No 1, Vol. 15, 2012, pages 9-25

ON THE BASE OF SURFACE DISPLACEMENTS

The aim of our work is to discuss how the surface displacements caused by an
applied force can be used for the identification of defects placed in near-surface layers of the
body. As an illustrative example of the possibility for such identification, the elastic problem
for the half-space weakened by a circular hole is considered. First of all we present the
complete and correct analytical solution of the plane elasticity problem for the concentrated
force acting on the surface of a half-space with a hole. We describe the biharmonic stressfunction
used for the derivation of stresses and strains in the half-space with a hole and the
associated biharmonic function that allows to determine the displacement field. Both
functions are given in the form of Fourier series with the compact coefficients. It is shown
that the found analytical formulas of surface displacements give the way to find the circular
hole diameter and position when the applied force and elastic modules of the material are
known.
Keywords: defect identification; half-space weakened by a circular hole; concentrated load; elastic fields; surface displacements |

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