A torsion load transfer problem for a class of non-homogeneous elastic solids

Abstract This paper is concerned with the axisymmetric torsion of a finite (long) cylindrical bar which is partially embedded in a non-homogeneous transversely isotropic elastic layer underlaid by a rigid base. The non-homogeneity of the elastic layer is represented by both linear and non-linear variations of shear moduli with depth. The bar-elastic layer system is decomposed to a real bar and an elastic layer with a cylindrical cavity identical to the embedded bar, instead of adopting the conventional fictitious bar-extended elastic medium decomposition. The proposed decomposition allows the imposition of displacement compatibility and traction continuity along the true contact surface in the analysis. A solution scheme based on a classical variational theorem is presented to analyse the load transfer problem. The displacement and traction Green's functions of the nonhomogeneous elastic layer are required in the analysis and these are derived explicitly using Hankel integral transforms. Numerical results are presented to illustrate the effect of non-homogeneity and transverse isotropy on the torque twist relationship at the top end of the bar and twist angle and torque transfer curves along the length of the bar.