Abstract
An asymptotic expansion method is applied to nonlinear three-dimensional elastic straight slender rods. Nonlinear ordinary differential equations for approximate displacements and explicit formulas for approximate stress distributions are obtained. Mathematical properties of these models are studied.
Résumé
On applique la méthode des développements asymptotiques à des poutres tridimensionnelles droites, élancées et non linéairement élastiques. On en déduit des équations différentielles ordinaires non linéaires pour des déplacements approchés, ainsi que des formules explicites pour des approximations des distributions de contraintes. On étudie les propriétés mathématiques de ces modèles.
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Cimetière, A., Geymonat, G., Le Dret, H. et al. Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods. J Elasticity 19, 111–161 (1988). https://doi.org/10.1007/BF00040890
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DOI: https://doi.org/10.1007/BF00040890