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 coefficients of each material involved and the type of boundary conditions (Dirichlet, Neumann or mixed conditions). Our method is particularly useful with anisotropic materials and allows to "follow" the dependency of singularity exponents along a curved edge. 1. Introduction In linear elasticity, problems are usually solved with industrial codes using the finite element method. However, when the elastic body has corners on its boundary, such as a polygon or a polyhedron, the solution obtained is inaccurate near the corners. The reason is that on such domains, el..