Keywords: underwater explosion, tripping, arbitrary Lagrangian-Eulerian method, parametric study, ring-stiffened cylinder.

Underwater explosions are a highly important and complex problem for naval surface ships and submarines. Detonating high explosives underwater generates a shock wave and a pulsating gas bubble. When underwater explosions occur in the vicinity of a structure, structural deformation occurs as a result of shock wave pressure and gas bubble oscillation. This study investigates the dynamic behaviour of a ring-stiffened cylindrical structure subjected to an underwater explosion. Stiffener tripping is regarded as a critical panel collapse. When tripping occurs the plating is left with no stiffening effect and collapse immediately follows. This type of failure is caused by a high resistance to bending in one plane and low resistance to bending in another plane, torsional and buckling effects, imperfections in the beam, and a sufficiently large force pushing in a direction perpendicular to the beam's largest moment of inertia [1].

To identify the region that is unstable against stiffener tripping and cylindrical shell deformation, parametric studies were performed through the modelling and simulation. Two types of submerged structures were investigated. One is a rectangular ring-stiffened cylindrical shell structure with hemispherical end caps and the other is a tee ring-stiffened cylindrical structure with hemispherical end caps. For the rectangular ring-stiffened cylindrical structure, two parametric studies were carried out: one featured a variation in web height, with constant web thickness, while the other involved a change in the thickness of the web, with web height kept constant. For the tee ring-stiffened cylindrical structure, three types of simulations were performed: the first involved a change in the web height, with web thickness, flange width, and flange thickness kept constant: the second featured variations in the flange width, with flange thickness, web height and web thickness kept constant: and the third involved a change in flange thickness, with flange width, web height and web thickness kept constant.

True-Grid is used for modelling and LS-DYNA is employed for the analysis. The response of the structure was calculated using the arbitrary Lagrangian-Eulerian (ALE) method, which is used to determine the fluid-structure interaction effect. ALE is a popular tool for simulating continuum mechanics problems with large shear deformations, such as fluid flow and metal forming. The simulation results of the rectangular ring-stiffened cylindrical structure shows that varying web thickness is a better approach than changing the web height in determining the tendency of tripping behaviour. Moreover, reducing the web height more effectively reduces the cylindrical structure deformation than does increasing the web thickness. The findings of the tee ring-stiffened cylindrical structure simulation indicate that the flange width does not affect tripping the behaviour, but web height and flange thickness do. Cylindrical shell deformation increases as web height rises. Decreasing the flange thickness results in an increase in the cylindrical shell deformation. The possibility of cylindrical shell tripping and deformation is more sensitive to web height than to flange width and thickness.

1

T.V. Galambos, A.E. Surovek, "Structural stability of steel: concepts and applications for structural engineers", John Wiley & Sons, Inc, New Jersey, USA, 2008.

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