Ciarlet, Philippe G.; Paumier, Jean-Claude 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 C. R. Acad. Sci., Paris, Sér. I 301, 857-860 (1985). 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 Cited in 1 ReviewCited in 4 Documents MSC: 74K15 Membranes 74B20 Nonlinear elasticity 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) Keywords:shallow shells; Marguerre-von Kármán equations; asymptotic expansion technique; three-dimensional nonlinear elastic shells × Cite Format Result Cite Review PDF