Nonlinear Dynamics of Curved Cable Elements

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Abstract
A finite element analog to the dynamic response of nonlinear cables has been developed which employs straight cable elements to model the curved geometry of the cable system. Temporal as well as spatial variations in cable properties and stress were admitted. Thus, large deflections and rotations could be considered. The purpose of this note is to present the extension of the finite element analog to the case in which strongly-curved elements are used to model the cable system. Straight cable elements are inadequate for strongly-curved cables, in that a large number of straight elements are required to approximate the cable. Furthermore, unless numerous small elements are used, the existence of nodal discontinuities inherent in the straight element assumption leads to spurious results because of the membrane nature of the real problem. Therefore, a curved element is presented for which the continuity of the slope across the nodal points is enforced using direction cosine approximations. A comparison of curved and straight element results demonstrate that more accurate answers are obtained with fewer curved elements.

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