Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry

By the theory of complex functions, a penny_shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self_similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self_similarity under the ladder_shaped loads. The problems dealt with can be transformed into Riemann_Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov_Sobolev, the solutions of arbitrary complicated problems can be obtained.