Calculus of Variations and Geometric Measure Theory

L. Freddi - M. G. Mora - R. Paroni

Nonlinear thin-walled beams with rectangular cross-section - Part II

created by freddi on 14 Mar 2011
modified on 11 Jan 2017


Published Paper

Inserted: 14 mar 2011
Last Updated: 11 jan 2017

Journal: Mathematical Models and Methods in Applied Sciences (M3AS)
Volume: 23
Number: 4
Pages: 743–775
Year: 2013
Doi: 10.1142/S0218202512500595


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 rectangular cross-section. Denoting by $h$ and $\delta_h$ the length of the sides of the cross-section of the beam, we analyse the limit behaviour of a non-linear elastic energy which scales as $\varepsilon_h^2$ when $\varepsilon_h/\delta_h\to0$.

Keywords: $\Gamma$-convergence, dimension reduction, nonlinear elasticity, thin-walled cross-section beams