几何非线性机翼本征梁元素模型的高效化改进

doi:10.7527/S1000-6893.2013.0233

固体力学与飞行器总体设计

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几何非线性机翼本征梁元素模型的高效化改进

王睿¹, 周洲¹, 祝小平², 肖伟¹

1. 西北工业大学无人机特种技术重点实验室, 陕西西安 710072;
2. 西北工业大学无人机研究所, 陕西西安 710072

收稿日期:2012-07-25 修回日期:2012-12-17 出版日期:2013-06-25 发布日期:2012-12-27
通讯作者: 周洲, Tel.: 029-88453368 E-mail: zhouzhou@nwpu.edu.cn E-mail:zhouzhou@nwpu.edu.cn
作者简介:王睿男, 博士, 工程师。主要研究方向: 无人机飞行动力学、飞行控制与仿真。 Tel: 029-88453368 E-mail: wangrui@nwpu.edu.cn;周洲女, 博士, 教授, 博士生导师。主要研究方向: 无人机系统总体设计、先进气动布局设计。 Tel: 029-88453368 E-mail: zhouzhou@nwpu.edu.cn;祝小平男, 博士, 教授, 博士生导师。主要研究方向: 无人机系统总体设计、控制与制导。 Tel: 029-88453368 E-mail: zhouzhou@nwpu.edu.cn
基金资助:
国家自然科学基金(11202162);国家"863"计划(2011AA7052002)

Improving the Geometrically Nonlinear Intrinsic Beam Element Model of Wing for High Efficiency

WANG Rui¹, ZHOU Zhou¹, ZHU Xiaoping², XIAO Wei¹

1. Science and Technology on UAV Laboratory, Northwestern Polytechnical University, Xi'an 710072, China;
2. Institute of UAV, Northwestern Polytechnical University, Xi'an 710072, China

Received:2012-07-25 Revised:2012-12-17 Online:2013-06-25 Published:2012-12-27
Contact: 10.7527/S1000-6893.2013.0233 E-mail:zhouzhou@nwpu.edu.cn
Supported by:
National Natural Science Foundation of China (11202162); National High-tech Research and Development Program of China (2011AA7052002)

摘要/Abstract

摘要：

采用Hodges等提出的时间-空间离散化的几何精确非线性本征梁通用模型处理柔性机翼结构动力学问题时,当离散化的节点数增大时,该方法的未知数数量成倍地增长,而且方程组是严重病态的,因此数值模拟计算的速度非常缓慢。针对机翼中最常见的悬臂梁结构,根据空间离散化的边界条件,提出了空间缩聚法把空间离散差分方程缩聚为常系数矩阵格式,得到了只与时间相关的微分方程组,进一步推导得到了该方程组的雅可比矩阵,因而大大减少了方程组的数量以及求解过程的循环和迭代步数。采用Gear方法分别求解了原始的本征梁元素模型和本文提出的缩聚模型,结果表明空间缩聚模型在相同条件下可提高运算速度约5.1倍,而且对不同类型的外载荷都具有较好的通用性、稳定性和高效性。

关键词: 柔性机翼, 几何非线性, 结构动力学, 空间缩聚, 雅可比矩阵, 高效性

Abstract:

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.

Key words: flexible wing, geometrical nonlinearity, structural dynamics, space condensation, Jacobian matrix, high efficiency

中图分类号:

V212

王睿, 周洲, 祝小平, 肖伟. 几何非线性机翼本征梁元素模型的高效化改进[J]. 航空学报, 2013, 34(6): 1309-1318.

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.

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E-mail：hkxb@buaa.edu.cn

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几何非线性机翼本征梁元素模型的高效化改进

Improving the Geometrically Nonlinear Intrinsic Beam Element Model of Wing for High Efficiency

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