A smoothed finite element method for shell analysis

N. Nguyen-Thanh; Timon Rabczuk; H. Nguyen-Xuan; Stéphane P.A. Bordas

doi:10.1016/j.cma.2008.05.029

A smoothed finite element method for shell analysis

N. Nguyen-Thanh, Timon Rabczuk, H. Nguyen-Xuan, Stéphane P.A. Bordas

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

214 Citations (Scopus)

Abstract

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

Original language	English
Pages (from-to)	165-177
Number of pages	13
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	198
Issue number	2
DOIs	https://doi.org/10.1016/j.cma.2008.05.029
Publication status	Published - 2008 Dec 1

Keywords

MITC4 elements
Shell elements
Smoothed finite elements (SFEM)

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2008.05.029

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title = "A smoothed finite element method for shell analysis",

abstract = "A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.",

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AU - Nguyen-Thanh, N.

AU - Rabczuk, Timon

AU - Nguyen-Xuan, H.

AU - Bordas, Stéphane P.A.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

AB - A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

KW - MITC4 elements

KW - Shell elements

KW - Smoothed finite elements (SFEM)

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 2

ER -

A smoothed finite element method for shell analysis

Abstract

Keywords

ASJC Scopus subject areas

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