一种考虑截面任意变形模式梁的有限元模型

doi:10.7527/S1000-6893.2018.22228

Abstract

Abstract: A cross-section interpolation beam model considering the complete deformation of the cross-section is proposed and used to model and analyze the wing structure. First, the Lagrange functions are introduced as the interpolation function to describe the shape of the beam cross-section, and the displacement vectors are used as unknown variables to describe the displacement of the cross-section. On this basis, the displacement field of the beam element is constructed according to the interpolation theory. While the displacements of the beam in the conventional beam element are determined by the deflection and rotation of the assumed neutral axis, the new beam element rejects the neutral axis hypothesis and flat section hypothesis, and the deformation of the beam cross-section is obtained by the interpolation functions. Then based on the finite element theory, the stiffness matrix and the mass matrix of the beam element are derived. Finally, the wing components are modeled by the cross-section interpolation beam element, and the static analysis and dynamic analysis under typical conditions are carried out. The validity of the beam model is verified by comparing the result with the results of Nastran solid model, showing that the model provides a one-dimensional beam simplified modeling method for the structural design and strength analysis of the wing.

Key words: arbitrary deformation of cross-section, Lagrange interpolation, finite element method, static analysis, mode

CLC Number:

V214.3

HE Huan, SONG Dapeng, ZHANG Chenkai, CHEN Guoping. Finite element model of beem considering arbitrary deformation mode of cross-section[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 222228-222228.

References

[1] 姚卫星, 顾怡. 飞机结构设计[M]. 北京:国防工业出版社, 2016:46-47. YAO W X, GU Y. Aircraft structure design[M]. Beijing:National Defend Industry Press, 2016:46-47(in Chinese).
[2] 蒋余芬, 朱纪洪, 刘世前. 弹性机翼动力学建模与仿真[J]. 系统仿真学报, 2006, 18(z2):5-7. JIANG Y F, ZHU J H, LIU S Q. Elastic wing dynamics modeling and simulation[J]. Journal of System Simulation, 2006, 18(z2):5-7(in Chinese).
[3] 欧阳星, 余雄庆, 王宇. 采用等效刚度有限元模型的复合材料机翼颤振分析[J]. 振动工程学报, 2015, 28(3):404-410. OUYANG X, YU X Q, WANG Y. Flutter analysis of composite wing based on equivalent stiffness finite element model[J]. Journal of Vibration Engineering, 2015, 28(3):404-410(in Chinese).
[4] WRIGHT J R, COOPERJ E. Introduction to aircraft aeroelasticity and loads[M]. Hoboken, NJ:John Wiley & Sons, Ltd., 2007.
[5] ZHAO Y H, HU H Y. Structural modeling and aeroelastic analysis of high-aspect-ratio composite wings[J]. Chinese Journal of Aeronautics, 2005, 18(1):25-30.
[6] 张旭, 吴志刚, 杨超. 基于等效梁模型的长直机翼动力学与颤振分析[J]. 北京航空航天大学学报, 2010, 36(11):1373-1377. ZHANG X, WU Z G, YANG C. Dynamic and flutter analysis of long straight wing based on equivalent beam model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(11):1373-1377(in Chinese).
[7] LIVNE E, NAVARRO I. Nonlinear equivalent plate modeling of wing-box structures[J]. Journal of Aircraft, 2012, 36(5):851-865.
[8] GILES G L. Equivalent plate analysis of aircraft wing box structures with general planform geometry[J]. Journal of Aircraft, 1986, 23(11):859-864.
[9] KRISHNAMURTHY T, TSAI F J. Static and dynamic structural response of an aircraft wing with damage using equivalent plate analysis[C]//49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, VA:AIAA, 2008.
[10] 王宇, 欧阳星, 余雄庆. 采用等效有限元模型的复合材料机翼结构优化[J]. 复合材料学报, 2015, 32(5):1487-1495. WANG Y, OUYANG X, YU X Q. Structural optimization of composite wing using equivalent finite element model[J]. Acta Materiae Compositae Sinica, 2015, 32(5):1487-1495(in Chinese).
[11] 周倩南. 基于位移变形理论的空间梁模型分析与研究[D]. 杭州:浙江大学, 2015:1-2. ZHOU Q N. Spatial beam model analysis and research based on displacement deformation theory[D]. Hangzhou:Zhejiang University, 2015:1-2(in Chinese).
[12] TIMOSHENKO S P. LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars[J]. Philosophical Magazine, 1950, 7(245):239-250.
[13] 胡海昌. 弹性力学的变分原理及其应用[M]. 北京:科学出版社, 1981:139-144. HU H C. Variational principle of elastic mechanics and its application[M]. Beijing:Science Press, 1981:139-144(in Chinese).
[14] HUGHES T J R, TAYLOR R L, KANOKNUKULCHAI W. A simple and efficient finite element for plate bending[J]. International Journal for Numerical Methods in Engineering, 2010, 11(10):1529-1543.
[15] ORAL S. Anisoparametric interpolation in hybrid-stress timoshenko beam element[J]. Journal of Structural Engineering, 1991, 117(4):1070-1078.
[16] OWEN D R J, HINTON E. Finite elements in plasticity:Theory and practice[M]. Swansea:Pineridge Press, 1980.
[17] 王勖成. 有限单元法[M]. 北京:清华大学出版社, 2003:111-113. WANG X C. Finite element method[M]. Beijing:Tsinghua University Press, 2003:111-113(in Chinese).
[18] BATHEK J. Finite element procedures in engineering analysis[M]. Englewood Cliffs, NJ:Prentice-Hall, Inc., 1982.
[19] OÑATE E. Structural analysis with the finite element method[M]. Netherlands:Springer, 2009.
[20] 陈桂彬. 气动弹性设计基础[M]. 北京:北京航空航天大学出版社, 2010:114-128. CHEN G B. Aeroelastic design basis[M]. Beijing:Beihang University Press, 2010:114-128(in Chinese).
[21] 赵永辉. 气动弹性力学与控制[M]. 北京:科学出版社, 2007:130-139. ZHAO Y H. Aeroelasticity mechanics and control[M]. Beijing:Science Press, 2007:130-139(in Chinese).

