Vol. 11, No. 4, 2016

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A refined 1D beam theory built on 3D Saint-Venant's solution to compute homogeneous and composite beams

Rached El Fatmi

Vol. 11 (2016), No. 4, 345–378
DOI: 10.2140/jomms.2016.11.345

This paper proposes a refined 1D beam theory (RBT) built on the 3D Saint-Venant (SV) solution established for arbitrary composite cross-section. In this theory (RBT/SV), the displacement model introduces sectional out-of-plane warpings, Poisson’s effects and distortions. For a given cross-section, the sectional displacement modes are extracted from the computation of the correspondent 3D SV’s solution. These sectional modes, which reflect the mechanical behavior of the cross-section, lead to a beam theory that really fits the section nature (shape and material(s)). As a result, RBT/SV allows to recover a more realistic spatial behavior for the beam, to catch a significant part of the edge effects, and hence to compute a relatively short beam. In order to apply RBT/SV, a package (named CSB) of two complementary numerical Matlab tools have been developed: CSection and CBeam. CSection computes by 2D-FEM the deformation modes of the cross-section, and CBeam uses these sectional modes to generate the correspondent beam theory and compute by 1D-FEM the beam. A significant set of homogeneous/composite beams have been computed and, to show the efficiency of such a theory, 3D RBT/SV results have been systematically compared with those provided by full 3D-FEM computations.

refined beam theory, Saint-Venant's solution, composite section, out-of-plane warpings, Poisson's effects, distortions, end-effects
Received: 31 August 2015
Revised: 28 December 2015
Accepted: 5 January 2016
Published: 4 August 2016
Rached El Fatmi
Ecole Nationale d’Ingénieurs de Tunis
Université de Tunis El Manar
LGC, BP 37, Le Belvédère
1002 Tunis