scholarly journals Hypersingular integral equation for triple inclined cracks problems in half plane elasticity

2019 ◽  
Vol 1366 ◽  
pp. 012023
Author(s):  
N H Husin ◽  
N M A Nik Long ◽  
N Senu
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Inclined Cracks

scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

scholarly journals SOLUTION OF CONTACT PROBLEM FOR AN ARC CRACK USING HYPERSINGULAR INTEGRAL EQUATION

2008 ◽  
Vol 05 (01) ◽  
pp. 119-133 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN ◽  
Z. X. WANG ◽  
N. M. A. NIK LONG
Keyword(s):  
Integral Equation ◽  
Contact Problem ◽  
Quadrature Rule ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Normal Contact Stress ◽  
Normal Contact ◽  
Hypersingular Integral ◽  
Numerical Examples ◽  
Arc Crack

This paper investigates the contact problem for an arc crack, for example, under a remote compression. A hypersingular integral equation (HSIE) for curved cracks in plane elasticity is suggested. It is found that the direct usage of HSIE cannot solve the mentioned contact problem. For the contact problem, one must take necessary modifications for solving the HSIE. The main modified points are as follows. First, one should assume some portion along the crack under contact. The margin or the end of the contacted portion is determined by the vanishing normal contact stress at the margin point. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE. Finally, several numerical examples are given.

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