Large Dynamic Plastic Deflection of Plates by Mode Method

The extension of the mode approximation technique to finite deflections is illustrated in this paper by application to a fully clamped circular plate that is impusively loaded and whose material exhibits rigid-perfectly plastic or viscoplastic behavior. Deflections up to about 10 plate thicknesses are treated. The approximation technique required finding instantaneous mode form solutions at a sequence of times, satisfying the current equations of material behavior, edge constraint, and dynamics including finite deflection terms. The modal form is defined as having velocity and acceleration fields differing by a scalar factor. Thus ordinary rather than partial differential equations are solved. Iterative methods are described which furnish these solutions efficiently in the present problem. The general approach furnishes some useful information about errors of the final deflection magnitudes. Comparisons are made with other solutions and experimental results.