле-дований [4][5][6][7][8][9][10][11][12][13][14][15]. Автор статьи планирует продолжить данные исследования, ввиду их очевидной полезности потребителям.…”

Section: N -1; а B C D E F -рассчитываются из (10) (11)unclassified

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Development of vector-parametric fifth-degree B-spline with control points incident the surface

Ковтун¹

2016

TAPR

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Section: результаты исследований и их обсуждениеunclassified

Section: N -1; а B C D E F -рассчитываются из (10) (11)unclassified

Development of vector-parametric fifth-degree B-spline with control points incident the surface

Ковтун¹

2016

TAPR

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A $$C^r$$ trivariate macro-element based on the Worsey–Farin split of a tetrahedron

Matt

2012

Numer. Math.

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Three-dimensional approximated isogeometric analysis via Bernstein–Bézier tetrahedron

Song,

Kang,

Kim

et al. 2024

Comput Mech

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Precise simulation of realistic physical phenomena and maintaining high efficiency will be the ultimate goal of computational mechanics. As an effort of such endeavor, an isogeometric analysis (IGA) was proposed by integrating finite element analysis (FEA) and computer-aided design. IGA efficiently predicts a physical behavior with higher fidelity than the original FEA. However, an application to various geometries will be cumbersome owing to the absence of an appropriate pre-processor. To alleviate such limitation, various reinforcements have been attempted, including a finite element (FE)-based IGA. Derived from those initiatives, alternatives will be suggested herein by using a Bernstein–Bézier FE. To obtain approximate $$C^1$$ C 1 continuity for a general tetrahedral FE, an approximated Worsey–Piper element split will be presented. Also, Bézier mesh generation will be adopted for an enhanced geometric representation. The present attempt will be validated by comparing the results for various curved geometry. Furthermore, the present method will be applied to a much more complicated configuration to demonstrate the geometric applicability.

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Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness

Cited by 5 publications

References 0 publications

Development of vector-parametric fifth-degree B-spline with control points incident the surface

Development of vector-parametric fifth-degree B-spline with control points incident the surface

A $$C^r$$ trivariate macro-element based on the Worsey–Farin split of a tetrahedron

Three-dimensional approximated isogeometric analysis via Bernstein–Bézier tetrahedron

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