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Research Papers

An Analytical Singular Element for Kirchhoff Plate Bending With V-Shaped Notches

[+] Author and Article Information
Weian Yao1

State Key Laboratory of Structural Analysis for Industrial Equipment,  Dalian University of Technology, Dalian 116024, Chinaywa@dlut.edu.cn

Shan Wang

State Key Laboratory of Structural Analysis for Industrial Equipment,  Dalian University of Technology, Dalian 116024, Chinawangshan1981@163.com

1

Corresponding author.

J. Appl. Mech 79(5), 051016 (Jun 29, 2012) (9 pages) doi:10.1115/1.4006448 History: Received April 06, 2011; Revised February 20, 2012; Posted March 26, 2012; Published June 28, 2012; Online June 29, 2012

An analytical singular element with arbitrary high-order precision is constructed using the analytical symplectic eigenfunctions of an annular sector thin plate with both straight sides free. These values can be used to describe the local stress singularities near an arbitrary V-notch or a crack tip. Numerical examples of Kirchhoff’s plate bending problem with V-shaped notches are given by applying the Local-Global method. This method combines the present analytical singular element and the conventional finite element method. The numerical results show that the present method is an effective numerical technique for analysis of Kirchhoff plate bending problems with boundary stress singularities.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The annular sector plate in the polar coordinate system

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Figure 2

The thin plate containing a square hole subjected to pure bending moment along opposite edges

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Figure 3

The thin plate containing a square hole subjected to uniform twist moment along all edges

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Figure 4

Meshes for the thin plate with a square hole

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Figure 5

Cloud maps of bending moments within the singular element for case 1

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Figure 6

Cloud maps of bending moments within the singular element for case 2

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Figure 7

The thin plate containing a rhombus hole subjected to pure bending moment along opposite edges

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Figure 8

Mode I notch stress intensity factors K1 of the thin plate with a rhombus hole

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