Complex variable function method fob hole shape optimization in an elastic plane

1987 ◽  
Vol 8 (2) ◽  
pp. 137-146 ◽  
Author(s):  
Sun Huan-chun ◽  
Zhang Ju-yong ◽  
Yan Guo-mei ◽  
Zhang Ji-zhu
Keyword(s):  
Shape Optimization ◽  
Complex Variable ◽  
Function Method ◽  
Elastic Plane ◽  
Complex Variable Function ◽  
Hole Shape ◽  
Variable Function ◽  
Complex Variable Function Method

Complex Potentials for Plane Problem of Two-Dimensional Quasicrystals with a Lip-Shape Crack

2014 ◽  
Vol 1004-1005 ◽  
pp. 1415-1418
Author(s):  
Qiong He ◽  
Hai Yun Xiong
Keyword(s):  
Conformal Mapping ◽  
Plane Problem ◽  
Complex Variable ◽  
Function Method ◽  
Potential Functions ◽  
Two Dimensional ◽  
Griffith Crack ◽  
Complex Variable Function ◽  
Variable Function ◽  
Complex Variable Function Method

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.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
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.

Some Properties of J-Integral in Plane Elasticity

2001 ◽  
Vol 69 (2) ◽  
pp. 195-198 ◽  
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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