A semi-meshless Lagrangian finite-volume framework based on Voronoi diagram for general elastoplastic Reissner-Mindlin shell

In this study, a semi-meshless Lagrangian finite -volume (FV) framework based on the Voronoi diagram is proposed for the Reissner-Mindlin shell considering general elastoplastic deformations. The governing equations of the strong form are derived rigorously based on Hamilton's principle. For elastoplastic deformations, an incremental nonlinear elastoplasticity algorithm of stress update is developed for the Reissner-Mindlin shell. Based on the general governing equations of the strong form, a novel semi-meshless finite -volume framework for the Reissner-Mindlin shell is developed, and the local control volume is constructed via a local Voronoi diagram through the local material point and its neighboring stress points. At the stress points, the stress state is calculated with a kernel function method. The compensation terms are devised for further suppressing the zero -energy modes in mid -plane and the rotational motions of the shell, ensuring high numerical robustness. A set of challenging cases is simulated by the present method, with which the geometrically nonlinear and elastoplastic behaviors are validated with reliable accuracy and high stability.