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Research Papers

Particular Solutions of a Two-Dimensional Infinite Wedge for Various Boundary Conditions With Weak Singularity

[+] Author and Article Information
Z. L. Li1

Digital Engineering and Simulation Research Center, School of Hydropower and Digitalization Engineering, Huazhong University of Science & Technology, Wuhan, Hubei 430074, China

Ch. Wang

Digital Engineering and Simulation Research Center, School of Hydropower and Digitalization Engineering, Huazhong University of Science & Technology, Wuhan, Hubei 430074, China

1

Permanent address: Solid Mechanics Research Center, Beijing University of Aeronautics and Astronautics, Beijing China.

J. Appl. Mech 77(1), 011004 (Sep 24, 2009) (13 pages) doi:10.1115/1.3168599 History: Received July 16, 2008; Revised April 15, 2009; Published September 24, 2009

The particular solutions of a two-dimensional infinite wedge for various boundary conditions with lnr weak singularity have been investigated in this paper. The relations of the weak singularities and the discontinuities of the first kind of the boundary variables at a corner of a two-dimensional elastic body have been established. By using the relations, the singular behaviors of the unknown boundary variables at a corner of an elastic body can be obtained before solving the boundary value problem by using the boundary element method (BEM). Especially, if the boundary conditions at a corner are displacements prescribed, the values of the unknown tractions at the corner can be determined in advance. Thus, the difficulty related to the multivalued tractions at a corner in BEM analysis for problems with boundary displacements prescribed has been overcome completely. In addition, more appropriate shape functions for the unknown boundary field variables of a corner element can be constructed, and the accuracy of the BEM may be greatly increased.

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Figures

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Figure 1

An infinite wedge with angle 2α

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Figure 4

Square ABCD under antisymmetric shear loading at corner A

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Figure 5

Numerical and theoretical results of traction component t1 on side AB for 0≤x1≤0.5

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Figure 8

Numerical results of traction component t2 on side AB by using BEM3n_TU

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Figure 2

Tractions of a symmetric (a) and an antisymmetric (b) wedge

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Figure 3

Weak singularity intensities of tractions at an antisymmetric wedge-tip

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Figure 6

Numerical and theoretical results of traction component t2 on side AB for 0≤x1≤0.5

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Figure 7

Numerical results of traction component t1 on side AB by using BEM3n_TU

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