Nonlinear dynamic response analysis of supercavitating vehicles

Abstract

A finite element model for the supercavitating underwater vehicle was developed by employing 16-node shell elements of relative degrees of freedom. The nonlinear structural dynamic response was performed by introducing the updated Lagrangian formulation. The numerical results indicate that there exists a critical thickness for the supercavitating plain shell for the considered velocity of the vehicle. The structure fails more easily because of instability with the thickness less than the critical value, while the structure maintains dynamic stability with the thickness greater than the critical value. As the velocity of the vehicle increases, the critical thickness for the plain shell increases accordingly. For the considered structural configuration, the critical thicknesses of plain shells are 5 and 7 mm for the velocities of 300 and 400 m/s, respectively. The structural stability is enhanced by using the stiffened configuration. With the shell configuration of nine ring stiffeners, the maximal displacement and von Mises stress of the supercavitating structure decrease by 25% and 17% for the velocity of 300 m/s, respectively. Compared with ring stiffeners, longitudinal stiffeners are more significant to improve structural dynamic performance and decrease the critical value of thickness of the shell for the supercavitating vehicle.

Keywords

supercavitating vehicle / shell element of relative degrees of freedom / nonlinear finite element / dynamic response

References

[1] ZhangY.-wen.The applications of cavity theories [M], 2007Xi’anNorthwestern Polytechnical University Press113-179

[2] KulkarniS. S., PratapR.. Studies on the dynamics of a supercavitating projectile [J]. Applied Mathematical Modelling, 2000, 24: 113-129

[3] RUZZENE M, SORANNA F. Impact dynamics of elastic supercavitating underwater vehicles [C]// 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. Atlanta, Georgia, 2002: 1–11.

[4] CHOI J Y, RUZZENE M, BAUCHAU O A. Dynamic analysis of flexible supercavitating vehicles using modal based elements [C]//2003 ASME International Mechanical Engineering Congress. Washington D C, 2003: 1–12.

[5] AlyanakE., VenkayyaV., GramdhiR.. Structural response and optimization of a supercavitating torpedo [J]. Finite Elements in Analysis and Design, 2005, 41: 563-582

[6] AlyanakE., GramdhiR., PenmetsaR.. Optimum design of a supercavitating torpedo considering overall size, shape, and structural configuration [J]. International Journal of Solids and Structures, 2006, 43: 642-657

[7] YangC.-w., LiuG., WangA.-wen.. FEM analysis of structural response of supercavitating bodies [J]. Journal of Naval University of Engineering, 2008, 20: 101-104

[8] YangC.-w., WangA.-wen.. Structural response of supercavitating underwater vehicles subjected to impact loads [J]. Journal of Huazhong University of Science and Technology, 2008, 36: 129-132

[9] ZhangJ.-s., ZhangJ.-z., WeiY.-j., CaoWei.. Structural dynamic response characteristics of supercavitating underwater vehicles [J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36: 411-414

[10] Kanok-nukulchaiW., TaylorR. L., HughesT. J. R.. A large deformation formulation for shell analysis by finite element method [J]. Computers & Structures, 1981, 13: 19-27

[11] LiJ. Z., HungK. C., CenZ. Z.. Shell element of relative degree of freedom and its application on buckling analysis of thin-walled structures [J]. Thin-Walled Structures, 2002, 40: 865-876

[12] ChenL.-h., ChengJ.-g., HuangW.-bin.. Nonlinear dynamic analysis of shell element with a relative degree of freedom [J]. J Tsinghua Univ, 2002, 42: 228-231

[13] WangX.-cheng.Finite element method [M], 2003BeijingTsinghua University Press406-418

[14] CookR. D., MalkusD. S., PleshaM. E.Concepts and Applications of finite element analysis [M], 2007Xi’anXi’an Jiaotong University Press515-552

[15] LingD.-s., XuXing.Nonlinear finite element and program [M], 2004HangzhouZhejiang University Press153-187

[16] HeJ.-y., LinX.-du.Numerical method of nonlinear engineering structures [M], 1993BeijingNational Defense and Industry Press102-137

[17] AHN S S. An integrated approach to the design of supercavitating underwater vehicles [D]. Atlanta, GA, USA: School of Aerospace Engineering, Georgia Institute of Technology, 2007: 1–36.

[18] KirschnerI. N., KringD. C., StokesA. W.. Control strategies for supercavitating vehicles [J]. Journal of Vibration and Control, 2002, 9: 219-242

[19] DzielskiJ., KurdilaA.. A benchmark control problem for supercavitating vehicles and an initial investigation of solutions [J]. Journal of Vibration and Control, 2003, 9: 791-804

[20] NGUYEN V, BALACHANDRAN B, VARGHESE A N. Supercavitating vehicle dynamics with non-cylindrical, non-symmetric cavities [C]// 2007 ASME International Mechanical Engineering Congress and Exposition, Seattle, Washington, USA, 2007: 1–8.

[21] AhnS. S., RuzzeneM.. Optimal design of cylindrical shells for enhanced buckling stability: Application to supercavitation underwater vehicles [J]. Finite Elements in Analysis and Design, 2006, 42: 967-976