| Analysis of certain two dimensional problems containing cracks and holes is elaborated in this dissertation. The integral transforms method is used to formulate the two parallel cracks problem, which results in two pairs of dual integral equations. The solution is correctly carried out and yields good agreement with other method, which clarifies some ambiguities in some precursors' study. The singular integral equations containing Cauchy or Hilbert kernels are studied. A collocation method based on the Fejer's quadrature is devised to attack the singular integral equations of the second kind.; Distributed dislocation method is one of the most powerful techniques particularly in solving multiple arbitrarily orientated crack problems. This technique has the merits of both the complex variable method of Muskhelishvili-Kolosov in deriving the elementary dislocation solution, and also the Green's function method in applying the elementary dislocation solution. Once the elementary, solution is available, the problems of mode I, mode II, mode III, and/or their combinations, as well as the hole problem, can be formulated through a standard procedure which is especially in favor of a digital computer programming.; Derivations of the elementary solutions for a point screw dislocation located in an infinite strip or rectangular plate are accomplished by means of the method of images and also conformal mapping technique. A number of numerical examples presented in this study have shown excellent accuracy with the analytical solution, some of the numerical results can even coincide with the exact solutions to the round-off error.; Topics on antiplane shear crack are studied, where the heuristic derivation of SIF for a curved crack and the treatment of the hole problem are of practical importance in studying the cracks of generalized shapes. Investigation of the current study also includes some laborious in plane crack examples such as 100 surface breaking cracks and the growth pattern of a fluid filled crack. In conclusion, various numerical examples presented in the dissertation have demonstrated the accuracy, efficiency, versatility of the proposed methods of analysis, which are of value and promise in the studies of fracture mechanics. |
