Scattering of a Nanoscale Circular Elastic Inclusion on SH Wave in a Semi-Space

2018 ◽  
Vol 07 (02) ◽  
pp. 66-74
Author(s):  
志英 欧
1974 ◽  
Vol 96 (3) ◽  
pp. 228-233
Author(s):  
P. Prakash ◽  
K. P. Rao

The problem of a circular elastic inclusion in a thin pressurized spherical shell is considered. Using Reissner’s differential equations governing the behavior of a thin shallow spherical shell, the solutions for the two regions are obtained in terms of Bessel and Hankel functions. Particular cases of a rigid circular inclusion free to move with the shell and a clamped rigid circular inclusion are also considered. Results are presented in nondimensional form which will greatly facilitate their use in the design of spherical shells containing a rigid or an elastic inclusion.


2013 ◽  
Vol 753-755 ◽  
pp. 1846-1850
Author(s):  
Chun Xiang Zhao ◽  
Hui Qi ◽  
Jing Fu Nan

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.


2008 ◽  
Vol 76 (1) ◽  
Author(s):  
X. Wang ◽  
E. Pan

We investigate a partially debonded circular elastic inclusion embedded in a particular class of harmonic materials by using the complex variable method under finite plane-strain deformations. A complete (or full-field) solution is derived. It is observed that the stresses in general exhibit oscillatory singularities near the two tips of the arc shaped interface crack. Particularly the traditional inverse square root singularity for stresses is observed when the asymptotic behavior of the harmonic materials obeys a constitutive restriction proposed by Knowles and Sternberg (1975, “On the Singularity Induced by Certain Mixed Boundary Conditions in Linearized and Nonlinear Elastostatics,” Int. J. Solids Struct., 11, pp. 1173–1201). It is also found that the number of admissible states under finite plane deformations for given external loads can be two, one, or even zero.


1966 ◽  
Vol 33 (3) ◽  
pp. 637-640 ◽  
Author(s):  
A. H. England

The problem of a circular elastic inclusion bonded to a different elastic material except over an arc crack is considered. It is found that the solution yields an oscillation phenomenon near the ends of the crack of a form found previously by several authors, indicating that linear elasticity may not be used to predict the stresses and displacements in these regions.


2017 ◽  
Vol 34 (5) ◽  
pp. 617-627 ◽  
Author(s):  
C. K. Chao ◽  
C. H. Wu ◽  
K. Ting

AbstractThe problem of a circular elastic inclusion perfectly bonded to a matrix of infinite extent and subjected to arbitrarily thermal loading has been solved explicitly in terms of the corresponding homogeneous problem based on the inversion and Kelvin's transformation. It is to be noted that the relations established in this paper between the stress functions are algebraic and do not involve integration or solution of some other equations. Furthermore, the transformation leading from the solution for the homogeneous problem to that for the heterogeneous one is very simple, algebraic and universal in the sense of being independent of loading considered. The case of two bonded half-planes is obtained as a limiting case.


2009 ◽  
Vol 25 (4) ◽  
pp. 411-419 ◽  
Author(s):  
J.X. Zhao ◽  
H. Qi

ABSTRACTThe scattering of plane SH-wave from a partially debonded shallow cylindrical elastic inclusion in half space is investigated in this paper by complex function method and expansion method of wave function. The debonding regions are considered as multiple arc-shaped interface cracks with non-contacting faces. Firstly, in the inclusion district, the standing wave function in the elastic inclusion with unknown coefficients which satisfies the boundary condition is constructed and generated into the Fourier series; in the half space, the stress and displacement boundary condition around the elastic inclusion can be modeled as the same as the standing wave function in the elastic inclusion. Then, a set of infinite algebraic equations can be obtained around the same boundary and the solution of problem can be gained. In the end, numerical examples of the surface displacement are provided and discussed. It is found that the interface cracks can raise the surface displacement amplitudes to a certain degree.


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