Static and kinematic limit analysis of orthotropic strain-hardening pressure vessels involving large deformation

Abstract

This paper analytically investigates plastic limit pressure of orthotropic strain-hardening cylindrical vessels under internal pressure. It is an interesting problem to illustrate the interaction between strengthening and weakening behavior during the deformation process. The Voce hardening law and Hill's yield criterion were adopted in the paper. A sequence of static and kinematic limit analysis problems were performed by updating the yield criterion and the deformed configuration. The equality relation between the greatest lower bound and the least upper bound was confirmed explicitly. Accordingly, exact solutions of plastic limit pressure were developed with an integral term. Particularly, exact closed-form solutions were obtained for certain values of the hardening exponent of the Voce hardening law. Finally, numerical efforts were also made for rigorous validations.