A fast semi-analytic method for the computation of elastic edge singularities

Martin Costabel (1) , Monique Dauge (1) , Yvon Lafranche (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Singularity exponent; Edge singularities; Anisotropic elasticity; Stress concentration; Material interface

Domaines: Analyse numérique [math.NA]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Martin Costabel, Monique Dauge, Yvon Lafranche. A fast semi-analytic method for the computation of elastic edge singularities. Computer Methods in Applied Mechanics and Engineering, 2001, 190, pp.2111--2134. ⟨hal-00276711⟩