Etude du comportement post-critique des coques cylindriques avec une méthode asymptotique-numérique

Abstract : An asymptotic numerical method is presented for computing the post-buckling behaviour of perfect and imperfect shells of revolution. The expansion of the bifurcationg branch into an integro-power series permits to bring the nonlinear post-buckling problem into a sequence of linear problems. These problems have the same linear part and they are solved numerically (F.E.M) with a single inversion of the matrix. The use of symbolic algebra system helped us to get the recurrence relations. Hence, a great number of terms of the series can be easily computed. So a large part of initial post-buckling is determined in an inexpansive and automatic way. However the range of validity of these solutions is limited to a neighbourhood of the bifurcating point. This range of validity can be increased by using Padé approximants. Finally, we get an analytical expression for the post-buckling branch and we can determine this branch for different amplitudes of imperfection
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Lahcen Azrar. Etude du comportement post-critique des coques cylindriques avec une méthode asymptotique-numérique. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1993. Français. ⟨NNT : 1993METZ006S⟩. ⟨tel-01748953⟩

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