Part I - Task 3.2.9. Bending and Buckling of a One-Dimensional Model Simulating a Conical Shell. Part II - Task 3.2.11. Nonlinear Analysis and Computer Program for Axisymmetric Static Response of Shells of Revolution

摘要

A new method for analysis of bending and buckling of conical shells is presented. The method shows that a constraint of conical shell can be brought into the system by the variational method in conjection with the Lagrange multiplier. The constraint was erroneously considered as a boundary condition in most of the literature. The method is demonstrated by a one dimensional model which simulates an element of a symmetrically deformable elastic conical shell. A set of equations for bending of large deflection and buckling for the model is derived. The exact solutions of one element with both ends simply supported are given. A finite difference solution and a corresponding computer program is presented which determines the nonlinear axisymmetric static response of thin shells of revolution. The boundary conditions are taken in a general form which allows the program to handle any combination of elastic restraints at the edges. The analysis and computer program are described in detail and sample calculations are included. (Author)