Spheroidal Cavity With Prescribed Asymmetric Displacements in Three‐Dimensional Transverse Isotropy

A general three‐dimensional analytical solution, exact within elastostatics, is presented to the problem of an infinite transversely isotropic elastic medium containing a spheroidal cavity with zero body forces, prescribed asymmetric displacements on the surface of the cavity, and vanishing stresses and displacement at infinity. The approach is applied to obtain the solution to the problem of a transversely isotropic medium containing a perfectly rigid spheroidal inclusion, where the medium is subject at infinity to uniform tension in the direction perpendicular to the axis of elastic symmetry of the material. Numerical results and the effect of anisotropy on the interfacial normal stress are discussed.