Abstract
This thesis is divided into two main parts: (i) the first one is about an original purely geometrical deduction of the kinematics of thin structures, as plates and shells; (ii) the second one concerns the modelling of rigid shell-like inclusions in a three-dimensional medium and the modelling of layered elastic beams through the asymptotic methods. (i) The geometrical derivation of plates and shells kinematics is based on the Saint-Venant compatibility equations and the integral formula of Cesàro-Volterra. The appellation "geometrical" is due to the fact that we do not use any information coming from the constitutive behavior or the loading. Let us consider a simply connected plate (likewise, we consider a simply connected shell). We apply a formal asymptotic development to the Saint-Venant equations and the Cesàro-Volterra formula. By characterizing the main terms of this expansion, we deduct the classical kinematical assumptions of the Kirchhoff-Love plate models (in the case of the shell, the generalized Kirchhoff-Love shell model) and the Reissner-Mindlin plate model (in the case of the shell, the Naghdi shell model). (ii) In the second part we perform an asymptotic analysis to find the transmission conditions between a thin shell-like layer with high rigidity and the surrounding 3D continuum. We derive the limit problems when the elastic modula of the central layer are of the order of magnitude 1/epsilon and 1/epsilon^3 with respect to the modula of the 3D medium. Moreover, we study the asymptotic behavior of three different layered elastic strips by varying the orders of magnitude among the thicknesses of each layer and their elastic modula.