ANALYTICAL SOLUTIONS OF MODE Ⅲ DYNAMIC CRACK UNDER THE ACTION OF DIFFERENT LOADS

By the theoretical approaches of complex functions, the problems concerning mode Ⅲ dynamic crack under the action of unit-step loads and constant loads located at the origin of the coordinates respectively, are researched. Analytical solutions of stresses, displacements, stress intensity factors, strain energy density factors, strain energy release rates and dislocation distribution functions are acquired by means of self-similar functions. The problems considered can be very readily translated into Riemann-Hilbert problems and their closed solutions are attained rather straightforward in terms of this technique. Utilizing those solutions and superposition theorem, the solutions of arbitrarily complex problems can be attained.