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Une justification des équations de Marguerre-von Kármán pour les coques peu profondes. (A justification of the Marguerre-von Kármán equations for shallow shells). (French) Zbl 0594.73066
A justification of the Marguerre-von Kármán equations for shallow shells is made. An asymptotic expansion technique is applied to a general nonlinear model of three-dimensional nonlinear elastic shells. Without any a priori assumption regarding the variations of the displacement and stress components across the thickness of the shell it is shown that the first term of the expansion can be identified in a specified sense to the solution of the two-dimensional Marguerre-von Kármán equations. This method also delineates the situations in which a shell is qualified as ”shallow”.
The complete demonstration of the obtained results shows that the same technique may be applied to the treatement of the case of a clamped shell, by generalizing the results for thin plates.
Reviewer: G.V.Vasiliev

74K15 Membranes
74B20 Nonlinear elasticity
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)