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

2008 ◽  
Vol 372 (4) ◽  
pp. 510-514 ◽  
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

STUDY ON ELASTIC ANALYSIS OF CRACK PROBLEM OF TWO-DIMENSIONAL DECAGONAL QUASICRYSTALS OF POINT GROUP 10, $\overline {10}$

2009 ◽  
Vol 23 (16) ◽  
pp. 1989-1999 ◽  
Author(s):  
WU LI ◽  
TIAN YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Two Dimensional ◽  
Partial Differential ◽  
Decagonal Quasicrystal ◽  
Complex Variable Function ◽  
Variable Function ◽  
Group 10

By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, [Formula: see text] to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.

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.

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.

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.

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