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NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION - PART I
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DOI：10.1142/S0218202511500163.png)
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Abstract
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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).
Keywords:
Thin-walled cross-section beams
nonlinear elasticity
Gamma-convergence
dimension reduction
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