The Crack Problem for an Orthotropic Half Plane Stiffened by Elastic Films

1992 ◽  
Author(s):  
R. Mahajan ◽  
F. Erdogan ◽  
Y. T. Chou
Keyword(s):  
Half Plane ◽  
Crack Problem

The crack problem for an orthotropic half-plane stiffened by elastic films

1993 ◽  
Vol 31 (3) ◽  
pp. 403-424 ◽  
Author(s):  
Ravi Mahajan ◽  
F. Erdogan ◽  
Y.T. Chou
Keyword(s):  
Half Plane ◽  
Crack Problem

scholarly journals Periodic crack problem for a functionally graded half-plane an analytic solution

2011 ◽  
Vol 48 (21) ◽  
pp. 3020-3031 ◽  
Author(s):  
Bora Yıldırım ◽  
Özge Kutlu ◽  
Suat Kadıoğlu
Keyword(s):  
Half Plane ◽  
Analytic Solution ◽  
Crack Problem ◽  
Functionally Graded ◽  
Periodic Crack

Anti-plane stress analysis of a half-plane with multiple cracks by distributed dislocation technique in nonlocal elasticity

2018 ◽  
Vol 24 (5) ◽  
pp. 1567-1577
Author(s):  
Mohamad Tavakoli ◽  
Ali Reza Fotuhi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Nonlocal Elasticity ◽  
Crack Problem ◽  
Image Method ◽  
Multiple Cracks ◽  
Infinite Plane ◽  
Distributed Dislocation Technique ◽  
Distributed Dislocation ◽  
Dislocation Technique

The effective role of a distributed dislocation technique accompanied by a nonlocal elasticity model has been demonstrated for the crack problem in a half-plane. The dislocation solution is employed to model and analyze the anti-plane crack problem for nonlocal elasticity using the distributed dislocation technique. The solution of dislocation in the half-plane has been extracted through the solution of dislocation in an infinite plane by the image method. The dislocation solution has been utilized to formulate integral equations for dislocation density functions on the surface of a smooth crack embedded in the half-plane under anti-plane loads. The integral equations are of the Cauchy singular type, and have been solved numerically. Multiple cracks with different configurations have been solved; results demonstrate that the nonlocal theory predicts a certain stress value in the crack tip.

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE CURVED EDGE CRACKS EMANATING FROM BOUNDARY OF HALF-PLANE

2006 ◽  
Vol 03 (02) ◽  
pp. 205-217 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Edge Crack ◽  
Crack Problem ◽  
Infinite Plate ◽  
Complex Potentials ◽  
Edge Cracks ◽  
Edge Crack Problem

This paper provides, an elastic solution for multiple curved edge cracks emanating from the boundary of the half-plane. After placing the distributed dislocations at the prospective sites of cracks in an infinite plate, the principal part of the complex potentials is obtained. By using the concept of the modified complex potentials, the complementary part of the complex potentials can be derived. The whole complex potentials satisfy the traction free condition along the boundary of half-plane automatically. This is a particular advantage of the suggested method. This concept or method of the modified complex potentials is a counterpart of the Green's function method, which is universal in mathematical physics. The direct usage of this method cannot provide a solution in detail. Comparing with the line edge crack case, the following points are significant in the presented study. The relevant kernels in the integral equation are more complicated than in the line edge crack case and the relevant integrations in the problem should be completed on curves. This paper solves a rather complicated problem, the multiple curved edge crack problem, and gives the final solution. A singular integral equation is formulated with the dislocation distribution being unknown function and the traction being the right hand term. The singular integral equation is solved by using the curve length method in conjunction with the semiopening quadrature rule. Periodic curved edge crack problem is also addressed. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

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