-
To solve the contact/impact problem of flexible bodies in arbitrary shape, the finite element method is widely used to discretize the contact bodies. In the finite element method, two contact models are mainly used to compute the contact force, i.e., penalty function method and additional constraint method, which are different in constraint imposition strategy. The penalty function method regards the contact effect as a force function of local penetration at the contact point and its rate. This method has gained significant popularity because it does not bring extra dimensions to the dynamic equations and does not need to solve constraint equations either. However, as the non-penetration constraint is not precisely satisfied in the contact process when using the penalty function method, the accuracy of the numerical simulation depends on the choice of the penalty parameter. On the other hand, the additional constraint method can strictly satisfy the contact constraint condition by introducing the Lagrange multipliers into the dynamic equations, but the method poses some numerical difficulties due to the additional effort required to solve the multipliers. Considering the advantages and disadvantages of the two contact methods, the interactive mode method is proposed. This method divides the whole model into local static module and main dynamics module. The static module establishes a local finite element model of the contact region to compute the contact force, and the main dynamics module is used to obtain the kinematic variables of the whole body. In the simulation, the two modules are coupled by exchanging displacements and forces in each time step. In the current integration step, the main dynamics module provides the displacements of the boundaries of the local contact region at first, the values are transferred to the local finite model to compute the contact force next, and then the contact force is fed back to the dynamics module for the calculation of the next step. The proposed method combines the advantages of both the additional constraint method and the penalty function method, in which not only the artificial selection of penalty parameter is avoided, but also the non-penetration constraint of local contact region is satisfied and the numerical solution is convenient. The validity of the proposed method is verified by the comparison between simulation results and experimental results of a rod-plate impact case. Furthermore, a multi-point impact problem of a slider sliding in the gap chute is presented to validate the proposed method of dealing with the general impact problem.
-
Keywords:
- contact/impact /
- interactive mode method /
- penalty function method /
- additional constraint method
[1] Klisch T 1998 Multibody Syst. Dyn. 2 335
[2] Ambrsio J, Pombo J, Rauter F, Pereira M 2009 Multibody Dynamics: Computational Methods and Applications (Dordrecht: Springer Netherlands) p231
[3] Flores P, Koshy C, Lankarani H, Ambrsio J, Claro J C P 2011 Nonlinear Dynam. 65 383
[4] Lundberg O E, Nordborg A, Arteaga I L 2016 J. Sound Vib. 366 429
[5] Wang X H, Wang Q 2015 Chin. J. Theor. Appl. Mech. 47 814 (in Chinese) [王晓军, 王琪 2015 力学学报 47 814]
[6] Tur M, Fuenmayor F J, Wriggers P 2009 Comput. Method Appl. M. 198 2860
[7] Duan Y C, Zhang D G, Hong J Z 2013 Appl. Math. Mech. Engl. 34 1393
[8] Chen P, Liu J Y, Hong J Z 2016 Acta Mech. Sin. 32 1
[9] Weyler R, Oliver J, Sain T, Cante J C 2012 Comput. Method Appl. M. 205 68
[10] Tian Q, Zhang Y, Chen L, Flore P 2009 Comput. Struct. 87 913
[11] Qian Z J, Zhang D G 2015 J. Vib. Eng. 28 879 (in Chinese) [钱震杰, 章定国 2015 振动工程学报 28 879]
[12] Zhang J, Wang Q 2016 Multibody Syst. Dyn. 38 367
[13] Yang Y F, Feng H B, Chen H, Wu M J 2016 Acta Phys. Sin. 65 240502 (in Chinese) [杨永锋, 冯海波, 陈虎, 仵敏娟 2016 物理学报 65 240502]
[14] Brenan K E, Campbell S L, Petzold L R 1996 Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Philadelphia: SIAM) p45
[15] Dong F X, Hong J Z, Zhu K, Yu Z Y 2010 Acta Mech. Sin. 26 635
[16] Dan N, Haug E J, German H C 2003 Multibody Syst. Dyn. 9 121
[17] Taylor R L, Papadopoulos P 2010 Int. J. Numer. Meth. Eng. 36 2123
[18] Seifried R, Hu B, Eberhard P 2003 Multibody Syst. Dyn. 9 265
[19] Hong J Z 1999 Computational Dynamics of Multibody Systems (Beijing: Higher Education Press) p53 (in Chinese) [洪嘉振 1999计算多体系统动力学(北京:高等教育出版社) 第53页]
[20] Gradin M, Cardona A 2001 Flexible Multibody Dynamics: a Finite Element Approach (Chichester: John Wiley) p144
-
[1] Klisch T 1998 Multibody Syst. Dyn. 2 335
[2] Ambrsio J, Pombo J, Rauter F, Pereira M 2009 Multibody Dynamics: Computational Methods and Applications (Dordrecht: Springer Netherlands) p231
[3] Flores P, Koshy C, Lankarani H, Ambrsio J, Claro J C P 2011 Nonlinear Dynam. 65 383
[4] Lundberg O E, Nordborg A, Arteaga I L 2016 J. Sound Vib. 366 429
[5] Wang X H, Wang Q 2015 Chin. J. Theor. Appl. Mech. 47 814 (in Chinese) [王晓军, 王琪 2015 力学学报 47 814]
[6] Tur M, Fuenmayor F J, Wriggers P 2009 Comput. Method Appl. M. 198 2860
[7] Duan Y C, Zhang D G, Hong J Z 2013 Appl. Math. Mech. Engl. 34 1393
[8] Chen P, Liu J Y, Hong J Z 2016 Acta Mech. Sin. 32 1
[9] Weyler R, Oliver J, Sain T, Cante J C 2012 Comput. Method Appl. M. 205 68
[10] Tian Q, Zhang Y, Chen L, Flore P 2009 Comput. Struct. 87 913
[11] Qian Z J, Zhang D G 2015 J. Vib. Eng. 28 879 (in Chinese) [钱震杰, 章定国 2015 振动工程学报 28 879]
[12] Zhang J, Wang Q 2016 Multibody Syst. Dyn. 38 367
[13] Yang Y F, Feng H B, Chen H, Wu M J 2016 Acta Phys. Sin. 65 240502 (in Chinese) [杨永锋, 冯海波, 陈虎, 仵敏娟 2016 物理学报 65 240502]
[14] Brenan K E, Campbell S L, Petzold L R 1996 Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Philadelphia: SIAM) p45
[15] Dong F X, Hong J Z, Zhu K, Yu Z Y 2010 Acta Mech. Sin. 26 635
[16] Dan N, Haug E J, German H C 2003 Multibody Syst. Dyn. 9 121
[17] Taylor R L, Papadopoulos P 2010 Int. J. Numer. Meth. Eng. 36 2123
[18] Seifried R, Hu B, Eberhard P 2003 Multibody Syst. Dyn. 9 265
[19] Hong J Z 1999 Computational Dynamics of Multibody Systems (Beijing: Higher Education Press) p53 (in Chinese) [洪嘉振 1999计算多体系统动力学(北京:高等教育出版社) 第53页]
[20] Gradin M, Cardona A 2001 Flexible Multibody Dynamics: a Finite Element Approach (Chichester: John Wiley) p144
Catalog
Metrics
- Abstract views: 14712
- PDF Downloads: 214
- Cited By: 0
下载:
