Existence Theorem for a Nonlinear Elliptic Shell Model

In this paper we introduce a new nonlinear shell model with the following properties. First, we show that, if the middle surface of the undeformed shell is elliptic, then this new nonlinear shell model possesses solutions which are also elliptic surfaces. Second, we show that, if in addition the middle surface of the undeformed shell is a portion of a sphere, then the total energy of this nonlinear shell model coincides to within the first order, i.e., for “small enough” change of metric and change of curvature tensors, with the total energy of the well-known Koiter nonlinear shell model.