Limit and shakedown analysis of hollow spheres under monotonic and cyclic thermal loadings

This study proposes a practical analytical framework to assess the structural safety of hollow sphere subjected to monotonic and cyclic thermal loadings. By modeling the sphere as an elastic-perfectly plastic material obeying the von Mises criterion, we derive closed-form solutions for elastic–plastic and shakedown limits through Melan’s static theorem, explicitly characterizing radial, tangential, and equivalent stress distributions. Crucially, the analytical results reveal that no complete plastification occurs regardless of thermal loading intensity, and the elastoplastic region evolution is governed by geometric parameters — a finding validated against axisymmetric finite element simulations. Furthermore, a dual-criterion framework integrating a non-conservative safety factor and an unloading-path-dependent stress ratio is introduced to unify elastoplastic and shakedown analysis with engineering design principles for thermally loaded spherical structures. Finally, we demonstrate that the method is stable, accurate and efficient, enabling reliable prediction of elastic–plastic and shakedown boundaries for hollow sphere under monotonic and cyclic thermal loadings.