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

Lucia Scardia

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

Lucia Scardia

Research output: Contribution to journal › Article › peer-review

30 Citations (SciVal)

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.

Original language	English
Pages (from-to)	317-343
Number of pages	27
Journal	Asymptotic Analysis
Volume	47
Issue number	3-4
Publication status	Published - 15 May 2006

Keywords

Curved beams
Dimension reduction
Nonlinear elasticity

ASJC Scopus subject areas

Applied Mathematics

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

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 = "Curved beams, Dimension reduction, Nonlinear elasticity",

author = "Lucia Scardia",

year = "2006",

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day = "15",

language = "English",

volume = "47",

pages = "317--343",

journal = "Asymptotic Analysis",

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T1 - The nonlinear bending-torsion theory for curved rods as Gamma-limit of three-dimensional elasticity

AU - Scardia, Lucia

PY - 2006/5/15

Y1 - 2006/5/15

N2 - 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.

AB - 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.

KW - Curved beams

KW - Dimension reduction

KW - Nonlinear elasticity

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M3 - Article

AN - SCOPUS:33646420884

SN - 0921-7134

VL - 47

SP - 317

EP - 343

JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 3-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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