A nonlinear resonance (eigenvalue) approach for computing elastic collapse pressure of a moderately thick cross-ply imperfect ring

A hitherto unavailable nonlinear resonance (eigenvalue) based semi-analytical solution technique for prediction of the elastic mode 2 collapse pressure of a moderately thick cross-ply ring, weakened by a modal or harmonic type imperfection, is presented. A von Karman type iterative nonlinear analysis, that is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the imperfect cross-ply ring. Numerical results pertaining to the effect of modal imperfection on the hydrostatic collapse pressure of a moderately thick cross-ply ring and comparison with its perfect counterpart are also presented. These results further demonstrate that the present iterative analysis for solving a nonlinear eigenvalue problem reduces to the linearized buckling (linear eigenvalue) analysis, associated with the conventional bifurcation theory, for a perfect moderately thick cross-ply ring.