Analysis of Cable under Dynamic Contact and Large Deformation
- 23 Downloads
Abstract
For simulating contact interactions and high displacement gradients between the cable and the saddle at the middle tower of tripletower suspension bridges, a cable element is developed by combining the absolute nodal coordinate formulation and the quasi-conforming technique. New curvature strains are developed and elastic forces are explicitly formulated for the cable elements. Thereafter, it is compared to the original one to verify its locking remedies. The numerical solutions using the element are compared to analytical results and solutions by the original element. Compared to the original, the proposed element suppresses the high-frequency disturbances in the velocity and acceleration curves. Using the element, the contact and sliding behavior between the cable and the saddle is analyzed by employing parameters obtained experimentally. The saddle’s mechanical and frictional performance subjected to different friction coefficients and unbalanced cable forces is investigated. The proposed model exhibits excellent accuracy in the prediction of the sliding force and the contact status between the cable and the saddle.
Keywords
cables dynamics safety ANCF quasi-conforming techniquePreview
Unable to display preview. Download preview PDF.
References
- Belytschko, T., Liu, W., and Moran, B. (2000). Nonlinear finite elements for continua and structures, John Wiley & Sons, New York, NY, USA, pp. 114–159, DOI: 10.13140/RG.2.1.2800.0089.zbMATHGoogle Scholar
- Cepon, G. and Boltežar, M. (2009). “Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description.” China Civil Engineering Journal, Vol. 319, No. 3, pp. 1019–1035, DOI: 10.1016/j.jsv.2008.07.005.Google Scholar
- Cepon, G., Manin, L., and Boltežar, M. (2009). “Introduction of damping into the flexible multibody belt-drive model: A numerical and experimental investigation.” China Civil Engineering Journal, Vol. 324, No. 1, pp. 283–296, DOI: 10.1016/j.jsv.2009.02.001.Google Scholar
- Di Renzo, A. and Di Maio, F. P. (2004). “Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes.” China Civil Engineering Journal, Vol. 3, No. 59, pp. 525–541, DOI: 10.1016/j.ces.2003.09.037.Google Scholar
- García-Vallejo, D., Mikkola, A. M., and Escalona, J. L. (2007). “A new locking-free shear deformable finite element based on absolute nodal coordinates.” China Civil Engineering Journal, Vol. 50, Nos. 1–2, pp. 249–264, DOI: 10.1007/s11071-006-9155-4.zbMATHGoogle Scholar
- Gerstmayr, J., Matikainen, M. K., and Mikkola, A. M. (2008). “A geometrically exact beam element based on the absolute nodal coordinate formulation.” China Civil Engineering Journal, Vol. 20, No. 4, pp. 359–384, DOI: 10.1007/s11044-008-9125-3.MathSciNetzbMATHGoogle Scholar
- Guan, Y. and Tang L. M. (1993). “Nonlinear quasi-conforming finite element method.” China Civil Engineering Journal, Vol. 9, No. 3, pp. 269–276, DOI: 10.1007/BF02486804.zbMATHGoogle Scholar
- Hasegawa, K., Kojima, H., Sasaki, M., and Takena, K. (1989). “An experimental investigation on friction between cable and saddle of suspension bridge.” China Civil Engineering Journal, Vol. 1989, No. 404, pp. 277–286, DOI: 10.2208/jscej.1989.404_277 (in Japanese).Google Scholar
- He, D. S. and Tang, L. M. (2002). “The displacement function of quasi-conforming element and its node error.” China Civil Engineering Journal, Vol. 23, No. 2, pp. 12–137, DOI: 10.1007/BF02436553.MathSciNetzbMATHGoogle Scholar
- Ji, L., Chen, C. E., and Feng, Z. X. (2007). “Anti-slip test on cable and saddle on the intermediate tower of the triple-tower suspension bridge.” China Civil Engineering Journal, Vol. 6, pp. 1–6 (in Chinese).Google Scholar
- Kerkkänen, K. S., Sopanen, J. T., and Mikkola, A. M. (2005). “A linear beam finite element based on the absolute nodal coordinate formulation.” China Civil Engineering Journal, Vol. 127, No. 4, pp. 621–630, DOI: 10.1115/1.1897406.Google Scholar
- Kerkkänen, K. S., García-Vallejo, D., and Mikkola, A. M. (2006). “Modeling of belt-drives using a large deformation finite element formulation.” China Civil Engineering Journal, Vol. 43, No. 3, pp. 239–256, DOI: 10.1007/s11071-006-7749-5.zbMATHGoogle Scholar
