Characterization of the Membrane Theory of a Thin Clambed Shell of Revolution.The Parabolic Case

摘要

The authors study the membrane-dominated deformation state of a cylindrical orconical shell obtained by bending from a curved polygonal plate of thickness t much less than its diameter. Under clamped boundary conditions, a precise mathematical formulation is given for the asymptotic membrane theory corresponding to the limit where t -> 0. The asymptotic solution is constructed explicitly in case of smooth loading, 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.