Elastic-plastic large deflection analysis of axisymmetric shells

Abstract A new finite element formulation for elastic-plastic large deflection analysis of shells of revolution is presented. The new formulation contains most of the best features of nonlinear finite element analyses currently available in the literature, together with some new numerical schemes to improve the capability, accuracy and speed of the computation. It is thoroughly verified using a variety of problems. The doubly curved thin shell finite element used has been widely applied to linear elastic stress analysis and linear stability analysis by the present authors and their co-workers. In place of the widely-used relations of Donnell, Novozhilov or Sanders, more comprehensive nonlinear thin shell strain-displacement relations are used, which account for nonlinear strains caused by in-plane displacements. Unlike most previous nonlinear axisymmetric shell formulations, in-plane shearing is included throughout the treatment. For plastic analysis, a multi-layered approach is adopted, employing the Prandtl-Reuss normal flow rule with isotropic hardening or perfect plasticity. An efficient and accurate state determination algorithm, assuming incremental reversibility for plastic behaviour, is adopted and verified. Implementation of the variable arc-length method provides an efficient iterative procedure for tracing both the pre- and post-critical load-deflection path. Several examples demonstrate the accuracy, efficiency and capability of the present formulation.

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