Elastic-plastic deformation of cylindrical pressure vessels under cyclic loading

A numerical procedure based on the finite element method and incremental solution approach is presented for analyzing cylindrical pressure vessels deformed in the state of generalized plane strain. The structures considered are subjected to internal pressure, thermal gradients and axial forces, which are cyclic in nature. The materials are assumed to obey the von Mises yield criterion with kinematic strain hardening which, during the process of plastic deformation, the yield surface is permitted to translate in the stress space and may change its size as a function of temperature. Based on Drucker's postulates for stable materials in the incremental theory of plasticity, a noniso-thermal flow rule is deduced in the cylindrical coordinates. By use of the virtual work principle, the finite element equations with displacement formulations are derived. The numerical solution is then carried out by a step-by-step approach for small loading increments and an iteration scheme is employed for each loading step. Furthermore, the analysis method is extended to the determination of limit load and shakedown load of a vessel. Several problem cases are presented.