CHARACTERIZATION OF THE MEMBRANE THEORY OF A CLAMPED SHELL - THE PARABOLIC CASE

We study the membrane-dominated deformation state of a cylindrical or conical shell, the lateral shape of which is that of a curved polygon. The shell is assumed to be loaded by a smoothly varying surface traction distribution and rigidly supported (clamped) on its whole boundary. Under these assumptions, a precise mathematical formulation is given for the asymptotic membrane theory corresponding to the limit where the shell becomes infinitely thin. The asymptotic solution is constructed explicitly, and a convergence result relating the actual deformation field to the asymptotic field is proven. The analysis is based on the classical shell model of Koiter-Sanders-Novozhilov.