Construction of special shape functions for triangular elements with one edge lying in the crack front

This paper presents a new and general construction method of special triangular elements with one edge lying in the crack front. In our method, principal items which represent the asymptotic properties around the crack front in local coordinate system are constructed. Based on the principal items, two groups of basis functions for crack front elements are introduced. Combining undetermined coefficients and basis functions, two types of crack front elements, which are denoted by low order crack front elements and high order ones, are constructed. Secondly, a displacement extrapolation technique with these newly developed elements is proposed. Applying this technique in the BEM applications for crack problems, numerical difficulties, which arise when two vertexes of the assisted line both locate inside the element, can be circumvented conveniently. Finally, two types of elements are employed in the dual boundary element codes for crack problems. Numerical examples are presented to verify the three types of elements. Results show that the stress intensity factors computed by employing these three developed elements are all very accurate compared with the existing results.