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.