Finite element model of beem considering arbitrary deformation mode of cross-section

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Bo LI, Xiao WANG. Dynamic modeling and modal analysis of coaxial rotors/auxiliary propeller/drive train coupled system [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 528945-528945.
[2]	Zhuangzhuang CUI, Xin YUAN, Guoqing ZHAO, Simeng JING, Qijun ZHAO. Influence of control strategy on forward flight performance of coaxial rigid rotor high⁃speed helicopters [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529256-529256.
[3]	Jiaqi LIU, Rongqian CHEN, Jinhua LOU, Xu HAN, Hao WU, Yancheng YOU. Aerodynamic shape optimization of high-speed helicopter rotor airfoil based on deep learning [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529828-529828.
[4]	Yuqing QIU, Yan LI, Jinxi LANG, Yuxian LIU, Zhong WANG. Robust adaptive attitude control of high-speed helicopters in transition mode [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529927-529927.
[5]	Zixu WANG, Pan LI, Ke LU, Zhenhua ZHU, Renliang CHEN. Optimized design of trim strategy for coaxial rigid rotor high-speed helicopter [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529069-529069.
[6]	Xiaopeng SHI, Xinyan ZHONG, Haolei MOU, Jiang XIE, Zhiyu ZENG, Peiyao LI. Lumbar load of seated occupant under vertical impact [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 229108-229108.
[7]	Yuhan LI, Baoyu YANG, Yinong WU, Qiang ZHANG, Xiao TANG. Research on parameters correction method for thermal model of satellite optomechanical load [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 628814-628814.
[8]	Shusheng CHEN, Muliang JIA, Yanxu LIU, Zhenghong GAO, Xinghao XIANG. Deformation modes and key technologies of aerodynamic layout design for morphing aircraft: Review [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 629595-629595.
[9]	Shengxiang TONG, Zhiwei SHI, Xi GENG, Lishuang WANG, Zhikun SUN, Qichang CHEN. Combinable samara aircraft and controlled separation technique [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 629590-629590.
[10]	Shusheng CHEN, Cong FENG, Zhaokang ZHANG, Ke ZHAO, Xinyang ZHANG, Zhenghong GAO. Aerodynamic design of wide-speed-range waverider-wing configuration based on global & gradient optimization method [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 629596-629596.
[11]	Xiaofeng XUE, Miaoyan ZHAO, Qianyi DU, Yunwen FENG, Junling FAN, Ting JIAO. Detection reliability based on quantification of human and environmental factors [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 228859-228859.
[12]	Hailang SONG, Jiandong ZHANG, Guoqing SHI, Qiming YANG, Yaozhong ZHANG. Comprehensive evaluation techniques and methods for flight test of avionics fire control system [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(5): 529687-529687.
[13]	Weina HUANG, Fangjuan LI, Hongbin QI. Preliminary investigation and thoughts on aero-engine digital engineering development [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(5): 529693-529693.
[14]	Lianjie MA, Wenhao DU, Zhen ZHAO, Zhe QIU. Instantaneous milling force model of side milling hard and brittle materials in the state of tool eccentricity and runout [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(4): 428925-428925.
[15]	Minghui HU, Jinji GAO, Zhinong JIANG, Weimin WANG, Limin ZOU, Tao ZHOU, Yunfeng FAN, Yue WANG, Jiaxin FENG, Chenyang LI. Research progress on vibration monitoring and fault diagnosis for aero-engine [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(4): 630194-630194.