Application of Lagrangian Energy Approach to determine the response of isotropic circular plates subjected to air and underwater blasts

Abstract

This paper presents a simplified analytical formulation that uses Lagrangian Energy Approach to predict air and underwater blast response of air-backed simply-supported circular steel plates. Triangular and exponential pressure profiles are considered for air and underwater blast loading respectively. Calculation of the response is divided into two stages. In the first stage, maximum impulsive velocity is determined by assum-ing that the plate has negligible deformation and then by using the conservation of linear momentum for air blast and Taylor’s one-dimensional analytical model for underwater blast. In the second stage of calculation, elastic deformation is obtained by applying the initial conditions determined from the first stage, also taking into account the rotatory inertia and water-added inertia effect. The obtained analytical solutions are tested with various plate aspect ratios as well as various loading levels and the results are compared with those from non-linear finite element explicit simulations. It is found that the proposed formulations correlate well with the finite element results giving only 5–20% discrepancy provided that the plate deflections are supposed to remain small compared to its thickness. Finally, the advantages and limitations of the present method are discussed.