3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

doi:10.1007/s10483-012-1615-8

Abstract

Abstract: In the underwater-shock environment, cavitation occurs near the structural surface. The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects. It is also the difficulty in the field of underwater explosion. With the traditional boundary element method and the finite element method (FEM), it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion. To solve this problem, under the consideration of the cavitation effects and fluid compressibility, with fluid viscidity being neglected, a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built. The fluid spectral element method (SEM) and the FEM are adopted to solve this model. After comparison with the FEM, it is shown that the SEM is more precise than the FEM, and the SEM results are in good coincidence with benchmark results and experiment results. Based on this, combined with ABAQUS, the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed, and the cavitation region and its influence on the structural dynamic responses are presented. The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.

Key words: underwater explosion, spectral element method (SEM), fluid-structure interaction, cavitation, stiffened plate, generalized nonlinear implicit quasivariational inclusion, maximal monotone mapping, iterative algorithm, Hilbert space

2010 MSC Number:

A-man ZHANG;Shao-fei REN;Qing LI;Jia LI . 3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1191-1206.

TrendMD

References

[1] Kennard, E. H. Cavitation in an elastic liquid. Physical Review, 63(5-6), 172-181 (1943)
[2] Felippa, C. A. and Deruntz, J. A. Finite element analysis of shock-induced hull cavitation. Com-puter Methods in Applied Mechanics and Engineering, 44(3), 297-337 (1984)
[3] Ranlet, D., DiMaggio, F. L., Bleich, H. H., and Baron, M. L. Elastic response of submerged shellswith internally attached structures to shock loading. Computers and Structures, 7(3), 355-364(1977)
[4] Gong, Z. X., Lu, C. J., and Huang, H. X. Accuracy analysis of immersed boundary methodusing method of manufactured solutions. Applied Mathematics and Mechanics (English Edition),31(10), 1197-1208 (2010) DOI 10.1007/s10483-010-1353-x
[5] Astley, R. J. Transient wave envelope elements for wave problems. Journal of Sound and Vibration,192(1), 245-261 (1996)
[6] Geers, T. L. Residual potential and approximate methods for three-dimensional fluid-structureinteraction problems. Journal of the Acoustical Society of America, 49(5), 1505-1510 (1971)
[7] Einar, M. R. and Anthony, T. P. A Legendre spectral element method for the Stefan problem.International Journal for Numerical Methods in Engineering, 24(12), 2273-2299 (1987)
[8] Komatitsch, D. and Vilotte, J. P. The spectral element method: an efficient tool to simulatethe seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society ofAmerica, 88(2), 368-392 (1998)
[9] Mulder, W. A. Spurious modes in finite-element discretizations of the wave equation may not beall that bad. Applied Numerical Mathematics, 30(4), 425-445 (1999)
[10] Giannakouros, J. A spectral element-FCT method for the compressible euler equations. Journalof Computational Physics, 115(1), 65-85 (1994)
[11] Fornberg, B. A Practical Guide to Pseudo spectral Methods, Cambridge University Press, Cam-bridge (1998)
[12] Fischer, P. F. Analysis and application of a parallel spectral element method for the solution ofthe Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 80(1-3),483-491 (1990)
[13] Patera, A. T. A spectral element method for fluid dynamics: laminar flow in a channel expansion.Journal of Computational Physics, 54(3), 468-488 (1984)
[14] Michael, A. S. Advanced Computational Techniques for the Analysis of 3D Fluid-Structure Inter-action with Cavitation, Ph. D. dissertation, University of Colorado at Boulder, 10-65 (2002)
[15] Bleich, H. H. and Sandler, I. S. Interaction between structures and bilinear fluids. InternationalJournal of Solids and Structures, 6(5), 617-639 (1970)
[16] Priolo, E., Carcione, J. M., and Seriani, G. Numerical simulation of interface waves by high-orderspectral modeling techniques. Journal of the Acoustical Society of America, 95(2), 681-693 (1994)
[17] Taflove, A. A perspective on the 40-year history of FDTD computational electrodynamics. AppliedComputational Electromagnetics Society Journal, 22(1), 1-21 (2007)
[18] Felippa, C. A. and DeRuntz, J. A. Finite element analysis of shock-induced hull cavitation. Com-puter Methods in Applied Mechanics and Engineering, 44(3), 297-337 (1984)
[19] Hibbitt, Karlsson, and Sorensen Inc. ABAQUS Analysis User’s Manual, http://abaqus.civil.uwa.edu.au:2080/v6.10/index.html (2010)
[20] Geers, T. L. An objective error measure for the comparison of calculated and measured transientresponse histories. The Shock and Vibration Bulletin, 54(2), 99-108 (1984)
[21] Huang, H. Transient interaction of plane acoustic waves with a spherical elastic shell. Journal ofthe Acoustical Society of America, 45(3), 661-670 (1969)
[22] Huang, H. and Mair, H. U. Neoclassical solution of transient interaction of plane acoustic waveswith a spherical elastic shell. Shock and Vibration, 3(2), 85-98 (1996)
[23] Mu, J. L., Zhu, X., and Zhang, Z. H. A study on numerical simulation of stiffened plate responseunder underwater explosion (in Chinese). Ship and Ocean Engineering, 6, 12-16 (2006)