A SUPERELEMENT FOR 2-DIMENSIONAL SINGULAR BOUNDARY-VALUE-PROBLEMS IN LINEAR ELASTICITY

The finite element method for elliptic boundary value problems has bee n modified to deal with boundary singularities. We introduce a singula r-super-element (SSE) which incorporates the known expansion for the s ingular solution explicitly over the internal region surrounding the s ingular point, whilst using blended trial functions over the intermedi ate region, which joins the internal and external regions smoothly. Th e SSE conforms with the mesh used in the external region, and may be e asily incorporated into standard finite element programs. The calculat ions yield the expansion coefficients directly, as well as an accurate representation of the displacements in the vicinity of the singular p oint, for a crack or V-notch of any angle subject to any mode of loadi ng. The SSE has been applied to determine stress intensity factors for two-dimensional crack and V-notch problems, including mixed mode. The computations converge rapidly, yielding results of high accuracy.