Finite Element Method for Elastic Plastic Plates

A finite element method is developed for the analysis of elastic, perfectly plastic sandwich plates. The method is formulated by means of Greenberg's complementary energy rate theorem using constant moment elements. This formulation results in a quadratic programming problem. If it is assumed that no internal unloading takes place, formulation as a linear algebraic system of equations is possible; criteria are presented for checking this assumption. The method has several advantages over stiffness formulations: (1) Elastic-plastic boundary can occur only along element boundaries, and (2) calculation of governing equations requires no integration over elements as moments are constant. Results are presented for clamped and simply supported square plates and agreement with other available results is good. The method may be useful in error analysis for elastic plastic problems when combined with stiffness techniques as it provides complementary bounds on the same functional.