Asymptotic analysis of bending-dominated shell junctions

Abstract

The subject of this paper is the asymptotic analysis of a multi-structure made of two thin linearly elastic shells. It is assumed that the middle surfaces of the two shells are linked together on a part of their boundary, that at each point of their intersection, the two middle surfaces have distinct tangent planes and that the order of the applied body force density is ɛ 2 , where ɛ is the half-thickness of each shell. We then identify the limit when ɛ tends to zero of the solution of the ‘scaled’ three-dimensional linearized elasticity problem. It is shown in particular that this limit is constituted of inextensional displacement fields for each shell and such that the junction is rigid (the angle between the middle surfaces of the two shells at the junction is unchanged by the deformation of the multi-structure). Moreover this limit is the same as the limit of the solution of the classical shell model (or Koiter model) for the multi-structure with the condition of rigid junction.