An inextensible membrane at the interface of a transversely isotropic bi-material full-space

A theoretical formulation is presented for the determination of the dynamic interaction of a horizontally loaded inextensible circular membrane embedded at the interface of a transversely isotropic bi-material full-space, using cylindrical co-ordinate system and applying Hankel integral transforms in the radial direction and Fourier series, the problem will be changed to a system of four separate integral equations, which, in turn, are reduced to a pair of Fredholm equations of the second kind that are amenable to numerical treatments. The impedance functions have been evaluated in dynamic case, which can be directly used in soil–structure-interaction and engineering problems. It is shown that the present solutions are analytical and numerically in exact agreement with different degenerate cases. To validate the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy. The numerical scheme for solving Fredholm equation is also presented.