Browse > Article
http://dx.doi.org/10.12989/sem.2022.82.2.205

Nonlinear finite element formulation for sliding cable structures considering frictional, thermal and pulley-dimension effects  

Yang, Menggang (School of Civil Engineering, Central South University)
Chen, Shizai (School of Civil Engineering, Central South University)
Hu, Shangtao (School of Civil Engineering, Central South University)
Publication Information
Structural Engineering and Mechanics / v.82, no.2, 2022 , pp. 205-224 More about this Journal
Abstract
This paper presents a refined finite element formulation for nonlinear static and dynamic analysis of sliding cable structures, overcoming the limitation of the existing approaches that neglect or approximate the friction, pulley dimension, temperature and geometric nonlinearity. A new family of elements with the same framework is proposed, consisting of the cable-pulley (CP) elements considering sliding friction, and the non-sliding cable-pulley (NSCP) elements considering static friction. Thereafter, the complete procedure of static and dynamic analysis using the proposed elements is developed, with the capability of accurately dealing with the friction at each pulley. Several examples are utilized to verify the validity and accuracy of the proposed elements and analysis strategy, and investigate the frictional, thermal and pulley-dimension effects as well. The numerical examples show that the results obtained in this work are in good accordance with the existing works when using the same approximations of friction, pulley dimension and temperature. By avoiding the approximations, the proposed formulation can be effectively adopted in predicting the more precise nonlinear responses of sliding cable structures.
Keywords
cable-pulley elements; cable structures; friction; nonlinear analysis; sliding; temperature;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Liu, H. and Chen, Z. (2012a), "Influence of cable sliding on the stability of suspen-dome with stacked arches structures", Adv. Steel Constr., 8(1), 54-70.
2 Liu, H. and Chen, Z. (2012b), "Structural behavior of the suspendome structures and the cable dome structures with sliding cable joints", Struct. Eng. Mech., 43(1), 53-70. https://doi.org/10.12989/sem.2012.43.1.053.   DOI
3 Matsumoto, Y., Nishioka, T., Shiojiri, H. and Matsuzaki, K. (1978), "Dynamic design of footbridges", IABSE Proceedings.
4 Yang, M., Chen, Z. and Hua, X. (2010), "A new two-node catenary cable element for the geometrically non-linear analysis of cable-supported structures", J. Mech. Eng. Sci., 224, 1173-1183. https://doi.org/10.1243/09544062JMES1816.   DOI
5 Wei, J.D. (2004), "Cable sliding at supports in cable structures", J. Southwest Jiaotong Univ. (English Ed.), 12(1), 56-60.
6 Wei, J.D. and Xu, W.G. (2005), "Cable-pulley element to analyze pulley sliding on cable", Chin. J. Theor. Appl. Mech., 37(3), 322-328.
7 Yang, Y.B. and Tsay, J.Y. (2007), "Geometric nonlinear analysis of cable structures with a two-node cable element by generalized displacement control method", Int. J. Struct. Stab. Dyn., 7(4), 571-588. https://doi.org/10.1142/S0219455407002435.   DOI
8 Yu, X.M., Chen, D.W. and Bai, Z.Z. (2018), "A new method for analysis of sliding cable structures in bridge engineering", J. Civil Eng., 22, 4483-4489. https://doi.org/10.1007/s12205-017-0151-7.   DOI
9 Zhou, B., Accorsi, M.L. and Leonard, J.W. (2004), "Finite element formulation for modeling sliding cable elements", Comput. Struct., 82(2-3), 271-280. https://doi.org/10.1016/j.compstruc.2003.08.006.   DOI
10 Yu, Y., Chen, Z. and Yan, R. (2019), "Finite element modeling of cable sliding and its effect on dynamic response of cable-supported truss", Front. Struct. Civil Eng., 13, 1227-1242. https://doi.org/10.1007/s11709-019-0551-5.   DOI
11 Cao, L., Liu, J., Zhang, X. and Chen, Y.F. (2019), "Numerical study on the walking load based on inverted-pendulum model", Struct. Eng. Mech., 71(3), 245-255. https://doi.org/10.12989/sem.2019.71.3.245.   DOI
