A Non-Incremental Nonlinear Finite Element Solution for Cable Problems

Author:

Sugiyama Hiroyuki1,Mikkola Aki M.2,Shabana Ahmed A.3

Affiliation:

1. Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60607

2. Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finland

3. Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607

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 finite element absolute nodal coordinate formulation that guarantees the continuity of all 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 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. In particular it is 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 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 deformations. 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.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Reference30 articles.

1. Rohrs, J. H. , 1851, “On the Oscillations of a Suspension Cable,” Trans. Cambridge Philos. Soc., 9, pp. 379–398.

2. Routh, E. J., 1955, Advanced Rigid Dynamics, Dover.

3. Saxon, D. S., and Cahn, A. S., 1953, “Modes of Vibration of a Suspended Chain,” Q. J. Mech. Appl. Math., 6, pp. 273–285.

4. Irvine, H. M., and Caughey, T. K., 1974, “The Linear Theory of Free Vibration of a Suspended Cable,” Proc. R. Soc. London, Ser. A, 341, pp. 299–315.

5. Irvine, H. M., 1981, Cable Structures, MIT Press.

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