Influence of large deformations and midplane forces on the plastic behavior of impulsively loaded plates

Abstract

This dissertation deals with an analysis of impulsively loaded plastic plates that includes effects of large deformations and midplane forces. Specifically, it deals with a circular plate of uniform thickness simply supported at its edges. The impulsive loading is characterized by an initial velocity distribution. The analysis assumes that the plate is an isotropic, rigid, ideally plastic material. Shear deformations and longitudinal inertia are neglected. Both bending and midplane forces are considered. The midplane forces can be either applied prior to the impulse or generated by deformations of the midplane. Deformations of the cross section are based on the assumption that a line initially normal to the midplane remains straight and normal after deformation. Strains are nonlinear with respect to transverse displacements but contain only linear radial displacement terms. Finally, the Tresca yield criteria are used. An interaction equation is derived between the plastic moment and normal force. The relationship indicates that the greater the midplane force the smaller the required bending moment for plastic flow. When the midplane force reaches a maximum value, the plate no longer carries a moment. Equilibrium equations are derived for the motion of the plate which are consistent with the von Karman plate theory. Governing equations are then developed for the three possible phases of motion. The initial Phase 1 includes a bending hinge that travels from the support to the center of the plate. Phase 2, which is initiated when the hinge reaches the center, continues until either the motion ceases or a portion of the plate becomes a membrane. Phase 3 described the motion of the membrane hinge from its initial point of origin to its final stopping point. These governing equations are solved for two types of bending moment-midplane-force interaction relationships. One relationship is based on displacement of the neutral surface from the midplane surface. The second is based on the magnitude of the midplane forces. Both types of plastic plate behavior are examined. Plots of final central deformation for various applied midplane forces and impulses are presented that clearly illustrate that even small amounts of midplane forces have a significant effect on the final deformation of plastic plates. Numerical results of the large deformational analyses are also presented. Plots are given showing the influence of the magnitude of the impulse on bending hinge velocity, initiation of membrane behavior, location of the membrane hinge, and the final deformation of the plate. A comparison is made between results of the large deformational analysis and experimental data. It shows excellent agreement. For the small and intermediate range of impulses the agreement is within experimental scatter. For the large impulses the calculated deformations are slightly conservative. Reasons for this deviation are discussed. Finally a critical examination is made of the various other suggested approaches that have possible application to the behavior of plastic plates.