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Figure 8: Finite element mesh (one half of the fluid mesh is omitted).
Underwater Explosion:
Numerical analysis was performed using three-dimensional finite element models that simulate underwater explosion, pressure wave propagation, its interaction with a cylindrical shell and the subsequent onset of dynamic collapse. The models were developed so as to reproduce the physical experiments.
The pipe was discretized with S4R shell elements, usually consisting of 23520 nodes and 7840 elements. The external fluid was modelled with four node reduced integration acoustic elements AC3D4R. The outer boundary of the external fluid is represented by a non-reflecting cylindrical surface of radius 0.151 m. The surrounding fluid is thus assumed as an acoustic medium in which the shockwave generated by an underwater explosion propagates and its energy leaves the mesh through a non-reflecting boundary. Multiple layers having different internal radius were used to define the external fluid, being more refined around the pipe region and presenting a coarser mesh at increasing distances from the pipe. Only small displacements of the fluid are allowed. One half of the fluid mesh is omitted from Fig. 8 for better visualization of the mesh. The experimental pressure–time history of a given shockwave can be used as tabular input for the analyses.
FROM:
Luciana Loureiro Silva and Theodore A. Netto (Ocean Engineering Department, Federal University of Rio de Janeiro, Brazil), “On the dynamic collapse of cylindrical shells under hydrostatic and impulsive pressure loadings”, Mecánica Computacional Vol XXIX, págs. 7787-7797, Eduardo Dvorkin, Marcela Goldschmit, Mario Storti (Eds.) Buenos Aires, Argentina, 15-18 Noviembre 2010
ABSTRACT: The dynamic collapse of submerged cylindrical shells subjected to lateral impulsive pressure loads caused by underwater explosions is studied via coupled experimental and numerical work. The parent problem of the dynamic collapse of such structures under hydrostatic pressure is also investigated. Two sets of experiments were performed. Initially, 50.6mm outside diameter aluminum tubes with diameter-to-thickness ratio of 32.3 were tested inside a pressure vessel. Hydrostatic pressure was applied quasi-statically up to the onset of collapse in order to obtain the collapse pressure of the tubes tested. Subsequently, similar tubes were tested in a 5m x 5m x 1.6m deep water tank under various explosive charges placed at different distances. Explosive charges and standoff distances were combined so as to eventually cause collapse of the specimens. In both sets of experiments, dynamic pressure and strain measurements were recorded using a fit-for-purpose data acquisition system with sampling rates of up to 1 Mega Samples/sec per channel. In parallel, finite element models were developed using commercially available software to simulate underwater explosion, pressure wave propagation, its interaction with a cylindrical shell and the subsequent onset of dynamic collapse. The surrounding fluid was modeled as an acoustic medium, the shells as J2 flow theory based materials with isotropic hardening, and proper fluid-structure interaction elements accounting for relatively small displacements of the boundary between fluid and structure were used. Finally, the physical explosion experiments were numerically reproduced with good correlation between results.
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