Development of Analytical Formulae to Determine the Response of Submerged Composite Plates Subjected to Underwater Explosion

Abstract

Closed-form analytical formulae are developed to analyze the bending response of submerged composite rectangular plates subjected to underwater explosions (UNDEX). These explosions are supposed to occur at a sufficiently large stand-off distance so that a uniformly distributed pressure pulse can be applied and the corresponding bubble effects can be ignored. The plate is considered in an air-backed condition. The derivation steps are divided into two main stages. In the first stage, the impulsive velocity due to the interaction of shock wave and structure is determined by using Taylor's fluid-structure interaction (FSI) formulation while supposing a negligible structural deformation. Transmission of shock waves through the thickness of the plate is considered by assuming the material under uniaxial strain. At the end of the first stage, cavitation is supposed to occur all over the plate. In the second stage, deformation of the plate will commence which is followed by the collapse of the cavitation zone. The corresponding mechanical response of the plate is determined by imposing a simply-supported boundary conditions and by applying Lagrangian Energy approach to derive the motion equation, taking into account the water inertial effects. The proposed method is then tested with isotropic (steel) and laminated composite (carbon-fiber/epoxy) plates to analyze for both impulsive velocity and UNDEX responses. The obtained analytical results are compared with those from non-linear finite element explicit code, LS-DYNA. Finally, the advantages and limitations of the present method are evaluated.