An Exact Green Function for a Transient SH-wave in an Inhomogeneous Elastic Solid

2000 ◽  
Vol 2000.3 (0) ◽  
pp. 117-118
Author(s):  
Kazumi WATANABE
Keyword(s):  
Green Function ◽  
Elastic Solid ◽  
Sh Wave

Transient Study of Mode III Fracture in an Elastic Solid With a Single Plane of Material Symmetry

2003 ◽  
Vol 70 (2) ◽  
pp. 227-233 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Energy Release Rate ◽  
Release Rate ◽  
Crack Extension ◽  
Elastic Solid ◽  
Crack Edge ◽  
Material Symmetry ◽  
Sh Wave ◽  
Mode Iii ◽  
Single Plane ◽  
Transient Study

Diffraction of a plane SH-wave causes semi-infinite mode III crack extension in an unbounded linear elastic solid. The solid is nonorthotropic, with a single plane of material symmetry that is perpendicular to the crack edge. The crack plane itself lies at an arbitrary angle to the axes of material symmetry, the SH-wave direction is largely arbitrary, and extension is not necessarily instantaneous or at a constant speed. An exact transient study produces the fracture energy release rate, and uses a full-field analytical solution to derive the dynamic stress intensity factor on any plane radiating from the moving crack edge. A crack path stability analysis of the factor indicates that crack extension in the original plane can occur in directions associated with maximum and minimum values of the shear wave speed. The energy release rate for such extensions shows that, if an isotropic solid subjected to the same type of loading has the same specific fracture energy, then the nonorthotropic solid may fracture first.

Scattering of SH-Wave by an Interface Cylindrical Elastic Inclusion with a Semicircular Debonded above Subsurface Cavity

2013 ◽  
Vol 753-755 ◽  
pp. 1846-1850
Author(s):  
Chun Xiang Zhao ◽  
Hui Qi ◽  
Jing Fu Nan
Keyword(s):  
Green Function ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Fredholm Integral Equations ◽  
Circular Cavity ◽  
Sh Wave ◽  
Polar Coordinate ◽  
Set Up ◽  
Material Space ◽  
Horizontal Interface

The Scattering of SH-wave by a cylindrical elastic inclusion on horizontal interface in bi-material space with a semicircular debonded above subsurface circular cavity have been considered using the methods of complex function and Green function. Firstly, we divide the solution domain along the interface and disconnected boundary into two half-spaces, an upper one and a lower one. And Green function was constructed by using the methods of complex function and multi-polar coordinate. Secondly, the bi-material media was connected along the horizontal interface using the idea of interface conjunction, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of the first kind to determine that the unknown forces could be set up through continuity conditions on surface. Finally, some examples for DSCF around cylindrical elastic inclusion edge are presented and discussed. Numerical results show that subsurface circular cavitys existence notablely influences DSCF of around cylindrical elastic inclusion edge with a semicircular debonded above subsurface circular cavity.

The internal stability of an elastic solid

2000 ◽  
Vol 80 (12) ◽  
pp. 2827-2840 ◽  
Author(s):  
J. W. Morris Jr, C. R. K Renn
Keyword(s):  
Elastic Solid ◽  
Internal Stability

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

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