Nonlinear Analysis of Cable Structures with Geometric Constraints

Authors

  • 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

DOI:

https://doi.org/10.13052/ejcm2642-2085.3141

Keywords:

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

Abstract

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.

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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).

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Published

2023-02-06

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. https://doi.org/10.13052/ejcm2642-2085.3141

Issue

2022: Vol 31 Iss 4

Section

Original Article

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