Fast semi-analytic computation of elastic edge singularities

The singularities that we consider are the characteristic non-smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges. We describe here a method to compute their singularity exponents and the associated angular singular functions. We present the implementation of this method in a program whose input data are geometrical data, the elasticity coeecients of each material involved and the type of boundary conditions (Dirichlet, Neu-mann or mixed conditions). Our method is particularly useful with anisotropic materials and allows to \follow" the dependency of singularity exponents along a curved edge.