Optimal design of stiffened cylindrical shell

Abstract

Buckling under action of external lateral pressure of the cylindrical shell stiffened by identical rings with rectangular cross-sections and a non-stiffened shell of a neutral surface having the same sizes and made of the same material is considered. It is supposed, that the stiffened and non-stiffened shell lose stability at identical critical pressure. To get approximate formulas for the critical pressure a combination of asymptotic method is used. First we seek solutions as a sum of slowly varying functions and edge effect integrals. Thus the initial singularly perturbed system of differential equations is reduced to an approximate system of the smaller order. Assuming that the rings may be considered as circular beams we obtain the solution of the approximate eigenvalue problem describing buckling of ring-stiffened shell by means of homogenization procedure. Using the simple asymptotic formulas for critical pressure the approximate relations for calculation of optimal stiffened shell parameters corresponding to the minimal value of its weight are received in closed form. It is shown that at increase in the ratio of ring width to ring thickness the ratio of weights of stiffened shell to weights of non-stiffened shell decreases. The examples of calculations of optimal parameters are presented. Results of the paper may be used at designing thin-walled structures. Refs 6. Figs 2.

Keywords:

stiffened cylindrical shell, buckling, asymptotic methods, optimal design