Elasto/Visco-Plastic dynamic Response of Moderately Thick Shells of Revolution : Case of Consideration of Rotatory Inertia

Abstract

An analytical method for the elasto/visco-plastic dynamic problems of general moderately thick shells of revolution is developed in consideration of the effect of shear deformation and rotatory inertia. The equations of motion and the relations between the resulting stresses and displacements are derived by extending the Naghdi theory in elastic shells with given consideration to the effect of shear deformation and rotatory inertia. For the constitutive relations, the elasto/visco-plastic equations by Fyfe based on the model developed by Perzyna are employed. The numerical method selected for this problem is a method using finite difference in both space and time. As a numerical example a cylindrical shell under a semisinusoidal internal pressure with respect to time is analyzed, and the results are compared with those from the theory which neglects the effect of rotatory inertia.