An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 2: Applications

Abstract

In an accompanying paper an extended shakedown theory was described for structures subjected to constant mechanical loads and cyclically varying thermal loads, a circumstance of interest in Fast Reactor design. In this paper the upper bound theorem is used to construct interactive diagrams for a sequence of sample problems. These examples imply that for many shell problems, where the temperature variations occur along the surface, ratchetting occurs in two distinct ways. For low thermal loading the structure deforms in the same mechanism that occurs at plastic collapse when only the mechanical loads are applied. For high levels of thermal loading the mechanism changes to a local concentration of strain. This behavior differs significantly from that of the Bree problem. In one example this mechanism involves through-thickness shear deformation of a plate; as a consequence the use of thin shell theory which ignores shear deformation in numerical solutions of problems of this type is likely to result in nonconservative estimates of inelastic deformations.