The extension of Stroh formalism to three-dimensional anisotropic elasticity 

[[abstract]]Plane problems in anisotropic elastic media have been examined extensively using two-dimensional Stroh formalism. Using a set of arbitrarily chosen orthogonal vectors on an oblique plane, the mathematical framework of Stroh formalism is established for applying to three-dimensional problems of anisotropic materials. The generalized eigenrelation problem, eigenvalues and eigenvectors have associated with the choice of orthogonal vectors and elastic moduli of materials, but not the position vector. The Barnett-Lothe tensors, which appear frequently in the real form solutions to two-dimensional anisotropic elasticity problems, are generalized and evaluated using the concept of impedance tensors. Explicit expressions of impedance tensors and Barnett-Lothe tensors are obtained for transversely isotropic media. One of the Barnett-Lothe tensors has been shown related to the Green's functions for an infinite anisotropic medium, and its result is evaluated on the oblique plane whose normal vector is the position vector. The formulation of generalized Stroh formalism can also be applied to two-dimensional cases.[[note]]SC