Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

N. Nguyen-Thanh; H. Nguyen-Xuan; S. P.A. Bordas; T. Rabczuk

doi:10.1016/j.cma.2011.01.018

Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

N. Nguyen-Thanh, H. Nguyen-Xuan, S. P.A. Bordas, T. Rabczuk

College of Engineering

Research output: Contribution to journal › Article › peer-review

216 Citations (Scopus)

Abstract

Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.

Original language	English
Pages (from-to)	1892-1908
Number of pages	17
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	200
Issue number	21-22
DOIs	https://doi.org/10.1016/j.cma.2011.01.018
Publication status	Published - 2011 May 1

Keywords

Isogeometric analysis
PHT-spline
T-meshes
T-spline

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/j.cma.2011.01.018

Cite this

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title = "Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids",

abstract = "Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.",

keywords = "Isogeometric analysis, PHT-spline, T-meshes, T-spline",

author = "N. Nguyen-Thanh and H. Nguyen-Xuan and Bordas, {S. P.A.} and T. Rabczuk",

note = "Funding Information: The support of the “Academic Research Collaboration (ARC/DAAD)” is gratefully acknowledged. The second author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED). The authors acknowledge Professor Jiansong Deng from the University of Science and Technology of China for his suggestion and advice in the PHT approach.",

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AU - Nguyen-Thanh, N.

AU - Nguyen-Xuan, H.

AU - Bordas, S. P.A.

AU - Rabczuk, T.

N1 - Funding Information: The support of the “Academic Research Collaboration (ARC/DAAD)” is gratefully acknowledged. The second author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED). The authors acknowledge Professor Jiansong Deng from the University of Science and Technology of China for his suggestion and advice in the PHT approach.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.

AB - Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method.

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KW - PHT-spline

KW - T-meshes

KW - T-spline

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Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

Abstract

Keywords

ASJC Scopus subject areas

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