ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Improving the Geometrically Nonlinear Intrinsic Beam Element Model of Wing for High Efficiency
Received date: 2012-07-25
Revised date: 2012-12-17
Online published: 2012-12-27
Supported by
National Natural Science Foundation of China (11202162); National High-tech Research and Development Program of China (2011AA7052002)
The geometrically exact, nonlinear intrinsic beam element model proposed by Hodges, et al. is known as its space-time conservation law. Its shortcoming is that, in dealing with the structural dynamics of a flexible wing, the number of independent variables increase exponentially while the discrete nodes increase; furthermore, the set of equations become stiff and lead to low efficiency in numerical calculation. In order to improve the structural dynamics model of a common cantilever wing, this paper derives a spatial condensation method according to the boundary conditions of a spatial discrete model to convert the spatial discrete equations to ordinary matrix equations, and then the original equations become ordinary differential equations related to time domain only. Thus, the number of equations and the looping steps in their solution can be decreased greatly, and the Jacobian matrix can also be derived easily from the improved equations. The Gear method is employed to solve the original intrinsic beam element model and the condensation model proposed in this paper respectively. The results show that the proposed spatial condensation model can improve the operating rate by about 5.1 times as compared with the original model under the same conditions, and it exhibits high universality, stability and efficiency for different force models.
WANG Rui , ZHOU Zhou , ZHU Xiaoping , XIAO Wei . Improving the Geometrically Nonlinear Intrinsic Beam Element Model of Wing for High Efficiency[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013 , 34(6) : 1309 -1318 . DOI: 10.7527/S1000-6893.2013.0233
[1] Nickol C L, Guynn M D, Kohout L L, et al. High altitude long endurance UAV analysis of alternatives and technology requirements development. NASA/TP-2007-214861, 2007.
[2] Noll T E, Ishmael S D, Henwood B, et al. Technical findings, lessons learned, and recommendations resulting from the Helios prototype vehicle mishap. RTO-MP-AVT-145, 2007.
[3] Hodges D H. A mixed variational formulation based on exact intrinsic equation for dynamics of moving beams. International Journal of Solids and Structures, 1990, 26(11): 1253-1273.
[4] Hodges D H. Geometrically exact, intrinsic theory for dynamics of curved and twisted anisotropic beams. AIAA Journal, 2003, 41(6): 1131-1137.
[5] Sotoudeh Z, Hodges D H. Nonlinear aeroelastic analysis of joined-wing aircraft with intrinsic equations. AIAA-2009-2464, 2009.
[6] Sotoudeh Z, Hodges D H, Chang C S. Validation studies for aeroelastic trim and stability analysis of highly flexible aircraft. Journal of Aircraft, 2010, 47(4): 1240-1247.
[7] Cesnik C E S, Brown E L. Modeling of high aspect ratio active flexible wings for roll control. AIAA-2002-1719, 2002.
[8] Su W H. Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft. Ann Arbor: University of Michigan, 2008.
[9] Palacios R, Cesnik C E S. Geometrically nonlinear theory of composite beams with deformable cross sections. AIAA Journal, 2008, 46(2): 439-450.
[10] Cesnik C E S, Senatore P J, Su W H, et al. X-HALE: a very flexible UAV for nonlinear aeroelastic tests. AIAA-2010-2715, 2010.
[11] Palacios R, Murua J, Cook R. Structural and aerodynamic models in nonlinear flight dynamics of very flexible aircraft. AIAA Journal, 2010, 48(11): 2648-2659.
[12] Zhang J, Xiang J W. Static and dynamic characteristics of coupled nonlinear aeroelasticity and flight dynamics of flexible aircraft. Acta Aeronautica et Astronautica Sinica, 2011, 32(9): 1569-1582. (in Chinese) 张健, 向锦武. 柔性飞机非线性气动弹性与飞行动力学耦合静、动态特性. 航空学报, 2011, 32(9): 1569-1582.
[13] Pan D, Wu Z G, Yang C, et al. Nonlinear flight load analysis and optimization for large flexible aircraft. Acta Aeronautica et Astronautica Sinica, 2010, 31(11): 2146-2151. (in Chinese) 潘登, 吴志刚, 杨超, 等. 大柔性飞机非线性飞行载荷分析及优化. 航空学报, 2010, 31(11): 2146-2151.
[14] Xie C C, Yang C. Linearization method of nonlinear aeroelastic stability for complete aircraft with high-aspect-ratio wings. Scientia Sinica: Technologica, 2011, 41(3): 385-393. (in Chinese) 谢长川, 杨超. 大展弦比飞机几何非线性气动弹性稳定性的线性化方法. 中国科学: 技术科学, 2011, 41(3): 385-393.
[15] Patil M J, Hodges D H. Flight dynamics of highly flexible flying wings. Journal of Aircraft, 2006, 43(6): 1790-1798.
[16] Sotoudeh Z, Hodges D H. Modeling beams with various boundary conditions using fully intrinsic equation. AIAA-2010-3034, 2010.
[17] Xu X H, Zhu F S. Numerical method of stiff ordinary differential equations. Wuhan: Wuhan University Press, 1997. (in Chinese) 徐绪海, 朱方生. 刚性微分方程的数值方法. 武汉: 武汉大学出版社, 1997.
[18] Radhakrishnan K, Hindmarsh A C. Description and use of LSODE, the livermore solver for ordinary differential equations. NASA RP-1327, UCRL-ID-I 13855, 1993.
/
| 〈 |
|
〉 |
CJA