The generation of elements with singularities

Abstract

Abstract A procedure is given for generating two‐dimensional conforming singularity elements from standard conforming elements. Three new elements with 0( r‐ p ) derivative singularities are introduced. The technique is based on the use of elements defined by numerically integrated shape functions. Special quadrature rules are suggested for triangular elements. The degeneration of these elements to crack tip elements and the direct evaluation near the singularity of element quantities, such as the stress intensity factors, is discussed.