Time-Harmonic Elastic-Wave Scattering: The Role of Hypersingular Boundary Integral Equations

1991 ◽  
pp. 311-319 ◽  
Author(s):  
G. Krishnasamy ◽  
F. J. Rizzo
Keyword(s):  
Elastic Wave ◽  
Integral Equations ◽  
Wave Scattering ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Harmonic Elastic Wave ◽  
Elastic Wave Scattering ◽  
Time Harmonic

Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water: Part I: Applied Tractions at the Liquid-Solid Interface

1986 ◽  
Vol 53 (2) ◽  
pp. 326-332 ◽  
Author(s):  
S. M. Gracewski ◽  
D. B. Bogy
Keyword(s):  
Elastic Wave ◽  
Integral Equations ◽  
Half Space ◽  
Interface Crack ◽  
Wave Scattering ◽  
Plane Waves ◽  
Crack Tip ◽  
Solid Interface ◽  
Elastic Wave Scattering ◽  
Layered Half Space

In Part I of this two-part paper, the analytical solution of time harmonic elastic wave scattering by an interface crack in a layered half space submerged in water is presented. The solution of the problem leads to a set of coupled singular integral equations for the jump in displacements across the crack. The kernels of these integrals are represented in terms of the Green’s functions for the structure without a crack. Analysis of the integral equations yields the form of the singularities of the unknown functions at the crack tip. These singularities are taken into account to arrive at an algebraic approximation for the integral equations that can then be solved numerically. Numerical results in the form of crack tip stress intensity factors are presented for the cases in which the incident disturbance is a harmonic uniform normal or shearing traction applied at the liquid-solid interface. These results are compared with a previously published solution for this problem in the absence of the liquid. In Part II, which immediately follows Part I in the same journal issue, the more realistic disturbances of plane waves and bounded beams incident from the liquid are considered.

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