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M.T.A. Chaudhary, "Semiclosed-Form Solution for Static Nonlinear Analysis of Extensible Cables," Mech. Solids. 49 (4), 468-476 (2014)
Year 2014 Volume 49 Number 4 Pages 468-476
DOI 10.3103/S0025654414040128
Title Semiclosed-Form Solution for Static Nonlinear Analysis of Extensible Cables
Author(s) M.T.A. Chaudhary (Al Imam Mohammad Ibn Saud Islamic University, College of Engineering, P.O. Box 5701, Riyadh, Saudi Arabia, mtariqch@hotmail.com)
Abstract The analysis of a cable deforming under statically applied body forces leads to a series of differential equations that are inherently nonlinear due to coupling of geometry and loading. These equations have been solved by nonlinear finite element technique, finite difference formulation, or a two-step shooting method. However, a semiclosed-form solution is presented herein in which the governing differential equations are integrated to yield exact expressions for the unknown cable forces and the parameters defining the geometry of the loaded cable. The formulation presented herein is capable of taking care of the large sag and deformation in the cable without employing any numerical solution procedure.
Keywords extensible cable, static nonlinear analysis, large deformation, semiclosed-form solution
References
1.  J. M. Bernoulli, "Solutions to the Problem of the Catenary, or Funicular Curve," Acta Eruditorum, 1691 [FIDELIO Magazine (Engl. Transl.) X (1), 2001].
2.  H. M. Irvine, Cable Structures (The MIT Press, Cambridge, 1981).
3.  P. Broughton and P. Ndumbaro, The Analysis of Cable and Catenary Structures (Thomas Telford, London, 1994).
4.  H. M. Irvine, "Studies in the Static and Dynamic Analysis of Single Cable Systems," Report No. DYNL 108 (California Institute of Technology, Pasadena, 1974).
5.  J. F. Fleming, "Nonlinear Static Analysis of Cable-Stayed Structures," Comput. Struct. 10 (4), 621-635 (1979).
6.  A. S. Nazmy and A. M. Abdel-Ghaffar, Three-Dimensional Nonlinear Static Analysis of Cable-Stayed Bridges," Comput. Struct. 34 (2), 257-271 (1990).
7.  R. Karoumi, "Some Modeling Aspects in the Nonlinear Finite Element Analysis of Cable Supported Bridges," Comput. Struct. 71 (4), 397-412 (1999).
8.  A. M. S. Freire, J. H. O. Negrão, and A. V. Lopes, Geometrical Nonlinearities on the Static Analysis of Highly Flexible Steel Cable-Stayed Bridges, Comput. Struct. 84 (31-32), 2128-2140 (2006).
9.  I. Freeman, A General Form of the Suspension Bridge Catenary," Bull. Am. Math. Soc. 31 (8), 425-429 (1925).
10.  A. G. Pugsley, The Theory of Suspension Bridges (Edward Arnold, London, 1957).
11.  H. M. Irvine and T. K. Caughey, "The Linear Theory of Free Vibrations of a Suspended Cable," Proc. Roy. Soc. London. Ser. A. 341 (1626), 299-315 (1974).
12.  H. M. Irvine, "Statics of Suspended Cables," J. Engng Mech. Div. 101 (3), 187-205 (1975).
13.  D. H. Tung and R. J. Kudder, "Analysis of Cables as Equivalent Two-Force Members," Engng J. AISC. 5 (1), 12-19 (1968).
14.  D. A. Levinson and T. R. Kane, "A Usable Solution of the Hanging Cable Problem," Comput. Struct. 46 (5), 821-844 (1993).
15.  H. Ozdemir, "A Finite Element Approach for Cable Problems," Int. J. Solids Struct. 15 (5), 427-437 (1979).
16.  H. Jayaraman and W. Knudson, "A Curved Element for the Analysis of Cable Structures," Comput. Struct. 14 (3-4), 325-333 (1981).
17.  I. Fried, "Large Deformation Static and Dynamic Finite Element Analysis of Extensible Cables," Comput. Struct. 15 (3), 315-319 (1982).
18.  P. D. Gosling and E. A. Korban, "A Bendable Finite Element for the Analysis of Flexible Cable Structures," Finite Elem. Anal. Des. 38 (1), 45-63 (2001).
19.  C. Wang, R. Wang, S. Dong, and R. Qian, "A New Catenary Cable Element," Int. J. Space Struct. 18 (4), 269-275 (2003).
20.  Y. B. Yang and J. Y. Tsay, "Geometric Nonlinear Analysis of Cable Structures with a Two-Node Cable Element by Generalized Displacement Control Method," Int. J. Struct. Stabil. Dyn. 7 (4), 571-588 (2007).
21.  W. X. Ren, M. G. Huang, and W. H. Hu, "A Parabolic Cable Element for Static Analysis of Cable Structures," Engng Comput. 25 (4), 366-384 (2008).
22.  H. Thai and S. Kim, "Nonlinear Static and Dynamic Analysis of Cable Structures," Finite Elem. Anal. Des. 47 (3), 237-246 (2011).
23.  C. M. Wang, H. F. Cheong, and S. Chucheepsakul, "Static Analysis of Marine Cables via Shooting-Optimization Technique," J. Waterways, Port, Coastal, Ocean Engng 119, 450-457 (1993).
24.  A. A. Tjavaras, Q. Zhu, Y. Liu, et al. "The Mechanics of Highly Extensible Cables," J. Sound Vibrat. 213 (4), 709-737 (1998).
25.  A. B. Mehrabi and H. Tabatabai, "Unified Finite Difference Formulation for Free Vibration of Cables," J. Struct. Engng 124 (11), 1313-1322 (1998).
26.  C. Vallabhan, "Two-Dimensional Nonlinear Analysis of Long Cables," J. Engng Mech. 134 (8), 694-697 (2008).
27.  N. Bouaanani and M. Ighouba, "A Novel Scheme for Large Deflection Analysis of Suspended Cables Made of Linear or Nonlinear Elastic Materials," J. Adv. Engng Software. 42 (12), 1009-1019 (2011).
28.  G. R. Buchanan, "Two-Dimensional Cable Analysis," J. Struct. Div. 96 (7), 1581-1587 (1970).
29.  A. Valiente, "Symmetric Catenary of a Uniform Elastic Cable of Neo-Hookean Material," J. Engng Mech. 132 (7), 747-753 (2006).
30.  J. Pietrzak, "Matrix Formulation of Static Analysis of Cable Structures," Comput. Struct. 9 (1), 39-42 (1978).
31.  G. R. Monforton and N. M. El-Hakim, "Analysis of Truss-Cable Structures," Comput. Struct. 11 (4), 327-335 (1980).
32.  H. A. F. A. Santos and C. I. Almeida Paulo, "On a Pure Complementary Energy Principle and a Force-Based Finite Element Formulation for Non-Linear Elastic Cables," Int. J. Nonlin. Mech. 46 (2), 395-406 (2011).
33.  F. Baron and M. S. Venkatesan, "Nonlinear Analysis of Cable and Truss Structures," J. Struct. Div. ASCE 97 (2), 679-710 (1971).
34.  W. J. Lewis, M. S. Jones, and K. R. Rushton, "Dynamic Relaxation Analysis of the Nonlinear Static Response of Pretenseoned Cable Roofs," Comput. Struct. 18 (6), 989-997 (1984).
35.  Y. Kanno, M. Ohsaki, and J. Ito, "Large-Deformation and Friction Analysis of Non-Linear Elastic Cable Networks by Second-Order Cone Programming," Int. J. Numer. Meth. Engng 55 (9), 1079-1114 (2002).
36.  D. S. Saxon and A. S. Cahn, "Modes of Vibration of a Suspended Chain," Quart. J. Mech. Appl. Math. 6 (3), 273-285 (1953).
37.  R. F. Dominguez and C. E. Smith, "Dynamic Analysis of Cable Systems," J. Struct. Div. 92 (8), 1817-1834 (1972).
38.  A. Bliek, Dynamic Analysis of Single Span Cables, PhD Thesis (MIT, Cambridge, 1984).
39.  S. P. Cheng and N. C. Perkins "Closed-Form Vibration Analysis of Sagged Cable/Mass Suspensions," J. Appl. Mech. 59 (4), 923-928 (1992).
40.  S. Mesarovic and D. A. Gasparini, "Dynamic Behavior of Nonlinear Cable System. I & II," J. Engng Mech. 118 (5), 890-920 (1992).
41.  J. C. Russell and T. J. Lardner, "Experimental Determination of Frequencies and Tension for Elastic Cables," J. Engng Mech. 124 (10), 1067-1072 (1998).
42.  K. Y. Volokh, O. Vilnay, and I. Averbuh, "Dynamics of Cable Structures," J. Engng Mech. 129 (2), 175-180 (2003).
43.  N. Impollonia, G. Ricciardi, and F. Saitta, "Statics of Elastic Cables under 3D Point Forces," Int. J. Solids Struct. 48 (9), 1268-1276 (2011).
44.  W. T. O'Brien "General Solution of Suspended Cable System," J. Struct. Div. ASCE 94, 1-26 (1967).
45.  H. M. Irvine and G. B. Sinclair, "The Suspended Elastic Cable under the Action of Concentrated Vertical Loads," Int. J. Solids Struct. 12 (4), 309-317 (1976).
46.  J. V. Huddleston, "Computer Analysis of Extensible Cables," J. Engng Mech. Div. ASCE 107 (EM1), 27-37 (1981).
47.  G. B. Sinclair and S. B. Hodder "Exact Solutions for Elastic Cable Systems," Int. J. Solids Struct. 17 (9), 845-854 (1981).
48.  S. I. Sagatun "The Elastic Cable under the Action of Concentrated and Distributed Forces," J. Offshore Mech. Arctic Engng 123 (1), 43-45 (2001).
49.  S. Chucheepsakul, N. Srinil, and P. Petchpeart, "A Variational Approach for Three Dimensional Model of Extensible Marine Cables with Specified Top Tension," Appl. Math. Mod. 27 (10), 781-803 (2003).
50.  J. D. Hoffman, Numerical Methods for Engineers and Scientists (McGraw Hill Inc., New York, 1992).
Received 21 November 2012
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