Two-Dimensional Nonlinear Shell Model of Koiter's Type with Variable Thickness

Abstract

In this paper, we propose a new model “of Koiter's type” for nonlinearly elastic shells with variable thickness, which generalizes a model recently proposed by P.G. Ciarlet for shells with constant thickness. We justify this model by means of an asymptotic analysis, by showing that its solution behaves either like that of a “membrane” or like that of a “flexural” shell as the thickness goes to zero.

Hadamard well-posedness for a class of nonlinear shallow shell problems

“…We note that the inner product above is on the space H which is defined in Eq. (17). Let X = [e 1 e 2 ].…”

“…In [3], Bernadou and Oden have proven that a solution to the static model exists and that it is unique provided the load is sufficiently small. Philippe G. Ciarlet proposed in [8] a model where the exact change of curvature tensor is modified and Liliana Gratie generalized this latter model to the case of nonconstant thickness in [17]. See [10] for the linear and nonlinear theories of shells.…”