Mode Approximation Technique Applied to Finite Deflections of an Impulsively Loaded Viscoplastic Plate,
BROWN UNIV PROVIDENCE R I DEPT OF ENGINEERING
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The extension of the mode approximation technique to finite deflections is illustrated in this paper by application to a fully clamped plate which is impulsively loaded and whose material exhibits rigid-perfectly plastic or viscoplastic behavior. Deflections up to about ten plate thicknesses are treated. The approximation technique requires finding instantaneous mode form solutions at a sequence of times, satisfying the current equations of material behavior, edge constraint, and dynamics including finite deflections 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.
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