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

被引：23

作者：

Freddi, Lorenzo ^{[1
]}

Mora, Maria Giovanna ^{[2
]}

Paroni, Roberto ^{[3
]}

机构：

[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

[2] SISSA, I-34136 Trieste, Italy

[3] Univ Sassari, Dipartimento Architettura & Pianificaz, I-07041 Piazza Duomo, Alghero, Italy

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2012年 / 22卷 / 03期

关键词：

Thin-walled cross-section beams; nonlinear elasticity; Gamma-convergence; dimension reduction; BENDING-TORSION THEORY; GAMMA-CONVERGENCE; 3-DIMENSIONAL ELASTICITY; INEXTENSIBLE RODS; CURVED RODS; DERIVATION; ENERGY; MODELS; LIMIT;

D O I：

10.1142/S0218202511500163

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 delta(h) the length of the sides of the cross-section, with delta(h) << h, and by epsilon(2)(h) the scaling factor of the bulk elastic energy, we analyze the cases in which delta(h)/epsilon(h) -> 0 (subcritical) and delta(h)/epsilon(h) -> 1 (critical).

引用

页数：34

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