Rocking rotation of a rigid disc in a half-space

Abstract

An analysis is presented for the determination of the rotational response of a rigid circular disc embedded in a semi-infinite elastic medium under the action of a rocking moment. With the aid of Hankel transforms, a relaxed treatment of the mixed boundary value problem is formulated as dual integral equations. On reduction of the dual integral equations to a Fredholm integral equation which features a closed-form kernel, solutions to the inclusion problem are computed. In addition to providing a unified view of existing solutions for zero and infinite embedments, the present analysis reveals a severe boundary-layer phenomenon which is apt to be of significance to this class of problem in general. As illustrations, numerical results on the load-displacement relation and the response of the embedding medium, as well as the contact load distribution, are included.