Discrete Model Analysis of Elastic-Plastic Plates

By invoking the usual assumptions of the classical theory of plates and shells, a discrete flexural model of a plate is deduced from a discrete model of three-space solids. All the flexural relations and equations, including boundary conditions, pertaining to a discrete set of field quantities can then be formulated directly through the model; these relations can also be shown consistently to be central difference analogs of the corresponding classical differential equations. On this basis, the treatment of nonlinear-inelastic material properties is quite transparent; material properties are treated in their most basic form and general properties are handled in the same manner as that of linearly elastic material. All these lead to a simple set of recursive equations which constitute the basis for an algorithmic approach to the flexural analysis of nonlinear-inelastic problems of plate structures. The solution for several square plates of elastic-perfectly plastic material are illustrated with different boundary conditions. In all cases, the numerically predicted load-carrying capacities are shown to be consistently within the bounds of limit analysis.