A Singular Integral Equation Method For The Branch Crack Problem In Antiplane Elasticity

In this dissertation, The branch crack problems in antiplane elasticity are investigated systematically by using theories of complex functions and the singular integral equation method.And this research is applied to solve a lot of branch crack problems in practice.It is studied that there is a single branch crack in an infinite body. When the singular integral equation method is used, the branch crack problem in antiplane elasticity is modeled by a reasonable distribution of the dislocation, and the innovated integration scheme developed by Y.Z.Chen is adopted. This new scheme in this dissertation is proposed in the following manner: A point dislocation is placed at the branch point and the distributed dislocations are assumed along all the branches. Thus, the singular integral equation and a constraint equation can be formulated for the branch crack problem. A semi-open quadrature rule is used, which can ensure that the number of unknowns is equal to the number of equations. The results of the numerical solution directly relate to the stress intensity factors (SIF) at the branch tips, which are paid more attention to by engineers in practice.The multiple branch crack problem and the periodic branch crack problem in an infinite region are also considered on the base of previous studies. The interactions end the reciprocal effects between cracks are exposed quantificationally.In order to find the numerical solution of the periodic branch crack problem, the relavant numerical method is proposed too.All the conclusions in this paper can be further used to investigate the branch crack problems in antiplane elasticity.Using the method proposed in this paper makes SIF values calculated more easily and more accurately. There are lots of numerical examples given. The numerical results and charts in this paper can be applied directly into practice.