Heat Conduction in Ring-Stiffened Shells of Revolution — a Structural Mechanics Analogy

Abstract

The basic equations of stationary heat conduction in shells of revolution taking into account surface heat exchange at the boundary surfaces are derived and further specified for the practically important axisymmetric case. A structural mechanics analogy is then established to the problem of out-of-plane loading and deformation of a plane grillage structure, consisting of shear-flexible beams on continuous elastic foundation, with the axes given by the meridians of the shell parts. This analogy provides an elegant and easy way of qualitative and quantitative understanding of the complicated thermal states in these components which are usually unfamiliar to the practising civil engineer. General and some specific solutions of the basic equations for practically important types of ring stiffened shells are worked out and presented in diagram form. The analysis procedure is demonstrated by an illustrative example.