Design of spherical vessels under steady-state thermal loading using thermo-elasto–plastic concept

Governing equilibrium equations of thick-walled spherical vessels made of material following linear strain hardening and subjected to a steady-state radial temperature gradient using elasto–plastic analysis are derived. By considering a maximum plastic radius and using the concept of thermal autofrettage for the strengthening mechanism, the optimum wall thickness of the vessel for a given temperature gradient across the wall thickness is obtained. Finally, in the case of thermal loading on a vessel, the effect of convective heat transfer on the optimum thickness is studied and a general formula for the optimum wall thickness and design graphs for several different cases are presented.