- Kim, K. W., Lee, J. W., and Yoo, W. S. (2012). “The motion and deformation rate of a flexible hose connected to a mother ship.” China Civil Engineering Journal, Vol. 26, No. 3, pp. 703–710, DOI: 10.1007/s12206-011-1202-5.Google Scholar
- Kim, K. D., Lomboy, G. R., and Voyiadjis, G. Z. (2003). “A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom.” China Civil Engineering Journal, Vol. 58, No. 14, pp. 2177–2200, DOI: 10.1002/nme.854.zbMATHGoogle Scholar
- Lomboy, G. R., Suthasupradit, S., Kim, K. D., and Oñate, E. (2009). “Nonlinear formulations of a four-node quasi-conforming shell element.” China Civil Engineering Journal, Vol. 16, No. 2, pp. 189–250, DOI: 10.1007/s11831-009-9030-9.zbMATHGoogle Scholar
- Lugrís, U., Escalona, J. L., Dopico, D., and Cuadrado, J. (2011). “Efficient and accurate simulation of the rope–sheave interaction in weightlifting machines.” China Civil Engineering Journal, Vol. 225, No. 4, pp. 331–343, DOI: 10.1177/1464419311403224.Google Scholar
- Mattiason, K. (1981). “Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals.” China Civil Engineering Journal, Vol. 17, No. 1, pp. 145–153, DOI: 10.1002/nme.1620170113.Google Scholar
- Mikkola, A. M. and Shabana, A. A. (2003). “A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications.” China Civil Engineering Journal, Vol. 9, No. 3, pp. 283–309.MathSciNetzbMATHGoogle Scholar
- Nachbagauer, K., Gruber, P., and Gerstmayr, J. (2013). “Structural and continuum mechanics approaches for a 3D shear deformable ANCF beam finite element: application to static and linearized dynamic examples.” China Civil Engineering Journal, Vol. 8, No. 2, pp. 021004–021015, DOI: 10.1002/nme.1620170113.Google Scholar
- Park, T., Kim, K., and Han, S. (2005). “Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element.” China Civil Engineering Journal, Vol. 37, Nos. 2–3, pp. 237–248.Google Scholar
- Rade, L. and Westergren, B. (1999). Mathematics handbook for science and engineering, 4th Ed., Springer-Verlag, Berlin Heidelberg, Germany, pp. 205–224, DOI: 10.1007/978-3-662-08549-3.Google Scholar
- Ren, H. (2015). “Fast and robust full-quadrature triangular elements for thin plates/shells with large deformations and large rotations.” China Civil Engineering Journal, Vol. 10, No. 5, pp. 051018–051031, DOI: 10.1115/1.4030212.Google Scholar
- Ruan, X., Zhou, J., and Caprani, C. C. (2016). “Safety assessment of the antisliding between the main cable and middle saddle of a threepylon suspension bridge considering traffic load modeling.” China Civil Engineering Journal, Vol. 21, No. 10, p. 04016069, DOI:10.1061/(ASCE)BE.1943-5592.0000927.Google Scholar
- Sanborn, G. G., Choi, J., and Choi, J. H. (2011). “Curve-induced distortion of polynomial space curves, flat-mapped extension modeling, and their impact on ANCF thin-plate finite elements.” China Civil Engineering Journal, Vol. 26, No. 2, pp. 191–211, DOI: 10.1007/s11044-011-9248-9.MathSciNetzbMATHGoogle Scholar
- Schwab, A. L. and Meijaard, J. P. (2005). “Comparison of threedimensional flexible beam elements for dynamic analysis: Finite element method and absolute nodal coordinate formulation.” Proc. 2005 Int. Design Engineering Technical Conf. and Computers and Information in Engineering Conf., ASME, CA, USA, pp. 1341–1349, DOI: 10.1115/DETC2005-85104.Google Scholar
- Shabana, A. A. (1996). An absolute nodal coordinate formulation for the large rotation and large deformation analysis of flexible bodies, Report MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois - Chicago, IL, USA.Google Scholar
- Shabana, A. A. (1997). “Flexible multibody dynamics: Review of past and recent developments.” China Civil Engineering Journal, Vol. 1, No. 2, pp. 189–222, DOI: 10.1023/A:1009773505418.MathSciNetzbMATHGoogle Scholar
- Shabana, A. A. (2015). “Definition of ANCF finite elements.” China Civil Engineering Journal, Vol. 10, No. 5, pp. 054506–054510, DOI: 10.1115/1.4030369.Google Scholar
- Shabana, A. A. and Maqueda, L. G. (2008). “Slope discontinuities in the finite element absolute nodal coordinate formulation: Gradient deficient elements.” China Civil Engineering Journal, Vol. 20, No. 3, pp. 239–249, DOI: 10.1007/s11044-008-9111-9.MathSciNetzbMATHGoogle Scholar
