Nonlinear thin-walled beams with a rectangular cross-section - Part I

The purpose of this paper is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results that concern the subcritical and the critical case.