Stresses on the surface of a rigid needle in an orthotropic elastic medium

Abstract

Using the general solution of the problem of stress concentrations on the surfaces of rigid ellipsoidal inclusions [1], the three-dimensional problem of stresses on the surface of a completely rigid needle in an unbounded elastic orthotropic medium under the action of a uniform external field is solved. By a needle we mean an ellipsoidal inclusion, one dimension of which is large compared with the other two. Explicit formulas are obtained and investigated for stresses along the principal sections of the needle in the orthotropic medium and over the entire surface of the needle in an isotropic medium. The calculations are performed, apart from the singular terms (large, but finite quantities).