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Closedness equation for biorthogonal system of functions has been derived. Closed-loop function systems characteristics are defined. They allow to solve contact problems of elasticity theory for finite bodies – a rectangle, a circular plate, a cylinder of finite length, etc.

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.

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.

Closedness equation for biorthogonal system of functions has been derived. Closed-loop function systems characteristics are defined. They allow to solve contact problems of elasticity theory for finite bodies – a rectangle, a circular plate, a cylinder of finite length, etc.