Asymptotic expansion of solution of the torsion problem for an elastic rod with a cavity and a thin bonded multilayer

Abstract

The first term of the asymptotic expansion of the solution of the torsion problem for an elastic rod is derived using the method of a matched asymptotic expansion. The prismatic rod is weakened by an internal cavity with angular points, one of which is situated on the exterior boundary. The exterior boundary of the rod is reinforced by a thin elastic multilayer. Difference be tween the exact and approximate solution of the problem are estimated by the norm of the Sobolev spaces. Relations for stress intensity factors in the angular points are found and verified.