Torsion of a punch attached to transversely-isotropic half-space with functionally graded coating

The paper focuses on analytical solution for the problem about torsion of a circular punch attached to a transversely-isotropic elastic half-space with functionally-graded coating. The problem is reduced to dual integral equations by using integral transformations technique. The scheme of numerical construction of the kernel transform of the integral equation is developed. Approximations of the kernel transform by analytical expressions of special kind are proposed and explicit solution is derived with these approximations. It is shown that the derived solutions are asymptotically exact at both large and small values of characteristic dimensionless geometrical parameter of the problem. The application of the solution is illustrated by example of a steel substrate with functionally graded yttrium stabilized zirconia coating.