- Shi, G. and Voyiadjis, G. (1991). “Geometrically nonlinear analysis of plates by assumed strain element with explicit tangent stiffness matrix.” China Civil Engineering Journal, Vol. 41, No. 4, pp. 757–763, DOI: 10.1016/0045-7949(91)90185-O.zbMATHGoogle Scholar
- Sopanen, J. T. and Mikkola, A. M. (2003). “Description of elastic forces in absolute nodal coordinate formulation.” China Civil Engineering Journal, Vol. 34, Nos. 1–2, pp. 53–74, DOI: 10.1023/B:NODY.0000014552.68786.bc.zbMATHGoogle Scholar
- Takena, K., Sasaki, M., Hata, K., and Hasegawa, K. (1992). “Slip behavior of cable against saddle in suspension bridges.” China Civil Engineering Journal, Vol. 118, No. 2, pp. 377–391, DOI: 10.1061/(ASCE)0733-9445.Google Scholar
- Tasora, A., Serban, R., Mazhar, H., Pazouki, A., Melanz, D., Fleischmann, J., Taylor, M., Sugiyama, H. and Negrut, D. (2015). “Chrono: An open source multi-physics dynamics engine.” Proc. High Performance Computing in Science and Engineering. HPCSE 2015, Vol. 9611. Springer, Cham, DOI: 10.1007/978-3-319-40361-8_2.Google Scholar
- Tur, M., García, E., Baeza, L., and Fuenmayor, F. J. (2014). “A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary.” China Civil Engineering Journal, Vol. 71, No. 1, pp. 234–243, DOI: 10.1016/j.engstruct.2014.04.015.Google Scholar
- Valkeapää, A. I., Yamashita, H., Jayakumar, P., and Sugiyama, H. (2015). “On the use of elastic middle surface approach in the large deformation analysis of moderately thick shell structures using absolute nodal coordinate formulation.” China Civil Engineering Journal, Vol. 80, No. 3, pp. 1133–1146, DOI: 10.1007/s11071-015-1931-6.MathSciNetGoogle Scholar
- Vohar, B., Kegl, M., and Ren, Z. (2008). “Implementation of an ANCF beam finite element for dynamic response optimization of elastic manipulators.” China Civil Engineering Journal, Vol. 40, No. 12, pp. 1137–1150, DOI: 10.1080/03052150802317457.MathSciNetGoogle Scholar
- Wang, C., Hu, P., and Xia, Y. (2012). “A 4-node quasi-conforming Reissner–Mindlin shell element by using Timoshenko’s beam function.” China Civil Engineering Journal, Vol. 61, pp. 12–22, DOI: 10.1016/j.finel.2012.06.003.MathSciNetGoogle Scholar
- Wang, Q., Tian, Q., and Hu, H. (2015). “Dynamic simulation of frictional multi-zone contacts of thin beams.” China Civil Engineering Journal, Vol. 83, No. 4, pp. 1–19, DOI: 10.1007/s11071-015-2456-8.Google Scholar
- Wasfy, T. and Noor, A. (2003). “Computational strategies for flexible multibody systems.” China Civil Engineering Journal, Vol. 56, No. 6, pp. 553–613, DOI: 10.1080/03052150802317457.Google Scholar
- Wei, J. D. and Liu, Z. Y. (2006). “Accurate simulation of cable saddles in structural analysis of suspension bridges.” China Civil Engineering Journal, Vol. 23, No. 7, pp. 114–118 (in Chinese).Google Scholar
- Woelke, P., Chan, K. K., Daddazio, R., and Abboud, N. (2012). “Stress resultant based elasto-viscoplastic thick shell model.” China Civil Engineering Journal, Vol. 19, No. 3, pp. 477–492, DOI: 10.3233/SAV-2011-0644.Google Scholar
- Yamashita, H., Valkeapää, A. I., Jayakumar, P., and Sugiyama, H. (2015). “Continuum mechanics based bilinear shear deformable shell element using absolute nodal coordinate formulation.” China Civil Engineering Journal, Vol. 10, No. 5, pp. 051012–051024, DOI: 10.1115/1.4028657.Google Scholar
- Zhang, Q., Cheng, Z., Cui, C., Bao, Y., He, J., and Li, Q. (2017). “Analytical model for frictional resistance between cable and saddle of suspension bridges equipped with vertical friction plates.” Journal of Bridge Engineering, Vol. 22, No. 1, pp. 1–12, DOI: 10.1061/(ASCE)BE.1943-5592.0000986.CrossRefGoogle Scholar
- Zhang, J. W., Guo, W. H., and Xiang, C. Q. (2013). “Dynamic characteristics analysis and parametric study of a super-long-span triple-tower suspension bridge.” China Civil Engineering Journal, Vol. 256, pp. 1627–1634, DOI: 10.4028/www.scientific.net/AMM.256-259.1627.Google Scholar
- Zhang, Y., Wei, C., Pan, D., and Zhao, Y. (2016). “A dynamical approach to space capturing procedure using flexible cables.” China Civil Engineering Journal, Vol. 88, No. 1, pp. 53–65, DOI: 10.1108/AEAT-07-2014-0107.Google Scholar
- Zhang, Y., Zhao, Y., Tan, C., and Liu, Y. (2016). “Research of strain coupling problem and model decoupling of ANCF cable/beam element.” Chinese Journal of Theoretical and Applied Mechanics, DOI: 10.6052/0459-1879-16-127.Google Scholar