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Research Papers

Antiplane Harmonic Elastodynamic Stress Analysis of an Infinite Wedge With a Circular Cavity

[+] Author and Article Information
Gang Liu

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Baohua Ji1 n2

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, Chinabhji@bit.edu.cn bhji@mail.tsinghua.edu.cn

Haitao Chen

 Marine Design and Research Institute of China, Shanghai 200011, China

Diankui Liu1

School of Civil Engineering, Harbin Engineering University, Harbin 150001, Chinadkliu@yahoo.cn

1

Corresponding authors.

2

Present address: Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China.

J. Appl. Mech 76(6), 061008 (Jul 23, 2009) (9 pages) doi:10.1115/1.3130451 History: Received November 29, 2007; Revised February 10, 2009; Published July 23, 2009

In this paper, the antiplane harmonic dynamics stress of an infinite isotropic wedge with a circular cavity is analyzed for the first time by using a novel method with Green’s function, complex functions, and multipolar coordinates. A basic solution for the displacement field of an elastic half-space containing a circular cavity subjected to antiplane harmonic point force is employed as the Green’s function. Based on the Green’s function, the infinite wedge problem is equivalently transformed into the problem of a half-space divided by a semi-infinite traction free line. The equivalent problem is solved numerically to determine the dynamic stress field in the wedge at different apex angles and cavity locations. We show that the wedge angle, cavity location, and incident angle and frequency of the external load have significant effect on the dynamic stress of the cavity surface. The dynamic stress concentration factor on the cavity surface becomes singular when the cavity is close to the boundary of the wedge.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The scattering model of the infinite wedge with a circular cavity

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Figure 2

(a) A half-space with a circular cavity loaded by a point force δ(z−z0). (b) A half-space with a cavity loaded by an external force with an incident angle α.

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Figure 3

Illustration of the construction of the infinite wedge problem by using Green’s function method and the division technique

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Figure 4

Verification of our method. ((a) and (b)) The surface displacement of a half-space predicted by this paper in comparison with the results of Lee and Trifunac (25-26) at L/a=1.5 and 5.0, respectively. (c) The displacement at vertex of a wedge predicated by this paper in comparison with the results of Sanchez-sesma (27).

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Figure 5

The DSCF on the cavity at φ=90 deg, where (a) α=0 deg, η=0.1; (b) α=0 deg, η=1.0; (c) α=0 deg, η=2.0; (d) α=45 deg, η=0.1; (e) α=45 deg, η=1.0; (f) α=45 deg, η=2.0; (g) α=90 deg, η=0.1; (h) α=90 deg, η=1.0; and (i) α=90 deg, η=2.0

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Figure 6

The DSCF on the cavity at φ=75 deg, where (a) α=0 deg, η=0.1; (b) α=0 deg, η=1.0; (c) α=0 deg, η=2.0; (d) α=45 deg, η=0.1; (e) α=45 deg, η=1.0; (f) α=45 deg, η=2.0; (g) α=90 deg, η=0.1; (h) α=90 deg, η=1.0; and (i) α=90 deg, η=2.0

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Figure 7

The DSCF on the cavity at φ=45 deg, where (a) α=0 deg, η=0.1; (b) α=0 deg, η=1.0; (c) α=0 deg, η=2.0; (d) α=45 deg, η=0.1; (e) α=45 deg, η=1.0; (f) α=45 deg, η=2.0; (g) α=90 deg, η=0.1; (h) α=90 deg, η=1.0; and (i) α=90 deg, η=2.0

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Figure 8

The DSCF on the cavity at variable wedge angels with L=30, α=45 deg, where (a) η=0.1, (b) η=1.0, and (c) η=2.0

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Figure 9

The influence of the cavity positions on the DSCF when the cavity is biased from the bisector of the wedge angle at L=30, φ=45 deg. ((a) and (b)) α=0 deg, ((c) and (d)) α=45 deg, and ((e) and (f)) α=90 deg, where (a), (c), and (e) show the DSCF when the cavity is on the bisector of the apex angle, while (b), (d), and (f) show the DSCF when the cavity is biased from the bisector.

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Figure 10

The influence of the cavity position on the DSCF as the distance between the cavity center and the wedge apex decreases

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