Complex variable methods and closed form solutions to dynamic crack and punch problems in the classical theory of elasticity

Closed form solutions to dynamical problems in the classical theory of elasticity are rare. In this paper we demonstrate how complex variable techniques may be used to obtain closed form solutions to several problems of practical importance. We consider an elastic strip, and firstly obtain closed form solutions when the surface of the strip is subjected to mixed moving boundary conditions. Next we consider the problem of a pair of punches moving along the lateral boundaries of the strip and opening a crack along the mid surface. To the best of our knowledge the closed form solutions presented are new.