Nonsmooth dynamic analysis of rigid-flexible interaction collision

doi:10.1007/s10483-022-2922-9

Abstract

Abstract: This paper aims to explore the deformation of the collided bodies in multibody systems and to effectively simulate the motion path of colliding bodies. First, we describe the geometrically nonlinear problems of materials by the total Lagrangian formulation. Second, a first-order integration scheme is used to solve the dynamics equations. An algorithm combining the bi-potential method with the node-to-point contact identification is proposed to solve the interface problems of rigid-flexible interaction collision. To observe the collision process more intuitively, the internal software FER/VIEW is introduced to visualize the results. The accuracy is proved by comparing the proposed method with the analytical solution or another numerical solution. Moreover, the proposed method has more numerical robustness, such as occupying less computer storage, saving the computational cost, and broadening the application range of the bi-potential method.

Key words: collision, bi-potential method, node-to-point, rigid-flexible, FER/VIEW

2010 MSC Number:

37J55
74M20

Ling TAO, Zhongpan LI, Yan LI, Huijian CHEN, Zhiqiang FENG. Nonsmooth dynamic analysis of rigid-flexible interaction collision. Applied Mathematics and Mechanics (English Edition), 2022, 43(11): 1731-1746.

TrendMD

References

[1] TIMOSHENKO, S. P. and GOODIER, J. N. Theory of Elasticity, McGraw-Hill, New York, 343-395(1951)
[2] JOHNSON, K. L. Contact Mechanics, Cambridge University Press, Cambridge, 1-425(1987)
[3] WRIGGERS, P. Computational Contact Mechanics, Springer, New York, 11-473(2006)
[4] ACARY, V. Numerical Methods for Nonsmooth Dynamical Systems:Applications in Mechanics and Electronics, Springer, New York, 1-165(2008)
[5] BROGLIATO, B. Nonsmooth Mechanics, Springer, New York, 1-477(2016)
[6] LAURSEN, T. A. Computational Contact and Impact Mechanics, Springer, New York, 7-435(2003)
[7] YAO, W. L., CHEN, B., LIU, C. S., and XU, J. Sliding state stepping algorithm for solving impact problems of multi-rigid-body system with joint friction. Applied Mathematics and Mechanics (English Edition), 28(11), 1621-1627(2007) https://doi.org/10.1007/s10483-017-2272-7
[8] STRONGE, W. J. Impact Mechanics, Cambridge University Press, Cambridge, 1-317(2018)
[9] ZHONG, Z. H. Finite Element Procedures for Contact-Impact Problems, Oxford University Press, Oxford, 1-245(1993)
[10] GALVEZ, J., CAVALIERI, F. J., COSIMO, A., BRÜLS, O., and CARDONA, A. A nonsmooth frictional contact formulation for multibody system dynamics. International Journal for Numerical Methods in Engineering, 121(2), 3584-3609(2020)
[11] WANG, G. X., WANG, L., and YUAN, Y. Investigation on dynamics performance of multibody system with rough surface. Applied Mathematical Modelling, 104, 358-372(2022)
[12] PENNESTRÌ, E., ROSSI, V. D., SALVINI, P., and VALENTINI, P. P. Review and comparison of dry friction force models. Nonlinear Dynamics, 83(4), 1785-1801(2016)
[13] KIKUUWE, R., AKESUE, N. T., SANO, A., MOCHIYAMA, H., and FUJIMOTO, H. Fixedstep friction simulation:from classical Coulomb model to modern continuous models. IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Edmonton, 1009-1016(2005)
[14] POUILLY-CATHELAIN, M. and FEYEL, P. A friction model based on parallelization of original lugre models and the corresponding compensator. IFAC-PapersOnLine, 54(7), 499-504(2021)
[15] MAJDOUB, K. E., OUADI, H., BELBOUNAGUIA, N., KHEDDIOUI, E., and AMMARI, O. Optimal control of semi-active suspension quarter car employing magnetorheological damper and Dahl model. Renewable Energies, Power Systems and Green Inclusive Economy (2018) https://doi.org/10.1109/REPSGIE.2018.8488781
