The Effect of Initial Imperfections on Shell Stability

Abstract

The development of “DISDECO”, the Delft Interactive Shell DEsign COde is described. The purpose of this project is to make the accumulated theoretical, numerical and practical knowledge of the last 20 years readily accessible to users interested in the analysis of buckling of sensitive structures. With this open ended, hierarchical, interactive computer code the user can access from his workstation successively programs of increasing complexity.

The intial level consists of semi-analytical solutions for the buckling load of perfect anisotropic circular cylindrical shells under axial compression, internal or external lateral pressure and torsion. Also included are modules that contain Koiter’s imperfections sensityvity theory extended to anisotropic shell structures under combined loading. The nonlinear Donnell-type shell equations in terms of the radial displacement W and the Airy stress function F are used. Using a procedure that is equivalent to an approximate minimization of the second variation of the potential energy by the Rayleigh-Ritz method simple eigenvalue equations are obtained in terms of the integers m and n, representing the number of half-waves in the axial and the number of full waves in the circumferential directions, and Khot’s skewedness parameter τ_K. Results of the search for the minimum eigenvalue and its imperfection sensitivity are displayed in convenient graphical form.

As a first update of DISDECO the computational modules of the initial level have been modified so as to be able to handle combined loads consisting of axial compression, internal or external pressure and clockwise or counter-clockwise torque. The applied load is assumed to have a uniform spatial distribution and is divided into a fixed and a variable part. The magnitude of the variable part is allowed to vary in proportion to a load parameter Λ. This leads to an eigenvalue problem for the critical load Λ_c.