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Elastic solution for a hole in an infinite space

Dear All,

the solution of an elastic half space subjected to any generalized load may be seen as the solution of another elastic problem, that is elastic space with an infinite length hole when the hole radius goes to infinite.

Is there a "general" solution for that elastic problem? For general I mean a solution that can be used e.g. like a kernel in a convolution operation.

I've expanded the Navier equation in cylindrical coordinate (radial, theta, z), with a Fourier approach; assigning periodicity to theta variable and the "square summability" along the z-direction, the problem is reduced to the r-direction.

However I'm not able to de-couple the displacements in order to obtain a Bessel-like equation... therefore the question!

Thanks for any suggestions!

MS 

 

 

Comments

Mike Ciavarella's picture

If your geometry is halfspace, I mean halfplane, the best I can suggest is simplified solutions, see

On the stress concentration around a hole in a
half-plane subject to moving contact loads

International
Journal of Solids and Structures
, Volume 43, Issue 13, June
2006
, Pages 3895-3904
L. Afferrante, M. Ciavarella, G. Demelio

which in turn refers to a solution by Greenwood

Greenwood,
1989
J.A. Greenwood, Exact formulae for stresses around circular previous<br />
termholesnext<br />
term and
inclusions, Int. J. Mech. Sci. 31 (1989) (3),
pp. 219–227. Abstract
| PDF (443 K)
| View Record in Scopus | Cited By in Scopus (6)

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

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