Theoretical investigation of the strength and stability of special pseudospherical shells under external pressure

•A new shape of a shell of revolution is presented based on Huygens׳ tractrix.•The shell has stable equilibrium path.•Geometry of cylindrical–pseudospherical and tori-pseudospherical shells is described.•Buckling load and buckling shapes obtained with the use of FE method are presented.

The paper is devoted to a new shape of a shell of revolution with negative Gaussian curvature. The main part of the meridian of the shell is a plane curve of the Huygens tractrix. Geometrical properties of the middle surface of the shell of revolution are presented. The membrane state of stress for a family of shells with constant capacity and constant mass under uniform external pressure is analysed. The critical pressure, buckling modes and equilibrium paths for the family of shells are calculated with the use of the FEM (the ANSYS system). Results of the analytical and numerical investigations are presented in tables and figures. A stable post-critical behaviour of presented shells is pointed out which is not typical for most shell structures.