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Continuation dans les problèmes à frontières libres de type bifurcations plastiques

Abstract : This paper deals with the buckling problem of elastic-plastic beams. We first examine a simple model. Then the main part of this work is concerned with the equilibrium states of an elastic-plastic beam. Elastic-plastic are free boundary problems, since the boundary between the elastic zone and the plastic zone is unknown. This problem has become an usual one in the coercive case, for which the computation of the boundary is naturally solved by an incremental procedure. For the non coercive case, we are led to a new formulation of the problem in order to determine this boundary. Then the study of this boundary leads to an analysis of the spectrum and of the bifurcated branches. On the one hand, the set of the points for which there exist at least two initial velocities is made of successive closed intervals whose intersection is not necessarily empty. On the other hand, all these points are actually bifurcated points and we establish the existence and the asymptotic behavior of the corresponding branches. We study also the imperfection sensitivity
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Abdelmajid El Koulani. Continuation dans les problèmes à frontières libres de type bifurcations plastiques. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1996. Français. ⟨NNT : 1996METZ029S⟩. ⟨tel-01777140⟩

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