New integral equation for curve crack problem in plane elasticity with arbitrary loading condition

1990 ◽  
Vol 46 (3) ◽  
pp. R43-R46 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Integral Equation ◽  
Loading Condition ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Curve Crack ◽  
Arbitrary Loading

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.

scholarly journals The Crack Problem for a Nonhomogeneous Plane

1983 ◽  
Vol 50 (3) ◽  
pp. 609-614 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Integral Equation ◽  
Poisson’S Ratio ◽  
Crack Problem ◽  
Surface Displacement ◽  
Plane Elasticity ◽  
Poisson's Ratio ◽  
Cauchy Type ◽  
Crack Tips ◽  
Square Root Singularity ◽  
Crack Surface Displacement

In this paper the plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson’s ratio of the medium is constant and the Young’s modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy-type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson’s ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. On the other hand, the results are highly affected by the parameter β describing the material nonhomogeneity in E (x) = E0exp(βx).

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