Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Application of Hilber-Hughes-Taylor- method to dynamics of flexible multibody system with contact and constraint

Guo Xian Zhang Ding-Guo Chen Si-Jia

Citation:

Application of Hilber-Hughes-Taylor- method to dynamics of flexible multibody system with contact and constraint

Guo Xian, Zhang Ding-Guo, Chen Si-Jia
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Numerical characteristics of the Hilber-Hughes-Taylor- (HHT-) method for the differential-algebraic equations (DAEs) in impact dynamics of flexible multibody systems are investigated. The research is based on a dynamic process of a flexible beam rotating about a fixed axis, whichis under the action of gravity and collides with a rigid plane. Therefore, the dynamic transformation and solution of flexible multibody system are divided into two parts. The Lagrange's equations of the second kind are used to derive the dynamic equations before and after impact, whereas the contact constraint method (CCM) is adopted to simulate the contact process. Compared with other methods, the CCM can describe the contact process accurately and avoid choosing the additional parameters. A set of the differential equations are transformed into a set of the DAEs due to the added constraint equations into impact process. Normally the dynamic equations of the flexible multibody system are index-3 DAEs. Solving a system of the index-3 DAEs directly by an integration algorithm would be subject to ill-conditioning and poor global convergence properties, so it is reasonable to find the methods that avoid both drawbacks and dependence on the constraint information. In order to solve this complex process, the HHT- method is used in the impact dynamic simulation by introducing the Gear-Gupta-Leimkuhler formulation. The coefficient of the HHT- method can be used to control the numerical dissipation, and it also represents asymptotic annihilation of the high frequency response. The smaller the value of , the more the damping is induced in the numerical solution. The Baumgarte's stabilization method is the most famous one for index-3 DAEs. Unfortunately, no general way can be adopted to determine the coefficients of the Baumgarte's stabilization method. It is the main reason for the numerical stability problems. It is necessary to study the influences of coefficients of the former two methods. Simultaneously, the simulation results from the HHT- method are compared with those from the Baumgarte's stabilization method to calculate the CCM model, and the Newmark method is used to solve the ODEs by using the continuous contact force model. The influence of the modal truncation N on the numerical method is also taken into account. Furthermore, the influences of N and the coefficient of HHT- method on the velocity and acceleration constraints in the multibody system are analyzed. Results have shown that the choice of the stabilization coefficients exerts a greater influence on the simulation results, such as the dynamic responses and the constraints, than that of the coefficient . Meanwhile, the HHT- method has an influence on the choice of coefficient and numerical damping properties. This numerical damping property can reduce the effect of high order modes induced by impact. Finally, the increase of N causes the sharpening default of both velocity and acceleration constraints.
      Corresponding author: Zhang Ding-Guo, zhangdg419@njust.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272155, 11302192) and the Fundamental Research Funds for Central Universities (Grant No. 30917011103).
    [1]

    Petzold L R 1992 Physica D 60 269

    [2]

    Hilber H, Hughes T, Taylor R 1977 Earthq Eng. Struct. D 5 283

    [3]

    Newmark N M 1959 J. Eng. Mech. Div.-ASCE 85 67

    [4]

    Cardona A, Géradin M 1989 Comput. Struct. 33 801

    [5]

    Negrut D, Rampallir R, Ottarsson G 2007 J. Comput. Nonlin. Dyn. 2 73

    [6]

    Laurent O, Negrut D 2007 Electron Trans. Numer. Ana. 6 190

    [7]

    Chung J, Hulbert G 1993 J. Appl. Mech. 60 371

    [8]

    Hussein B A, Negrut D, Ahmed A 2008 Nonlinear Dynam. 54 283

    [9]

    Shabana A A, Hussein B A 2009 J. Sound Vib. 327 557

    [10]

    Hussein B A, Shabana A A 2011 Nonlinear Dynam. 65 369

    [11]

