Computer modelling of thin-walled shell structures with geometric imperfections

Abstract

The study presented in the article focuses on modelling of thin-walled cylindrical shell structures with initial geometrical imperfections under external radial pressure. The critical pressure of the perfect shell obtained using linear analysis significantly exceeded that calculated by the Papkovich formula. This discrepancy can be attributed to the shell displacement constraints and the fact that linear analysis provides non-conservative estimates. Initially, the geometric imperfections were assumed to follow an eigenmode-affine pattern with varying amplitudes. Critical pressure values iteratively determined using the modified Ricks method were found to be lower than the critical pressure of the first buckling mode. Importantly, all these values remained notably higher than the normative value. Subsequently, the initial imperfections were modelled as combinations of sinusoidal deviations with different amplitudes and varying numbers of waves along the perimeter. Short-wavelength eigenmode-affine imperfections were superimposed on longer-wavelength deviations. The research indicated that while the long-wavelength imperfections had a marginal impact on the critical pressure values, they notably altered the post-buckling behaviour of the shell, as depicted in load-deflection figures in the form of loops. These processes occurred at pressure levels considerably higher than the normative value. The simulation results are in good agreement with established theories regarding the pre- and post-buckling behaviour of thin-walled shells. Nonlinear analysis revealed that the actual critical pressure values exceeded the normative value by 30-45%, and the post-buckling pressure values exhibited a gradual decrease without posing a threat to abrupt changes in the geometry of the shells. This outcome provides a basis for a more accurate estimation of the load-carrying capacity of the shell structures.