Green’s functions of a surface-stiffened transversely isotropic half-space

Green’s functions of a transversely isotropic half-space overlaid by a thin coating layer are analytically obtained. The surface coating is modeled by a Kirchhoff thin plate perfectly bonded to the half-space. With the aid of superposition technique and employing appropriate displacement potential functions, the Green’s functions are expressed in two parts; (i) a closed-form part corresponding to the transversely isotropic half-space with surface kinematic constraints, and (ii) a numerically evaluated part reflecting the interaction between the half-space and the plate in the form of semi-infinite integrals. Some limiting cases of the problem such as surface-stiffened isotropic half-space, Boussinesq and Cerruti loadings, and extremely flexible and rigid plates are also studied. For the classical Cerruti problem in transversely isotropic materials, the effects of incompressibility are highlighted. Numerical results are provided to show the effects of material anisotropy, relative stiffness factor, and load buried depth. The obtained Green’s functions play a key role in treating further mixed-boundary-value problems in surface stiffened transversely isotropic half-spaces.