Complex variable function method for the scattering of plane waves by an arbitrary hole in a porous medium

By introducing a conformal mapping and applying the complex variable function method, two potential functions are determined for plane problem of two-dimensional quasicrystals with a lip-shape crack. When the height of the lip-shape crack approaches to zero, the results can be reduced to the solutions of the Griffith crack.

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Complex variable function method for the plane elasticity and the dislocation problem of quasicrystals with point group 10 mm

Physics Letters A ◽

10.1016/j.physleta.2007.07.043 ◽

2008 ◽

Vol 372 (4) ◽

pp. 510-514 ◽

Cited By ~ 5

Author(s):

Lian He Li ◽

Tian You Fan

Keyword(s):

Complex Variable ◽

Function Method ◽

Point Group ◽

Plane Elasticity ◽

Complex Variable Function ◽

Variable Function ◽

Complex Variable Function Method ◽

Group 10

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Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity

Mathematical Problems in Engineering ◽

10.1155/2015/637254 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 5

Author(s):

N. M. A. Nik Long ◽

M. R. Aridi ◽

Z. K. Eshkuvatov

Keyword(s):

Integral Equations ◽

Function Method ◽

Quadrature Rule ◽

Plane Elasticity ◽

Mode Iii ◽

Inclined Crack ◽

Complex Variable Function ◽

Curved Crack ◽

Variable Function ◽

Complex Variable Function Method

The interaction between the inclined and curved cracks is studied. Using the complex variable function method, the formulation in hypersingular integral equations is obtained. The curved length coordinate method and suitable quadrature rule are used to solve the integral equations numerically for the unknown function, which are later used to evaluate the stress intensity factor. There are four cases of the mode stresses; Mode I, Mode II, Mode III, and Mix Mode are presented as the numerical examples.

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Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

Advances in Mathematical Physics ◽

10.1155/2019/7203408 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Hongmei Wu

Keyword(s):

Wave Scattering ◽

Radial Stress ◽

Function Method ◽

Dynamic Stress ◽

Analytic Solutions ◽

Interface Effect ◽

Sh Wave ◽

Complex Variable Function ◽

Variable Function ◽

Complex Variable Function Method

This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.

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Some Properties of J-Integral in Plane Elasticity

Journal of Applied Mechanics ◽

10.1115/1.1432663 ◽

2001 ◽

Vol 69 (2) ◽

pp. 195-198 ◽

Cited By ~ 4

Author(s):

Y. Z. Chen ◽

K. Y. Lee

Keyword(s):

Function Method ◽

Infinite Plate ◽

Scalar Function ◽

Plane Elasticity ◽

Reciprocal Theorem ◽

J Integral ◽

Large Circle ◽

Complex Variable Function ◽

Variable Function ◽

Complex Variable Function Method

Some properties of the J-integral in plane elasticity are analyzed. An infinite plate with any number of inclusions, cracks, and any loading conditions is considered. In addition to the physical field, a derivative field is defined and introduced. Using the Betti’s reciprocal theorem for the physical and derivative fields, two new path-independent D1 and D2 are obtained. It is found that the values of Jkk=1,2 on a large circle are equal to the values of Dkk=1,2 on the same circle. Using this property and the complex variable function method, the values of Jkk=1,2 on a large circle is obtained. It is proved that the vector Jkk=1,2 is a gradient of a scalar function Px,y.

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