A numerical approach for calculating the static and dynamic response of general three-dimensional cable structures totally immersed in a moving fluid is presented. The finite element method is used to model the combined nonlinear effects of large displacements, velocity-squared drag loading, and nonlinear materials. Results obtained using incremental/iterative solution techniques are discussed. Advantages of this approach are seen in its generality and in the ability to treat the various combinations of nonlinear effects in a consistent and direct manner.


The behavior of underwater structures composed primarily of' long, flexible members is a highly complex phenomenon. Typical of this class of structures are towed bodies, underwater suspension systems, deep water moors and retrieval systems. The primary structural component of such systems has a span-to-diameter ratio sufficiently large that bending effects are negligible. The typical structural member is a synthetic or wire rope, a pipe or some composite construction. Such a flexible member is referred to herein simply as a cable. Various discrete bodies such as buoys, anchors and instrument packages may also be involved. Deceptively simple in construction, these systems present many problems to the structural analyst.

In this paper it is assumed that the structure is totally immersed in the fluid. Interactions of the structure with various surface phenomena are generally ignored with two exceptions. First, it is assumed that a portion of the system may be attached to a surface vessel and that the motion of the attachment point is known, a priori. Second, the effects of surface buoys on a calm sea are approximated by constraining the attachment point to remain on the surface until the resultant load is sufficient to submerge the buoy. The hydrodynamic and structural responses are assumed to be uncoupled, i.e., the general pattern and character of the fluid motion are assumed to be essentially undisturbed by the presence of the structure. The interaction between fluid and structure is then treated by drag loading (dependent on the square of the relative velocity) and an increase of mass (virtual mass effect).

The major nonlinearities associated with such a structure are due to the drag loading and the fact that flexible structures resist loading through a significant change in shape. The latter phenomenon is known as a geometric nonlinearity and it is characterized by a nonlinear strain-displacement relationship. Additional nonlinearities may be introduced through the use of cable materials which have a nonlinear stress-strain relationship or by a member which cannot support compression. Finally, a type of nonlinearity is introduced when surface and bottom limits are imposed. Various aspects of the cable response problem have been investigated by numerous researchers. No attempt will be made to give an exhaustive review, however, some classification of the approaches used will aid in the understanding of the present method. The governing partial differential equations for a representative cable segment are relatively easy to derive but the development of a general closed form solution has eluded researchers because the equations are highly nonlinear.

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