GFIFs Computation for Two-Dimensional Heat Conduction Problems

Having computed the eigenpairs associated with a 2-D singular point, the next task is the computation of the coefficients of the series expansion Ai ’s, called for the heat conduction equation “generalized flux intensity functions” (GFIFs). The eigenpairs may be viewed as characterizing the straining modes, and their amplitudes (the GFIFs) quantify the amount of “energy” residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs. As a simple example, consider a solution for which all eigenpairs are given. Although the first eigenvalue may be very small, if the corresponding GFIF is zero, the solution does not manifest this singular behavior.