The Behavior of Quadrangular Plates under Impulsive Loading: a Dimensional Analysis

In this paper, a non-dimensional analysis approach has been used to propose two empirical equations based on dimensionless numbers to predict the maximum transverse permanent deflection-thickness ratio of single-layered quadrangular plates under uniformly and locally distributed dynamic loading. In the presented dimensionless numbers, the effect of plate geometry, the impulse of the applied load, the mechanical properties of the plate, the strain-rate sensitivity, and the loading radius have been considered. To validate the empirical models, eight series of conducted experiments and 267 data points in the state of the art over the past forty years have been used. The obtained results show good agreement between the model prediction results and the experimental values so that in the total of 117 experimental data for uniform loading, 94% (110 data) and 98% (115 data) of the data points were distributed in the ±10% and ±20% error range, respectively. Besides, in the total of 150 experimental data for localized loading, 83% (124 data) and 97% (146 data) of data points were distributed in these two ranges, respectively. The results also showed that assuming the material constants as variables based on the plate thickness, in the Cooper-Symonds constitutive equation improves the prediction accuracy of the empirical models so that only 6% and 12% of the data for uniform and localized loading respectively, are not within the 10% error range.