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UBC Theses and Dissertations

A survey of boundary element methods for a two-dimensional fracture model James, Douglas L.


This thesis surveys boundary element methods for solving a two-dimensional pressurized line crack problem in a homogeneous infinite elastic medium. Starting with an overview of linear elastic fracture mechanics, the exact solution to the pressurized line crack problem is stated and results for several pressure distributions are provided. Various numerical methods for solving the crack problem are then introduced, such as the displacement discontinuity method (DDM) using point collocation and a Galerkin method. Crack tip elements and higher-order DDM are discussed. Self-effect correction methods, stated and developed for the piecewise constant DDM on a uniform grid, are shown to significantly improve the numerical solution. An accurate DDM correction for modelling crack tip element extensions is also presented. Finally, numerical results for the various methods are given and stress intensity factors are also presented for comparison.

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