A Hybrid Method for Crack Stress Analysis--Mapping Collocation Combined with Finite Element.

摘要

A new method for crack stress analysis has been developed by combining the modified mapping collocation method and the finite element method. The method of analytic stress functions of a complex variable is used for the immediate region around the crack tip. For regions away from the crack tip, where the stress function representation becomes ineffective or where the boundary becomes irregular, the finite element approach is used. At the junction between the collocation and the finite element regions, stress and/or displacement continuity conditions are implemented. The procedures involved are illustrated in the solutions of typical crack problems. It is demonstrated that this new algorithm is very powerful for solutions of crack stress problems with a wide range of geometric varieties. Finally, the numerical results for the sample problems are compared with the known data from the existing literature.