Approximation of a two dimensional problem of junctions

Abstract

We present an asymptotic and numerical study of a class of junctions between rods and bulk bodies in the framework of two-dimensional elasticity. The junctions under consideration are such that the depth of the embedding of the rod into the bulk is small: it is zero or of the same order than the thickness of the rod. As a result, the junction is modelized by a flexible clamping. The study, mainly devoted to the elastic displacements and stress fields within the bulk, is performed using the matched asymptotic expansions method with different expansions in the vicinity of the junction and far from it. Some terms of these expansions involve elasticity problems with point forces and moments, which are analyzed by the singularity theory. Numerical examples are given.