    Pan Z K, Zhao W J, Hong J Z, Liu Y Z 1996 Adv. Mech. 26 28 (in Chinese)[潘振宽, 赵维加, 洪嘉振, 刘延柱1996力学进展26 28]

    [12]

    Wang Q, Lu Q S 2011 Adv. Mech. 31 9(in Chinese)[王琪, 陆启韶2011力学进展31 9]

    [13]

    Ding J Y, Pan Z K 2013 Engineer. Mech. 30 380 (in Chinese)[丁洁玉, 潘振宽2013工程力学30 380]

    [14]

    Ma X T, Chen L P, Zhang Y Q 2009 J. Syst. Simulat. 21 6373(in Chinese)[马秀腾, 陈立平, 张云清2009系统仿真学报21 6373]

    [15]

    Ma X T, Zhai Y B, Luo S Q 2011 J. Southwest Jiaotong Univ. (Natural Science Edition) 33 151(in Chinese)[马秀腾, 翟彦博, 罗书强2011西南交通大学学报(自然科学版)33 151]

    [16]

    Zhang L, Zhang D G 2016 J. Mech. Engineer. 52 79(in Chinese)[张乐, 章定国2016机械工程学报52 79]

    [17]

    Zhang L, Zhang D G 2016 Nonlinear Dynam. 85 263

    [18]

    Kan Z Y, Peng H J, Chen B S, Zhong W X 2015 Chin. J. Computat. Mech. 32 707(in Chinese)[阚子云, 彭海军, 陈飙松, 钟万勰2015计算力学学报32 707]

    [19]

    Baumgarte J 1972 Comput. Method. Appl. M 1 1

    [20]

    Lin S T, Huang J N 2000 J. Guid. Control Dynam. 23 566

    [21]

    Lin S T, Huang J N 2002 J. Mech. Design 124 633

    [22]

    Duan Y C 2012 Ph. D. Dissertation (Nanjing:Nanjing University of Science & Technology) (in Chinese)[段玥晨2012博士学位论文(南京:南京理工大学)]

    [23]

    Wu S B, Zhang D G 2011 J. Vib. Engineer. 24 1(in Chinese)[吴胜宝, 章定国2011振动工程学报24 1]

    [24]

    Liu J Y, Hong J Z 2002 Chin. J. Solid Mech. 23 159(in Chinese)[刘锦阳, 洪嘉振2002固体力学学报23 159]

    [25]

    Gear C W, Gupta G K, Leumkuhler B 1985 J. Comput. Appl. Math. 12 77

  • [1]

    Petzold L R 1992 Physica D 60 269

    [2]

    Hilber H, Hughes T, Taylor R 1977 Earthq Eng. Struct. D 5 283

    [3]

    Newmark N M 1959 J. Eng. Mech. Div.-ASCE 85 67

    [4]

    Cardona A, Géradin M 1989 Comput. Struct. 33 801

    [5]

    Negrut D, Rampallir R, Ottarsson G 2007 J. Comput. Nonlin. Dyn. 2 73

    [6]

    Laurent O, Negrut D 2007 Electron Trans. Numer. Ana. 6 190

    [7]

    Chung J, Hulbert G 1993 J. Appl. Mech. 60 371

    [8]

    Hussein B A, Negrut D, Ahmed A 2008 Nonlinear Dynam. 54 283

    [9]

    Shabana A A, Hussein B A 2009 J. Sound Vib. 327 557

    [10]

    Hussein B A, Shabana A A 2011 Nonlinear Dynam. 65 369

    [11]

    Pan Z K, Zhao W J, Hong J Z, Liu Y Z 1996 Adv. Mech. 26 28 (in Chinese)[潘振宽, 赵维加, 洪嘉振, 刘延柱1996力学进展26 28]

    [12]

    Wang Q, Lu Q S 2011 Adv. Mech. 31 9(in Chinese)[王琪, 陆启韶2011力学进展31 9]

