MODELLING THE ELASTOPLASTIC DEFORMATION OF AN INTERNALLY PRESSURIZED TRANSVERSELY ISOTROPIC SHELL UNDER A TEMPERATURE GRADIENT

Abstract

In this study, the transition theory and generalized strain measure theory were used to model the elastoplastic deformation in a transversely isotropic spherical shell subjected to a thermal gradient and uniform pressure. The main difference in transition's theory from the classical plasticity theory is neglecting ad-hoc assumptions such as the deformation is infinitesimally small, material incompressibility and yield criterion. However, results obtained by transition theory satisfy the yield condition in plastic state, and it is important to determine elastoplastic and fully plastic stresses on the basis of Lebesgue measure. Results are obtained in non-dimensional quantities and are shown graphically and illustrated numerically. The validations of analytical results of particular cases were compared to other works published in the literature and found to be the same. It is concluded that the pressure required for the initial yielding of the thicker shell made of transversely isotropic material is lower than the pressure required for thinner shell at room temperature. Through adding thermal effects, the pressure required for initial yielding of a transversely isotropic shell decreases. The value of fully plastic circumferential stress at the outer surface of the shell decreases with the increase in temperature and pressure. It is seen that the stress distribution through the shell surface, induced by temperature and separately induced by pressure, is opposite.