Nonlinear Analysis of Cable Structures with Geometric Constraints


  • Pierre Joli LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France
  • Naoufel Azouz LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France
  • Manel Ben Wezdou LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France
  • Jamel Neji Lamoed, University of Tunis El Manar, Tunis 1068, Tunisia



Cables, nonlinear modelling, general displacement control method, geometric constraints, elastic catenary, penalty method


The purpose of this paper is the modelling in large displacement of systems composed of a rigid platform suspended by flexible cables, as can be observed in lifting systems of a construction crane or in cable-driven parallel robots (CDPRs). A recent approach has been proposed in the literature to model the nonlinear behavior of a cable element based on three dimensional catenary elastic modelling and the general displacement control method (GDCM) as solver. In this paper, two modifications of this method are proposed to take into account the geometric constraints coupling the large displacements of the cable extremities. The first approach is to consider these constraints using penalty functions thus modifying the tangent stiffness matrix and the second method by adding external explicit elastic forces. These two methods are tested and compared by using numerical examples. The first method is numerically safer because it is not dependent on the poor numerical conditioning of the cable’stiffness matrix encountered when internal cable’s tension cannot balance the external forces.


Download data is not yet available.

Author Biographies

Pierre Joli, LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France

Pierre Joli Assistant professor at the Evry_Paris-Saclay University. His activities within the LMEE Laboratory cover several areas of non linear computational solid mechanics. He has published articles dealing with frictional contact and large deformation mechanical problems, particularly in the case of hyperelastic material. He is responsible for the IC2M Master at Evry Paris-Saclay University.

Naoufel Azouz, LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France

Naoufel Azouz Associate professor at the Evry_Paris-Saclay University. He obtained the PhD of PhD of the university Paris 6 in cooperation with the Atomic Center of Saclay, France in 1994. In 1995 he joined the university of Evry in France, where he is now teaching in the mechanical department. His research interests are structural dynamics and aerodynamics modeling of flying objects. His researches are done in the LMEE laboratory in Evry, France.

Manel Ben Wezdou, LMEE, UnivEvry, Université Paris-Saclay, 91025, Evry, France

Manel Ben Wezdou PhD student in joint supervision between the University of Evry_Paris-Saclay and the University of Tunis_El-Manar. Her field of research concerns the development of numerical algorithms for the static and dynamic modeling of heavy flexible cables.

Jamel Neji, Lamoed, University of Tunis El Manar, Tunis 1068, Tunisia

Jamel Neji Full professor in Civil Engineering at the National School of Engineers of Tunis. He has published papers on a wide range of disciplines, in particular (design of pavement structures; dynamic study of railway structures; cracking of materials; rigidity of composite materials; transport infrastructures). He is director of the Civil Engineering department at ENIT and head of the Materials, Optimization and Energy for Sustainability Laboratory (LAMOED).


F. BenAbdallah, N. Azouz, L. Beji and A. Abichou, “Modeling of a heavy lift airship carrying a payload by a cable driven parallel manipulator,” International Journal of Advanced Robotic Systems, 2019.

N. Azouz, M. Khamlia, F. B. Abdallah and F. Guesmi, “Modelling and design of an airship crane,” in ASME-IMECE Conference, Pittsburgh, USA, 2018.

H. Yuan, E. Courteille and D. Deblaise, “Static and Dynamic Stiffness Analyses of Cable-Driven Parallel Robots with non-negligible cable mass and elasticity,” Mechanism and Machine Theory, pp. 64–81, 2015.

S. Bouchard and C. M. Gosselin, “Kinematic sensitivity of a very large cable-driven parallel mechanism,” in ASME International Design Engineering Technical Conferences, 2006.

D. Q. Nguyen, M. Gouttefarde, O. Company and F. Pierrot, “On the Simplifications of Cable Model in Static Analysis of Large Dimensions Cable-Driven Parallel Robots,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, 2013.

R. Nicolas, G. Marc, K. Sébastien, B. Cédric and P. François, “Effects of non-negligible cable mass on the static behavior of large workspace cable-driven parallel mechanisms,” in IEEE International Conference on Robotics and Automation, Kobe, Japan, 2009.

M. Gouttefarde, J.-F. Collard, N. Riehl and C. Baradat, “Simplified Static Analysis of Large-Dimension Parallel Cable Driven Robots,” in IEEE International Conference on Robotics and Automation, Minnesota, USA, 14–18 May, 2012.

M. Irvine, Cable Structures, New York: dover publications, Inc, 1981.

H. Jayaraman and W. Knudson, “A Curved Element for the Analysis of Cable Structures,” Computers & Structures, vol. 14, no. 3–4, pp. 325–333, 1981.

H.-T. Thai and Seung-EockKim, “Nonlinear Static and Dynamic Analysis of Cable Structures,” Finite Element in Analysis and Design, vol. 47, pp. 237–246, 2011.

E. Coarita and L. Flores, “Nonlinear Analysis of Structures Cable-Truss,” International Journal of Engineering and Technology, pp. 160–169, 2015.

Z. Wu and J. Wei, “Nonlinear Analysis of Spatial Cable of Long-Span Cable-Stayed Bridge considering Rigid Connection,” KSCE Journal of Civil Engineering, pp. 2148–2157, 2019.

Y. B. YANG and J.-Y. TSAY, “Geometric Nonlinear Analysis of Cable Structures with a Two-node Cable Element by Generalized Displacement Control Method,” International Journal of Structural Stability and Dynamics, vol. 7, no. 4, pp. 571–588, 2007.

C. M. Hoffmann and R. Joan-Arinyo, Handbook of Computer Aided Geometric Design, 2002.

M. A. Torkamani and M. Sonmez, “Solution Techniques for Nonlinear Equilibrium Equations,” in 18th Analysis and Computation Specialty Conference, 2008.

Y.-B. Y. a. M.-S. Shieh, “Solution Method for Nonlinear Problems with Multiple Critical Points,” AIAA JOURNAL, vol. 28, no. 12, pp. 2110–2116, 1990.

S. Damir, L. Zeljan and B. Andjela, “Nonlinear static isogeometric analysis of cable structures,” Archive of Applied Mechanics, vol. 89, p. pages 713–729, 2019.

H.-T. Thai and S.-E. Kim, “Nonlinear static and dynamic analysis of cable structures,” Finite Elements in Analysis and Design, vol. 47, p. 237–246, 2011.

A. A. M. Salehi, A. Shooshtari, V. Esmaeili and N. R. Alireza, “Nonlinear analysis of cable structures under general loadings”, Finite Elements in Analysis and Design, vol. 73, pp. 11–19, 2013.

J.L. Batoz, G. Dhatt, “Incremental displacement algorithms for nonlinear problems”, International Journal for Numerical Methods in Engineering, vol. 14, pp. 1262–1267, 1979.



How to Cite

Joli, P. ., Azouz, N. ., Wezdou, M. B. ., & Neji, J. . (2023). Nonlinear Analysis of Cable Structures with Geometric Constraints. European Journal of Computational Mechanics, 31(04), 433–458.



Original Article

Most read articles by the same author(s)