    [13]

    Ding J Y, Pan Z K 2013 Engineer. Mech. 30 380 (in Chinese)[丁洁玉, 潘振宽2013工程力学30 380]

    [14]

    Ma X T, Chen L P, Zhang Y Q 2009 J. Syst. Simulat. 21 6373(in Chinese)[马秀腾, 陈立平, 张云清2009系统仿真学报21 6373]

    [15]

    Ma X T, Zhai Y B, Luo S Q 2011 J. Southwest Jiaotong Univ. (Natural Science Edition) 33 151(in Chinese)[马秀腾, 翟彦博, 罗书强2011西南交通大学学报(自然科学版)33 151]

    [16]

    Zhang L, Zhang D G 2016 J. Mech. Engineer. 52 79(in Chinese)[张乐, 章定国2016机械工程学报52 79]

    [17]

    Zhang L, Zhang D G 2016 Nonlinear Dynam. 85 263

    [18]

    Kan Z Y, Peng H J, Chen B S, Zhong W X 2015 Chin. J. Computat. Mech. 32 707(in Chinese)[阚子云, 彭海军, 陈飙松, 钟万勰2015计算力学学报32 707]

    [19]

    Baumgarte J 1972 Comput. Method. Appl. M 1 1

    [20]

    Lin S T, Huang J N 2000 J. Guid. Control Dynam. 23 566

    [21]

    Lin S T, Huang J N 2002 J. Mech. Design 124 633

    [22]

    Duan Y C 2012 Ph. D. Dissertation (Nanjing:Nanjing University of Science & Technology) (in Chinese)[段玥晨2012博士学位论文(南京:南京理工大学)]

    [23]

    Wu S B, Zhang D G 2011 J. Vib. Engineer. 24 1(in Chinese)[吴胜宝, 章定国2011振动工程学报24 1]

    [24]

    Liu J Y, Hong J Z 2002 Chin. J. Solid Mech. 23 159(in Chinese)[刘锦阳, 洪嘉振2002固体力学学报23 159]

    [25]

