[Conditions aux limites pour une flexion élastique des poutres]
Dans le problème de la flexion des poutres nous utilisons le théorème de réciprocité et la solution de Papkovich–Neuber pour trouver, de manière inédite, les conditions mixtes de tension aux limites avec une exactitude appropriée à tous les ordres d'approximation. En généralisant la méthode proposée par Gregory et Win, on établit l'ensemble des conditions nécessaires pour les données sur les cotés assurant l'existence des solutions évanescentes. Dans le cas où les conditions sur les tensions mixtes sont imposées sur le coté d'une poutre, les conditions assurant l'apparition d'états évanescents sont dérivées explicitement. Nous les utilisons par la suite dans une formulation correcte des conditions aux limites pour la solution intérieure. Nos conditions sur les tensions coïncident avec celles obtenues par la théorie de la flexion des poutres usuelle. Le résultat le plus important est l'obtention, pour la première fois, des conditions aux limites appropriées avec deux ensembles différents des données mixtes sur le bord de la poutre.
For beam bending problem, the reciprocal theorem and P–N solution are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. Through generalizing the method proposed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions are derived explicitly, and they are used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two different sets of mixed edge-data are obtained for the first time.
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Mots-clés : Mécanique des solides numérique, Conditions aux limites, Fléxion des poutres, États évanescents, États réguliers
Yang Gao 1 ; Si-Peng Xu 2 ; Bao-Sheng Zhao 3
@article{CRMECA_2007__335_1_1_0, author = {Yang Gao and Si-Peng Xu and Bao-Sheng Zhao}, title = {Boundary conditions for elastic beam bending}, journal = {Comptes Rendus. M\'ecanique}, pages = {1--6}, publisher = {Elsevier}, volume = {335}, number = {1}, year = {2007}, doi = {10.1016/j.crme.2006.11.001}, language = {en}, }
Yang Gao; Si-Peng Xu; Bao-Sheng Zhao. Boundary conditions for elastic beam bending. Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 1-6. doi : 10.1016/j.crme.2006.11.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.11.001/
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