A new variable-order singular boundary element for two-dimensional stress analysis

A new variable-order singular boundary element for two-dimensional stress analysis is developed. This element is an extension of the basic three-node quadratic boundary element with the shape functions enriched with variable-order singular displacement and traction elds which are obtained from an asymptotic singularity analysis. Both the variable order of the singularity and the polar pro le of the singular elds are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element’s great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature