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# A Non-Incremental Nonlinear Finite Element Solution for Cable Problems

[+] Author Affiliations
Hiroyuki Sugiyama, Ahmed A. Shabana

University of Illinois at Chicago, Chicago, IL

Aki M. Mikkola

Lappeenranta University of Technology, Lappeenranta, Finland

Paper No. DETC2003/VIB-48321, pp. 171-181; 11 pages
doi:10.1115/DETC2003/VIB-48321
From:
• ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
• Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C
• Chicago, Illinois, USA, September 2–6, 2003
• Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
• ISBN: 0-7918-3703-3 | eISBN: 0-7918-3698-3

## abstract

In this investigation, a nonlinear finite element method for the large deformation and rotation of cable problems is presented. This method is based on the finite element absolute nodal coordinate formulation that guarantees the continuity of all the displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal coordinate formulation are obtained in this investigation using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite element coordinate system. The results obtained using the absolute nodal coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite element formulation in the nonlinear analysis of cables that experience large rotations and large deformations. It is also shown that the use of perturbation methods to linearize the finite element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.

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