A nonlinear resonance (eigenvalue) approach for computation of elastic collapse pressures of harmonically imperfect relatively thin rings

Abstract

A nonlinear resonance (eigenvalue) based semi-analytical approach is employed here for computation of the elastic mode 2 collapse pressures of moderately-thick to thin isotropic rings, weakened by harmonic or modal type imperfections. The mode 2 collapse pressure is, by definition, associated with the buckled mode shape of cos(2θ) type, and is the harmonically imperfect ring counterpart to the Euler type buckling pressure of a hydrostatically pressurized thin perfect ring. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of a harmonically imperfect ring. Interesting and hitherto unavailable numerical results pertaining to the effects of harmonic imperfections on the hydrostatic collapse pressures of imperfect metallic rings are also presented.