The numerical analysis of the elasto/visco-plastic dynamic response of the axisymmetrical shells to the time-varying load is carried out by the use of the elasto/visco-plastic overlay model which is able to express the Bauschinger effect and the strain rate dependency. Namely Perzyna’s equation is used for the constitutive relation of each layer of the overlay model and as a whole, the Bauschinger effect and the influence of viscosity in plastic range of the materials are taken into account. The basic differential equations for the shells subjected to axisymmetrical loads are derived by extending Sanders’ elastic shell theory and the equations are numerically solved by the finite difference method. As a numerical example, the pressure vessel under semi-sinusoidal pressure load with respect to time is analyzed and the results are compared with ones in the case of isotropic hardening.

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