NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II

In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with a rectangular cross-section. Denoting by h and δh ≪ h the length of the sides of the cross-section of the beam, we analyze the limit behavior of a nonlinear elastic energy which scales as [Formula: see text] when ϵh/δh → 0.

NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART I

Our aim 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. More precisely, denoting by h and δh the length of the sides of the cross-section, with δh ≪ h, and by [Formula: see text] the scaling factor of the bulk elastic energy, we analyze the cases in which δh/εh → 0 (subcritical) and δh/εh → 1 (critical).