Love solutions in the linear inhomogeneous transversely isotropic theory of elasticity

A general Love solution for the inhomogeneous transversely isotropic theory of elasticity with the elastic constants dependent on the coordinate z is proposed. This result may be considered as a generalization of the Love solutions we recently derived for the inhomogeneous isotropic theory of elasticity. The key steps of deriving the Love solution for the classical linear homogeneous transversely isotropic theory of elasticity are described for further use of the derivation procedure, which is then generalized to the inhomogeneous transversely isotropic case. Some particular cases of inhomogeneity traditionally used in the theory of elasticity are also examined. The significance of the derived solutions and their importance for the modeling of functionally graded materials are briefly discussed