12 Chopra, A.K. (2017), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice Hall, Inc., New Jersey.
13 Andreu, A., Gil, L. and Roca, P. (2006), "A new deformable catenary element for the analysis of cable net structures", Comput. Struct., 84, 1882-1890. https://doi.org/10.1016/j.compstruc.2006.08.021.   DOI
14 Rezaiee-Pajand, M., Esfehani, S.A.H. and Ehsanmanesh, H. (2021), "An efficient weighted residual time integration family", Int. J. Struct. Stab. Dyn., 21(08), 2150106. https://doi.org/10.1142/S0219455421501066.   DOI
15 Aufaure, M. (1993), "A finite element of cable passing through a pulley", Comput. Struct., 46(5), 807-812. https://doi.org/10.1016/0045-7949(93)90143-2.   DOI
16 Aufaure, M. (2000), "A three-node cable element ensuring the continuity of the horizontal tension; a clamp-cable element", Comput. Struct., 74, 243-251. https://doi.org/10.1016/S0045-7949(99)00015-2.   DOI
17 Bel Hadj Ali, N., Sychterz, A.C. and Smith, I.F.C. (2017), "A dynamic-relaxation formulation for analysis of cable structures with sliding-induced friction", Int. J. Solid. Struct., 126-127, 240-251. https://doi.org/10.1016/j.ijsolstr.2017.08.008.   DOI
18 Bruno, D. and Leonardi, A. (1999), "Nonlinear structural models in cableway transport systems", Simul. Pract. Theory, 7(3), 207-218. https://doi.org/10.1016/S0928-4869(98)00024-X.   DOI
19 Cai, J.G., Lim, J., Feng, J., Xu, Y.X. and Wang, K. (2012), "Elastic catenary cable element considering frictional slip effect", Sci. Chin. Tech. Sci., 55(6), 1489-1495. https://doi.org/10.1007/s11431-012-4833-6.   DOI
20 Cao, H., Zhou, Y., Chen, Z. and Wahab, M.A. (2017), "Form-finding analysis of suspension bridges using an explicit iterative approach", Struct. Eng. Mech., 62(1), 85-95. https://doi.org/10.12989/sem.2017.62.1.085.   DOI
21 Chen, Z.H., Wu, Y.J., Yin, Y. and Shan, C. (2010), "Formulation and application of multi-node sliding cable element for the analysis of suspen-dome structures", Finite. Elem. Anal. Des., 46(9), 743-750. https://doi.org/10.1016/j.finel.2010.04.003.   DOI
22 Chen, Z.Q. and Agar, T.J.A. (1993), "Geometric nonlinear analysis of flexible spatial beam structures", Comput. Struct., 49(6), 1083-1094. https://doi.org/10.1016/0045-7949(93)90019-A.   DOI
23 Chung, K.S., Cho, J., Park, J.I. and Chang, S. (2011), "Three-dimensional elastic catenary cable element considering sliding effect", J. Eng. Mech., 137, 276-283. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000225.   DOI
24 McDonald, B.M. and Peyrot, A.H. (1988), "Analysis of cables suspended in sheaves", J. Struct. Eng., 114(3), 693-706. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:3(693).   DOI
25 Chen, S., Yang, M., Meng, D. and Hu, S. (2020), "Theoretical solution for multi-span continuous cable structures considering sliding", Int. J. Solid. Struct., 207, 42-54. https://doi.org/10.1016/j.ijsolstr.2020.09.024.   DOI
26 Ju, F. and Choo, Y.S. (2005), "Super element approach to cable passing through multiple pulleys", Int. J. Solid. Struct., 42(11), 3533-3547. https://doi.org/10.1016/j.ijsolstr.2004.10.014.   DOI
27 Pauletti, R.M.O. and Pimenta, P.M. (1995), "Formulacao de um elemento finito de cabo incorporando o efeito do atrito (elemento de cabo escorregando)", Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria, 11, 565-576.
