A proof of the equivalence of the Stroh and Lekhnitskii sextic equations for plane anisotropic elastostatics

Plane problems in anisotropic elastostatics are usually treated using either a formalism developed by Stroh or a framework due to Lekhnitskii. Each technique has associated with it a sextic polynomial whose roots must be determined, usually numerically, in order to generate an elastic solution. Although it has always been assumed that the two sextic polynomials are identical, a formal proof of their equivalence has never been given. The present work provides this proof in a rather direct fashion.