Lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space

The asymmetric problem of lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space is addressed. With the aid of appropriate Greenʹs functions, the governing equations of the problem are written as a set of coupled integral equations. With further mathematical transformations, the system of dual integral equations is reduced to two coupled Fredholm integral equations of the second kind which are amenable to numerical treatments. The exact closed-form solutions corresponding to two limiting cases of a membrane resting on the surface of a half-space and embedded in a full-space are derived. The jump behavior of results at the edge of the membrane for the case of an infinitesimal embedment is highlighted analytically. For the special case of an isotropic half-space, the results are in exact agreement with those available in the literature. The detailed numerical scheme for solving the coupled Fredholm integral equations is presented. Selected numerical results are depicted and the effects of anisotropy on the lateral stiffness factor are discussed.