On the methods of critical load estimation of spherical circle axially symmetrical shells

•Novel method of shells׳ critical load prediction using the Hausdorff metrics and modified Chebyshev׳s method is proposed.•High target information and data compression of the method is illustrated.•Results validation is presented.

A relaxation method is applied to estimate and predict a critical set of parameters responsible for stability loss (buckling) of spherical circle axially symmetric shells. The buckling phenomenon under static loading was investigated by solving the Cauchy problem for a set of ordinary differential equations and the Hausdorff metrics was applied while quantifying the data obtained within the novel approach.