Loading and structural response models of circular plates subjected to near field explosions

Abstract Loading and structural response models were developed to estimate the elastic deformation of a circular plate due to near field explosions. The loading model generates the nonuniform loading characteristic of a near field explosion on a circular plate. This loading model is unique as it uses the TNT equivalence factors for pressure and impulse separately when deriving the pressure profile. Most loading models either average the two factors together or use only one of them. An analytical model and two finite element models were developed to capture the response of the circular plate due to this nonuniform loading. The analytical model utilizes the von Karman thin plate equations with a new assumed deformation profile. The typical deformation profile for a circular plate uses two constants to satisfy the boundary conditions. By adding torsional springs to the boundary of the plate and equating the springs' moment to the plate's internal moment, as well as carrying through with the von Karman model, a new assumed profile is derived which has one parameter representing the boundary. This allows for a sensitivity analysis to be performed on the boundary condition parameter. In addition, this parameter has physical meaning, as it represents the stiffness of the torsional springs. The plate center deflections for the three structural models were found to be in good agreement with the experimental data provided by the U.S. Department of Homeland Security. The results show that the loading becomes less accurate at very small scaled distances because the loading model is more phenomenological than physics-based. The sensitivity of the maximum plate center deflection to parameter changes was estimated. The maximum deflection was found to be most sensitive to plate thickness.