CHARACTERIZATION OF THE MEMBRANE THEORY OF A CLAMPED SHELL: THE HYPERBOLIC CASE

Abstract

We study the membrane-dominated deformation state of a thin shell, the midsurface of which is located on a hyperbolic surface of revolution whose boundary is a curvilinear polygon. The shell is loaded by a surface tractions on both faces, and clamped all along the edge. Proceeding from the classical shell model of Koiter–Sanders–Novozhilov, an asymptotic membrane theory model is constructed to describe the limit behavior of the shell as the thickness tends to zero. The mathematical properties of the membrane theory are analyzed and the convergence rate estimate between the two models is proven.