Closure to “Discussion of ‘Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading’” (1988, ASME J. Appl. Mech., 55, pp. 248–249)

1988 ◽  
Vol 55 (1) ◽  
pp. 249-249
Author(s):  
H. F. Nied
Keyword(s):  
Half Plane ◽  
Periodic Array ◽  
Arbitrary Loading

scholarly journals Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading

1987 ◽  
Vol 54 (3) ◽  
pp. 642-648 ◽  
Author(s):  
H. F. Nied
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Crack Surface ◽  
Mixed Boundary ◽  
Crack Opening ◽  
Periodic Array ◽  
Hypersingular Integral Equation ◽  
Opening Displacement ◽  
Surface Displacements ◽  
Displacement Based

The plane elastic problem for a periodic array of cracks in a half-plane subjected to equal, but otherwise arbitrary normal crack surface tractions is examined. The mixed boundary value problem, which is formulated directly in terms of the crack surface displacements, results in a hypersingular integral equation in which the unknown function is the crack opening displacement. Based on the theory of finite part integrals, a least squares numerical algorithm is employed to efficiently solve the singular integral equation. Numerical results include crack opening displacements, stress intensity factors, and Green’s functions for the entire range of possible periodic crack spacing.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

Rayleigh Wave in a Rotating Magneto-Thermo-Elastic Half-Plane

2012 ◽  
Vol 42 (4) ◽  
Author(s):  
Baljeet Singh ◽  
Sangeeta Kumari ◽  
Jagdish Singh
Keyword(s):  
Rayleigh Wave ◽  
Half Plane
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