Simplified theoretical solution of circular toroidal shell with ribs under uniform external pressure

• A simplified curve beam model is presented out for ring-stiffened toroidal shell.
• Stress and deformation of toroidal shell with ribs are obtained in simplified theoretical method.
• Verification and comparing is done among simplified theory, numerical method and model test.

The toroidal shell with stiffened ribs is a new-style structure in ocean engineering especially in underwater engineering. This paper attempts to provide a simple theoretical method to obtain the stress solution of toroidal shell with ribs for its strength assessment. Firstly according to the structural property of toroidal shell with ribs and theory of curve-beam, a simple model for toroidal shell with ribs has been developed; then coupled with theory of thin-shell and elastic beam, its stress and deformation have been solved and can be expressed into analytic formulas; lastly by finite element method (FEM) and model experiment method, this simple theoretical solution has been verified to be reasonable and quite accurate. Thus this simple theoretical solution could be applied for analysis and design of pressure equipment in such toroidal structure type.