Elastic buckling of clothoidal–spherical shells under external pressure – theoretical study

• A new shape of a shell of revolution – clotho spherical shell – is presented.
• The shell may join a cylinder and a sphere keeping continuous meridional curvature.
• Analytical formulae for membrane resultants and membrane stresses are derived.
• Buckling load and buckling shapes obtained with the use of FE method are presented.

The paper is devoted to a non-typical shape of a shell of revolution with positive Gaussian curvature. The meridian of the shell is a plane curve composed of a clothoid and a circular arc. Geometrical properties of the middle surface of the shell of revolution are presented. Pre-buckling state of the shell under uniform pressure is described analytically. The critical pressure and buckling modes for the shell are calculated with the use of the FEM (the ANSYS system). Post-buckling behaviour of the shells is shown. Results of analytical and numerical investigations are presented in tables and figures.