An extended Galerkin representation for a transversely isotropic linearly elastic medium

An algorithm for splitting an equilibrium displacement equation system with bulk forces for a transversely isotropic linearly-elastic medium is described that leads to three uncoupled equations with certain canonical fourth-order differential operators in the three components of the displacement vector. It is shown that, in the special case of isotropy, the proposed algorithm is mathematically equivalent to the Galerkin representation, well-known in the theory of elasticity.