An extended isogeometric thin shell analysis based on Kirchhoff-Love theory

N. Nguyen-Thanh; N. Valizadeh; M. N. Nguyen; H. Nguyen-Xuan; X. Zhuang; P. Areias; Goangseup Zi; Y. Bazilevs; L. De Lorenzis; Timon Rabczuk

doi:10.1016/j.cma.2014.08.025

An extended isogeometric thin shell analysis based on Kirchhoff-Love theory

N. Nguyen-Thanh, N. Valizadeh, M. N. Nguyen, H. Nguyen-Xuan, X. Zhuang, P. Areias, Goangseup Zi, Y. Bazilevs, L. De Lorenzis, Timon Rabczuk

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

303 Citations (Scopus)

Abstract

An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff-Love theory where C¹-continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.

Original language	English
Pages (from-to)	265-291
Number of pages	27
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	284
DOIs	https://doi.org/10.1016/j.cma.2014.08.025
Publication status	Published - 2015 Feb 1

Keywords

Fracture mechanics
Isogeometric analysis
NURBS
Thin shells
XFEM
XIGA

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.2014.08.025

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title = "An extended isogeometric thin shell analysis based on Kirchhoff-Love theory",

abstract = "An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff-Love theory where C1-continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.",

keywords = "Fracture mechanics, Isogeometric analysis, NURBS, Thin shells, XFEM, XIGA",

author = "N. Nguyen-Thanh and N. Valizadeh and Nguyen, {M. N.} and H. Nguyen-Xuan and X. Zhuang and P. Areias and Goangseup Zi and Y. Bazilevs and {De Lorenzis}, L. and Timon Rabczuk",

note = "Funding Information: Nhon Nguyen-Thanh and Laura De Lorenzis would like to acknowledge the financial support from the European Research Council Starting Researcher Grant “INTERFACES” , Grant agreement No. 279439 . Xiaoying Zhuang gratefully acknowledges the support of NSFC ( 41130751 ), National Basic Research Program of China (973 Program: 2011CB013800 ), and Shanghai Pujiang Program ( 12PJ1409100 ). Publisher Copyright: {\textcopyright} 2014 Elsevier B.V.",

year = "2015",

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day = "1",

doi = "10.1016/j.cma.2014.08.025",

language = "English",

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journal = "Computer Methods in Applied Mechanics and Engineering",

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T1 - An extended isogeometric thin shell analysis based on Kirchhoff-Love theory

AU - Nguyen-Thanh, N.

AU - Valizadeh, N.

AU - Nguyen, M. N.

AU - Nguyen-Xuan, H.

AU - Zhuang, X.

AU - Areias, P.

AU - Zi, Goangseup

AU - Bazilevs, Y.

AU - De Lorenzis, L.

AU - Rabczuk, Timon

N1 - Funding Information: Nhon Nguyen-Thanh and Laura De Lorenzis would like to acknowledge the financial support from the European Research Council Starting Researcher Grant “INTERFACES” , Grant agreement No. 279439 . Xiaoying Zhuang gratefully acknowledges the support of NSFC ( 41130751 ), National Basic Research Program of China (973 Program: 2011CB013800 ), and Shanghai Pujiang Program ( 12PJ1409100 ). Publisher Copyright: © 2014 Elsevier B.V.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff-Love theory where C1-continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.

AB - An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff-Love theory where C1-continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.

KW - Fracture mechanics

KW - Isogeometric analysis

KW - NURBS

KW - Thin shells

KW - XFEM

KW - XIGA

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

An extended isogeometric thin shell analysis based on Kirchhoff-Love theory

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Keywords

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