AN EXISTENCE THEOREM FOR A NONLINEARLY EL ASTIC FLEXURAL SHELL

We establish an existence theorem for the two-dimensional equations of a nonlinearly elastic ''flexural'' shell, recently justified by V. Lo ds and B. Miara by the method of formal asymptotic expansions applied to the corresponding three-dimensional equations of nonlinear elastici ty. To this end, we show that the associated energy has at least one m inimizer over the corresponding set of admissible deformations. The st rain energy is a quadratic expression in terms of the ''exact'' change of curvature tensor, between the deformed and undeformed middle surfa ces; the set of admissible deformations is formed by the deformations of the undeformed middle surface that preserve its metric and satisfy boundary conditions of clamping or simple support. (C) Academie des Sc iences/Elsevier, Paris.