Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity

Details Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity

2011-06-30

arxiv.org/abs/1106.6245v1

Mathematics

Analysis of PDEs

Scientific paper

The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order {\epsilon}_h^2, with {\epsilon}_h/{\delta}_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of {\delta}_h with respect to h.

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