    Gear C W, Gupta G K, Leumkuhler B 1985 J. Comput. Appl. Math. 12 77

  • [1] Yang Jian-Zhi, He Yong-Qing, Jiao Feng, Wang Jin. Influence factors and kinetic analysis of liquid marbles colliding with sessile droplets. Acta Physica Sinica, 2023, 72(16): 164702. doi: 10.7498/aps.72.20230815
    [2] Peng Jia-Lue, Guo Hao, You Tian-Ya, Ji Xian-Bing, Xu Jin-Liang. Behavioral characteristics of droplet collision on Janus particle spheres. Acta Physica Sinica, 2021, 70(4): 044701. doi: 10.7498/aps.70.20201358
    [3] Yang Yong-Feng, Feng Hai-Bo, Chen Hu, Wu Min-Juan. Dynamical analysis of the flexible beam-cam oblique-impact system. Acta Physica Sinica, 2016, 65(24): 240502. doi: 10.7498/aps.65.240502
    [4] Liu Hui-Ping, Zou Xiu, Zou Bin-Yan, Qiu Ming-Hui. Effect of collision parameter on magnetized electronegative plasma sheath structure. Acta Physica Sinica, 2016, 65(24): 245201. doi: 10.7498/aps.65.245201
    [5] Lan Chun-Bo, Qin Wei-Yang. Vibration energy harvesting from a piezoelectric bistable system with two symmetric stops. Acta Physica Sinica, 2015, 64(21): 210501. doi: 10.7498/aps.64.210501
    [6] Hu Jun, You Lei. A cellular automata model of pedestrian evacuation in three-dimensional space. Acta Physica Sinica, 2014, 63(8): 080507. doi: 10.7498/aps.63.080507
    [7] Wang Zhi-Ping, Zhu Yun, Wu Ya-Min, Zhang Xiu-Mei. Time-dependent density functional theory studies of dynamics of hydroxy by proton impact. Acta Physica Sinica, 2014, 63(2): 023401. doi: 10.7498/aps.63.023401
    [8] Linghu Rong-Feng, Xu Mei, Lü Bing, Song Xiao-Shu, Yang Xiang-Dong. Theoretical study on He-N2 interaction potential. Acta Physica Sinica, 2013, 62(1): 013103. doi: 10.7498/aps.62.013103
    [9] Jiang Tao, Lu Lin-Guang, Lu Wei-Gang. Numerical study of collision process between two equal diameter liquid micro-droplets using a modified smoothed particle hydrodynamics method. Acta Physica Sinica, 2013, 62(22): 224701. doi: 10.7498/aps.62.224701
    [10] Xu Mei, Wang Xiao-Lu, Linghu Rong-Feng, Yang Xiang-Dong. Study on ro-vibrational excitation cross sections of Ne-HF. Acta Physica Sinica, 2013, 62(6): 063102. doi: 10.7498/aps.62.063102
    [11] Zhang Feng-Kui, Ding Yong-Jie. Features of electron-wall collision frequency with saturated sheath in Hall thruster. Acta Physica Sinica, 2011, 60(6): 065203. doi: 10.7498/aps.60.065203
    [12] Xu Bin, Wu Zhen-Sen, Wu Jian, Xue Kun. Incoherent scatter spectrum of a collisional plasma. Acta Physica Sinica, 2009, 58(7): 5104-5110. doi: 10.7498/aps.58.5104
    [13] Wang Ji-Zhi, Wang Mei-Qin, Wang Ying-Long. The collision of one keyed Hash function based on chaotic map and analysis. Acta Physica Sinica, 2008, 57(5): 2737-2742. doi: 10.7498/aps.57.2737
    [14] Shen Shou-Feng, Zhang Jun. New foldons and their elastic interactions in the (2+1)-dimensional modified Veselov-Novikov system. Acta Physica Sinica, 2006, 55(4): 1548-1554. doi: 10.7498/aps.55.1548
    [15] Li Hong, Su Tie, Ouyang Liang, Wang Hui-Hui, Bai Xiao-Yan, Chen Zhi-Peng, Liu Wan-Dong. Numerical simulation of plasma of large-dimensions produced by injecting electron beam into air. Acta Physica Sinica, 2006, 55(7): 3506-3513. doi: 10.7498/aps.55.3506
    [16] Wang Ji-Zhi, Wang Ying-Long, Wang Mei-Qin. The collision problem of one kind of methods for constructing one-way Hash function based on chaotic map. Acta Physica Sinica, 2006, 55(10): 5048-5054. doi: 10.7498/aps.55.5048
    [17] Duan Fang-Li, Luo Jian-Bin, Wen Shi-Zhu. Repulsion mechanism of nanoparticle colliding with monocrystalline silicon surface. Acta Physica Sinica, 2005, 54(6): 2832-2837. doi: 10.7498/aps.54.2832
    [18] Gu Yun-Peng, Ma Teng-Cai. The influence of particle beams on the criterion of Bohm sheath. Acta Physica Sinica, 2003, 52(5): 1196-1202. doi: 10.7498/aps.52.1196
    [19] Wang Li-Guang, Wang Jun. Calculation of electron capture probabilities in collisions of O5+ ion with H atom. Acta Physica Sinica, 2003, 52(2): 312-315. doi: 10.7498/aps.52.312
    [20] Li Yan-Ling, Luo Cheng-Lin. . Acta Physica Sinica, 2002, 51(11): 2589-2594. doi: 10.7498/aps.51.2589
Metrics
  • Abstract views:  7058
  • PDF Downloads:  358
  • Cited By: 0
Publishing process
  • Received Date:  12 March 2017
  • Accepted Date:  07 June 2017
  • Published Online:  05 August 2017

/

返回文章
返回