WEIGHT FUNCTIONS FROM VIRTUAL CRACK EXTENSION

The stiffness‐derivative method of Parks1 for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector field2,3 which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3 on the weight function and of Zienkiewicz4 on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back‐substitution on the already‐factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three‐dimensional configurations is outlined. While this manuscript was under review, the authors became aware of the recent work of Vanderglas,21 in which the same approach as ours is used to extend the stiffness derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vanderglas noted. Copyright © 1979 John Wiley & Sons, Ltd