New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading

This study introduces an empirical analysis approach to assess mechanical behavior of thin circular mild steel plates subjected to uniform and localized impulsive loading. The empirical models have been derived by singular values decomposition procedure to predict midpoint deflection of circular plates. The essence of empirical analysis is based on dimensionless numbers. For this, Jones's dimensionless number lambda is considered as a dimensionless number for both uniform and localized loading. This number has some features such as considering plate geometries, mechanical properties of material, and loading conditions. The well-known Cowper-Symonds constitutive equation has been used to investigate the potential influence of material strain rate sensitivity where the constant parameters in this equation are considered as a function of plate thickness. In localized impulsive loading, two other dimensionless numbers are appended to investigate the effects of changing load ratio and standoff distance. The results of empirical models are compared to the other experimental and theoretical studies which have been performed by different researchers. Also, the obtained results show that the presented models have much less root mean square error than the other ones. Hence, these models are suitable to predict midpoint deflection of thin circular plates subjected to both uniform and localized impulsive loading.