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

LORENZO FREDDI

Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy

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MARIA GIOVANNA MORA

SISSA, via Bonomea 265, 34136 Trieste, Italy

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ROBERTO PARONI

Dipartimento di Architettura e Pianificazione, Università di Sassari, Palazzo del Pou Salit, Piazza Duomo, 07041 Alghero, Italy

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https://doi.org/10.1142/S0218202511500163Cited by:24 (Source: Crossref)

Abstract

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 δ_h the length of the sides of the cross-section, with δ_h ≪ h, and by the scaling factor of the bulk elastic energy, we analyze the cases in which δ_h/ε_h → 0 (subcritical) and δ_h/ε_h → 1 (critical).

Keywords:

AMSC: 74K10, 74B20, 49J45

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