Abstract
Using Gurtin's variational principle, a rational method for deducing the approximate one-dimensional theories of Medick from three-dimensional elasticity is presented.
By using suitable unknowns, matrix equations are obtained; these exhibit a hyperbolic structure.
Résumé
Dans le cadre des schématisations de Medick, on présente une méthode permettant de déduire de la théorie tridimensionelle des théories approchées à une dimension de plus en plus fines.
Après un choix convenable des inconnues, on obtient les équations matricielles du problème qui mettent en évidence une structure de système hyperbolique.
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Gamby, D. One-dimensional theories of motion for beams. J Elasticity 7, 353–367 (1977). https://doi.org/10.1007/BF00041728
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DOI: https://doi.org/10.1007/BF00041728