[16] JAYSWAL, A. and ARANA-JIMÉNEZ, M. Robust penalty function method for an uncertain multi-time control optimization problems. Journal of Mathematical Analysis and Applications, 505(1), 125-453(2022)
[17] BEHZAD, M. and ALVANDI, M. Friction-induced backward rub of rotors in non-annular clearances:experimental observations and numerical analysis. Tribology International, 152, 106430(2020)
[18] CUI, Y., DING, C., LI, X. D., and ZHAO, X. Y. Augmented Lagrangian methods for convex matrix optimization problems. Journal of the Operations Research Society of China, 10(2), 305-342(2021)
[19] ZHENG, X., ZHANG, R., and WANG, Q. Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint. Applied Mathematics and Mechanics (English Edition), 39(9), 1239-1258(2018) https://doi.org/10.1007/s10483-018-2371-9
[20] WANG, K., TIAN, Q., and HU, H. Nonsmooth spatial frictional contact dynamics of multibody systems. Multibody System Dynamics, 53(1), 1-27(2021)
[21] CHATTERJEE, A. and BOWLING, A. Modeling three-dimensional surface-to-surface rigid contact and impact. Multibody System Dynamics, 46, 1-40(2019)
[22] ZHOU, Z., ZHENG, X., WANG, Q., CHEN, Z., and LIANG, B. Modeling and simulation of point contact multibody system dynamics based on the 2D LuGre friction model. Mechanism and Machine Theory, 158(5), 104244(2021)
[23] LEE, J., LEE, M., and LEE, D. Large-dimensional multibody dynamics simulation using contact nodalization and diagonalization. Arxiv, 2201, 09212(2022)
[24] YAO, W., YANG, L., and GUO, M. Gauss optimization method for the dynamics of unilateral contact of rigid multibody systems. Acta Mechanica Sinica, 37(3), 1-13(2021)
[25] DE SAXCÉ, G. and FENG, Z. Q. The bipotential method:a constructive approach to design the complete contact law with friction and improved numerical algorithms. Mathematical and Computer Modelling, 28(4-8), 225-245(1998)
[26] DE SAXCÉ, G. and FENG, Z. Q. New inequality and functional for contact with friction:the implicit standard material approach. Mechanics of Structures and Machines, 19(3), 301-325(1991)
[27] AHMADIZADEH, M., SHAFEI, A. M., and JAFARI, R. Frictional impact-contacts in multiple flexible links. International Journal of Structural Stability and Dynamics, 21(6), 2150075(2021)
[28] SONG, N., PENG, H., KAN, Z., and CHEN, B. A novel nonsmooth approach for flexible multibody systems with contact and friction in 3D space. Nonlinear Dynamics, 102, 1-34(2020)
[29] FENG, Z. Q. and FENG, Z. G. FER/VIEW:An interactive finite element post-processor. Computational Mechanics, WCCM VI in Conjunction with APCOM04, Springer, Beijing (2004)
[30] YEOH, O. H. Some forms of the strain energy function for rubber. Rubber Chemistry and Technology, 66(5), 754-771(1993)
[31] WRIGGERS, P. Nonlinear Finite Element Methods, Springer, New York, 19-103(2008)
[32] ARMERO, F. and PETOCZ, E. Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems. Computer Methods in Applied Mechanics and Engineering, 158(3-4), 269-300(1998)
[33] MOREAU, J. J. Unilateral contact and dry friction in finite freedom dynamics. Nonsmooth Mechanics and Applications, 302, 31-48(1988)
[34] JEAN, M. Dynamics with partially elastic shocks and dry friction:double scale method and numerical approach. 4th Meeting on Unilateral Problems in Structural Analysis, Capri (1989)
[35] KUHL, D. and CRISFIELD, M. A. Energy-conserving and decaying algorithms in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering, 45(5), 569-599(1999)
[36] ZHU, D. C. and XING, Y. F. The analytical solution of the point elastic impact. Acta Mechanica Sinica, 28(1), 99-103(1996)