Stress analysis of simply and multiply connected regions containing cracks by the method of boundary collocation
Theoretical stress analyses were performed for the case of cracks emanating from, or in the vicinity of holes or boundaries of various shapes in two-dimensional. elastic bodies. The solution is based on the complex variable method developed by Muskhelishvili and a numerical technique known as collocation for approximating the stress or displacement conditions on the boundary with appropriate series stress functions. These stress functions automatically satisfy the boundary conditions on the crack surfaces. The boundary collocation method included techniques such as, specifying stresses at equally spaced points on the boundary, specifying the resultant forces along arcs on the boundary, and a least-squares technique used to minimize the resultant force or displacement residuals along the boundary. The types of configurations investigated included the case of cracks emanating from a circular hole, the case of a crack in the presence of multiple-circular holes and the case of cracks emanating from an elliptical hole in an infinite plate. The configurations investigated were subjected to a variety of loading conditions. The results of the analyses are presented in terms of the crack tip stress-intensity factor.