NUMERICAL-ANALYSIS OF SINGULARITIES IN 2-DIMENSIONS .1. COMPUTATION OF EIGENPAIRS

A numerical method is described for the computation of eigenpairs whic h characterize the exact solution of linear second-order elliptic part ial differential equations in two dimensions in the vicinity of singul ar points. The singularities may be caused by re-entrant corners and a brupt changes in boundary conditions or material properties. Such sing ularities are of great interest from the point of view of failure init iation: The eigenpairs characterize the straining modes and their ampl itudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involv e the eigenpairs and their amplitudes. This paper addresses the proble m of determining the eigenpairs numerically on the basis of the Steklo v formulation. Numerical results are presented for several cases. Impo rtantly, the method is applicable to three-dimensional cases.