This paper is the first to present the dynamic buckling behavior of spherical shell structures colliding with an obstacle block under the sea. The effect of deep water has been considered as a uniform external pressure by simplifying the effect of fluid–structure interaction. The calibrated numerical simulations were carried out via the explicit finite element package LS-DYNA using different parameters, including thickness, elastic modulus, external pressure, added mass, and velocity. The closed-form analytical formula of the static buckling criteria, including point load and external pressure, has been firstly established and verified. In addition, unprecedented parametric analyses of collision show that the dynamic buckling force (peak force), mean force, and dynamic force redistribution (skewness) during collisions are proportional to the velocity, thickness, elastic modulus, and added mass of the spherical shell structure. These linear relationships are independent of other parameters. Furthermore, it can be found that the max force during the collision is about 2.1 times that of the static buckling force calculated from the analytical formula. These novel insights can help structural engineers and designers determine whether buckling will happen in the application of submarines, subsea exploration, underwater domes, etc.

This paper is the first to highlight the vibrations of a hemispherical shell structure interacting with both compressible and incompressible fluids. To precisely calculate the pressure of the shell vibrating in the air, a novel analytical approach has been established that has existed in very few publications to date. An analytical formulation that calculates pressure was developed by integrating both the ‘small-density method’ and the ‘Bessel function method’. It was considered that the hemispherical shell vibrates as a simple harmonic function, and the fluid is non-viscous. For comparison, the incompressible fluid model has been analyzed. Surprisingly, it is the first to report that the pressure of the shell surface is proportional to the vibration acceleration, and the velocity amplitude decreased at the rate of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$r^2$}\right.$ when the fluid was incompressible. Otherwise, the surface pressure of the hemispherical shell was proportional to the vibration velocity, and the velocity amplitude decreased with the rate of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$r$}\right.$ when the fluid was compressible. The compressibility of fluid played an important role in the dynamic pressure of the shell structure. Furthermore, the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid ( ${\rho }_{o}c$ ) exactly. In this study, the analytical solutions were verified by the calibrated numerical simulations, and the analytical formulation were rigorously tested by extensive parametric studies. These new findings can be used to guide the optimal design of the spherical shell structure subjected to wind load, seismic load, etc.

This paper unprecedentedly addresses the effect of vibrations of a cylindrical structure on dynamic pressures in a compressible and incompressible fluid situation. To obtain analytical solutions, the density of the fluid is simplified as a constant, but the rates of the density with respect to time and to space are considered as a dynamic and time-dependent function. In addition, the low velocity of the vibration is taken into account so the lower order terms are negligible. According to the assumption that the vibration at the boundary of the structure behaves as a harmonic function, some interesting and new analytical solutions can be established. Both analytical solutions in the cases of the compressible and incompressible fluid are rigorously verified by the calibrated numerical simulations. New findings reveal that, in the case of the incompressible fluid, dynamic pressure at the surface of the cylindrical shell is proportional to the acceleration of the vibration, which acts like an added mass. In the case of the compressible fluid, the pressure at the surface of the cylindrical structure is proportional to the velocity of the vibration, which acts as a damping. In addition, the proportional ratio is derived as $\rho c$ .