COMPUTER ANALYSIS OF ASYMMETRIC BUCKLING OF RING-STIFFENED ORTHOTROPIC SHELLS OF REVOLUTION

A generalization of Stodola's iteration method for beams is developed for the calculation of buckling modes of axisymmetric shell structures. The equations governing small perturbations about an axisymmetric, torsionless equilibrium state are derived from small strain, moderate rotation Novozhilov shell and ring theory. These equations are recast into a selfadjoint system of eigenvalue equations with the load factor λ, to which the load distribution is assumed proportional, as parameter. Because of the nonlinear dependence of the prebuckling state on λ, in general it is necessary to approach the critical eigenvalue (for a given circumferential wave number) by the solution of a sequence of modified eigenvalue problems, the first of which corresponds to the linearized prebuckling state. Numerical results are presented for 1) the well-known case of a clamped spherical cap; 2) a ring-stiffened simply supported cylindrical shell previously studied as an equivalent orthotropic shell; 3) a prolate spheroidal shell previously studied by the Rayleigh-Ritz method; and 4) a ring-stiffened prolate spheroidal shell for which no previous theoretical results exist. The second example illustrates the effect of ring eccentricity, indicating that internal rings can be significantly more effective in resisting external hydrostatic pressure than external rings. In all cases, excellent agreement with previous theoretical and experimental results was obtained. © 1968 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.