Fredholm integral equation for the multiple circular arc crack problem in plane elasticity

1997 ◽  
Vol 67 (6) ◽  
pp. 433-446 ◽  
Author(s):  
Y. Z. Chen ◽  
N. Hasebe
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Circular Arc ◽  
Arc Crack ◽  
Circular Arc Crack

scholarly journals Concentric circular misfit and a circular arc crack in an infinite isotropic elastic plate

1975 ◽  
Vol 19 (2) ◽  
pp. 215-228
Author(s):  
R. D. Bhargava ◽  
Ram Narayan
Keyword(s):  
Elastic Plate ◽  
Elastic Field ◽  
Circular Cavity ◽  
Circular Arc ◽  
Circular Inhomogeneity ◽  
Arc Crack ◽  
Circular Arc Crack

AbstractA homogeneous isotropic infinite elastic plate contains a circular cavity and a circular arc crack symmetrically situated about the x-axis. The cavity and crack are concentric but are of different radii. A circular inhomogeneity of radius slightly larger than that of the cavity is inserted into the cavity; thus generating a system of stresses in the outer material as well as in the inhomogeneity. The elastic field in the inhomogeneity and in the outer material outside the inhomogeneity is evaluated in this paper.

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.

In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

2002 ◽  
Vol 18 (3) ◽  
pp. 145-151
Author(s):  
Y. C. Shiah ◽  
Jiunn Fang ◽  
Chin-Yi Wei ◽  
Y.C. Liang
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Stress ◽  
Bending Moments ◽  
Intensity Factors ◽  
Boundary Equation ◽  
Circular Arc ◽  
Stress Functions ◽  
Arc Crack ◽  
Circular Arc Crack

AbstractIn this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

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