Elasto-plastic analysis of Kirchhoff plates by high simplicity finite elements

This paper presents a mixed triangular finite element named High Simplicity (HS) element. The HS element is designed to analyze elasto-plastic Kirchhoff plates and is characterized by the linear assumption of the displacement field which makes it rigid in bending, and by the hypothesis of constant moments on the area surrounding each node. The additional hypothesis of continuity of the bending moment acting on the mesh sides allows the use of the standard Hellinger–Reissner formulation. The HS element is framed within an incremental iterative algorithm of initial stress type which uses arc-length strategy to reconstruct the whole equilibrium path. This introduces and highlights the advantages of the HS element which are its reasonable accuracy and very simple element algebra. Some numerical results relative to plates of simple form allow an analysis of the element's performance in the case of elastic-perfectly plastic behavior governed by Von Mises yield criterion.