Calculus of Variations and Geometric Measure Theory

L. Scardia

The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity

created by scardia on 24 Jan 2006
modified on 19 Oct 2006


Published Paper

Inserted: 24 jan 2006
Last Updated: 19 oct 2006

Journal: Asymptot. Anal.
Volume: 47
Number: 3,4
Pages: 317-343
Year: 2006


The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending-torsion theory for rods are deduced.

Keywords: dimension reduction, nonlinear elasticity, curved beams