Asymptotic behavior of solution to torsion problem for radially inhomogeneous transversally isotropic spherical shell

A torsion problem of the radially inhomogeneous transversally isotropic spherical shell is investigated by the method of homogeneous solutions. Asymptotic expansions of homogeneous solutions are obtained. It is shown that the stress-strain state is composed of the penetrating stress-strain state and the boundary layer character solution. In case of the essential anisotropy, some boundary layer solutions don't possess the damping property, and they may cover the whole area occupied by the shell.