Torsion of a circular compound bar with imperfect interface

The Saint-Venant torsion problem of a circular cylinder reinforced by a nonconcentric circular bar of a different material with an imperfect interface is studied. Conformai mapping together with a Laurent series expansion are employed to analyze the problem. The jump condition in either the warping function or the shear traction, characterizing the imperfect interface, is simulated in the transformed domain in an exact manner. Unlike the problem with perfectly bonded interface, the series solution has to be resolved by a truncation. Numerical illustrations are provided for the torsional rigidity of the cross section. In the case of perfect bonding case, our results agree with that reported in Muskhelishvili.