28 Coulibaly, J.B., Chanut, M.A., Lambert, S. and Nicot, F. (2018), "Sliding cable modeling: An attempt at a unified formulation", Int. J. Solid. Struct., 130-131, 1-10. https://doi.org/10.1016/j.ijsolstr.2017.10.025.   DOI
29 Crusells-Girona, M., Filippou, F.C. and Taylor, R.L. (2017), "A mixed formulation for nonlinear analysis of cable structures", Comput. Struct., 186, 50-61. https://doi.org/10.1016/j.compstruc.2017.03.011.   DOI
30 Ali, H.M. and Abdel-Ghaffar, A.M. (1995), "Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings", Comput. Struct., 54(3), 461-492. https://doi.org/10.1016/0045-7949(94)00353-5.   DOI
31 Rezaiee-Pajand, M. and Hashemian, M. (2016), "Time integration method based on discrete transfer function", Int. J. Struct. Stab. Dyn., 16, 1550009. https://doi.org/10.1142/S0219455415500091.   DOI
32 Rezaiee-Pajand, M. and Karimi-Rad, M. (2016), "A new explicit time integration scheme for nonlinear dynamic analysis", Int. J. Struct. Stab. Dyn., 16, 155005. https://doi.org/10.1142/S0219455415500546.   DOI
33 Rezaiee-Pajand, M., Mokhtari, M. and Masoodi, A.R. (2018), "A novel cable element for nonlinear thermo-elastic analysis", Eng. Struct., 167, 431-444. https://doi.org/10.1016/j.engstruct.2018.04.022.   DOI
34 Gao, Q., Yang, M.G. and Qiao, J.D. (2017), "A multi-parameter optimization technique for prestressed concrete cable-stayed bridges considering prestress in girder", Struct. Eng. Mech., 64(5), 567-577. https://doi.org/10.12989/sem.2017.64.5.567.   DOI
35 Guo, Y.L. and Cui, X.Q. (2003), "An unified analytical method for gliding cable structures-frozen-heated method", Eng. Mech., 20(4), 156-160.   DOI
36 Hincz, K. (2009), "Nonlinear analysis of cable net structures suspended from arches with block and tackle suspension system, taking into account the friction of the pulley", Int. J. Space Struct., 24(3), 143-152. https://doi.org/10.1260/026635109789867643.   DOI
37 Rezaiee-Pajand, M. and Mohammadi-khatami, M. (2021), "Nonlinear analysis of cable structures using the dynamic relaxation method", Front. Struct. Civil Eng., 15(1), 253-274. https://doi.org/10.1007/s11709-020-0639-y.   DOI
38 Rezaiee-Pajand, M., Esfehani, S.A.H. and Karimi-Rad, M. (2016), "Highly accurate family of time integration method", Struct. Eng. Mech., 67(6), 603-616. https://doi.org/10.12989/sem.2016.67.6.603.   DOI
39 Salehi Ahmad Abad, M., Shooshtari, A., Esmaeili, V. and Naghavi Riabi, A. (2013), "Nonlinear analysis of cable structures under general loadings", Finite Elem. Anal. Des., 73, 11-19. https://doi.org/10.1016/j.finel.2013.05.002.   DOI
40 Impollonia, N., Ricciardi, G. and Saitta, F. (2011), "Statics of elastic cables under 3D point forces", Int. J. Solid. Struct., 48, 1268-1276. https://doi.org/10.1016/j.ijsolstr.2011.01.007.   DOI
41 Irvine, H.M. (1992), Cable Structures, Dover Publications, New York.
42 Jayaraman, H.B. and Knudson, W.C. (1981), "A curved element for the analysis of cable structures", Comput. Struct., 14(3-4), 325-333. https://doi.org/10.1016/0045-7949(81)90016-X.   DOI
43 Liang, X. and Mosalam, K.M. (2016), "Lyapunov stability and accuracy of direct integration algorithms applied to nonlinear dynamic problems", J. Eng. Mech., 142(5), 04016022. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001073.   DOI
44 Such, M., Jimenez-Octavio J.R. and Carnicero, A. (2009), "An approach based on the catenary equation to deal with static analysis of three dimensional cable structures", Eng. Struct., 31, 2162-2170. https://doi.org/10.1016/j.engstruct.2009.03.018.   DOI
45 Thai, H.T. and Kim, S.E. (2011), "Nonlinear static and dynamic analysis of cable structures", Finite Elem. Anal. Des., 47, 237-246. https://doi.org/10.1016/j.finel.2010.10.005.   DOI
46 Vu, T., Lee, H. and Bui, Q. (2012), "Nonlinear analysis of cable-supported structures with a spatial catenary cable element", Struct. Eng. Mech., 43(5), 583-605. https://doi.org/10.12989/sem.2012.43.5.583.   DOI
47 Kan, Z., Peng, H. and Chen, B. (2019), "A simple linear complementarity approach for sliding cable modeling considering friction", Mech. Syst. Signal Pr., 130, 293-314. https://doi.org/10.1016/j.ymssp.2019.05.012.   DOI
48 Kan, Z., Peng, H., Chen, B. and Zhong, W. (2018), "A sliding cable element of multibody dynamics with application to nonlinear dynamic deployment analysis of clustered tensegrity", Int. J. Solid. Struct., 130, 61-79. https://doi.org/10.1016/j.ijsolstr.2017.10.012.   DOI
49 Lee, K.H., Choo, Y.S. and Ju, F. (2003), "Finite element modelling of frictional slip in heavy lift sling systems", Comput. Struct., 81, 2673-2690. https://doi.org/10.1016/S0045-7949(03)00333-X.   DOI