Flat crack under shear loading

Summary A solution is called complete when the explicit expressions are derived for the field of displacements as well as stresses in an elastic body. A new method is proposed here which allows us to obtain exact and complete solutions to various crack problems in elementary functions; no integral transforms or special function expansions are involved. The method is based on the new results in potential theory obtained earlier by the author. The method is applied to the case of a concentrated tangential loading of a penny-shaped crack. The main potential function and the relevant Green's functions are derived. An approximate analytical solution is obtained for a flat crack of general shape. A new set of asymptotic expressions is presented for the field of stresses and displacements near the crack tip in a transversely isotropic space. The use of the method is illustrated by examples.