Complex hypersingular integrals and integral equations in plane elasticity

1994 ◽  
Vol 105 (1-4) ◽  
pp. 189-205 ◽  
Author(s):  
A. M. Linkov ◽  
S. G. Mogilevskaya
Keyword(s):  
Integral Equations ◽  
Plane Elasticity ◽  
Hypersingular Integrals

Equivalent boundary integral equations with indirect variables for plane elasticity problems

2003 ◽  
Vol 24 (12) ◽  
pp. 1390-1397
Author(s):  
Zhang Yao-ming ◽  
Wen Wei-dong ◽  
Zhang Zuo-quan ◽  
Sun Huan-chun ◽  
Lü He-xiang
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Plane Elasticity ◽  
Boundary Integral ◽  
Equivalent Boundary ◽  
Elasticity Problems

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.

Equivalent boundary integral equations for plane elasticity

1997 ◽  
Vol 40 (1) ◽  
pp. 76-82 ◽  
Author(s):  
Haichang Hu ◽  
Haojiang Ding ◽  
Wenjun He
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Plane Elasticity ◽  
Boundary Integral ◽  
Equivalent Boundary

Integral Equation Methods for Multiple Crack Problems and Related Topics

2007 ◽  
Vol 60 (4) ◽  
pp. 172-194 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Point Sources ◽  
Fredholm Integral Equations ◽  
Hypersingular Integral Equation ◽  
Multiple Crack ◽  
Antiplane Elasticity ◽  
Crack Problems

The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

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