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The nonlinear bending–torsion theory for curved rods as $\varGamma $-limit of three-dimensional elasticity

Article type: Research Article

Authors: Scardia, Lucia

Affiliations: S.I.S.S.A., Via Beirut 2-4, 34014, Trieste, Italy E-mail: [email protected]

Abstract: 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, curved beams, nonlinear elasticity

Journal: Asymptotic Analysis, vol. 47, no. 3-4, pp. 317-343, 2006

Published: 2006
Price: EUR 27.50
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