A superposition method for the solution of crack problems

Abstract

AbstractWe discuss a two‐step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two‐step procedure is minimal since the solution matrix from step one may be reused with a new right‐hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.