A variational approach for three-dimensional model of extensible marine cables with specified top tension

Abstract

This paper presents a variational model formulation that can be used for analyzing the three-dimensional steady-state behavior of an extensible marine cable. The virtual work-energy functional, which involves virtual strain energy due to a cable stretching, and virtual works done by the gravitational, inertial and external drag forces, is formulated. Euler-Lagrange's equations, obtained by considering the first variation of the functional, are identical to those obtained by equilibrating forces on a cable infinitesimal segment. Two mathematical simulations, namely, the finite element method and the shooting-optimization technique, are employed to solve and evaluate the problems. The numerical investigations are carried out for the case of a specified end tension, whereas the specified cable unstrained length case can be applied in the algorithm procedure. The validity of the present model and the influence of various geometrical parameters on the cable equilibrium configuration are demonstrated. The effects of cable extensibility and the omnidirectionality of current actions are presented and discussed

Tension Analysis of Submarine Cables during Laying Operations

“…According to the vertical coordinate, at numbered i-th point, the difference iterative equations are selected as follows. Provided that coordinate Z ranges from 0 to H, the iterative equations are: (13) Then, (13) can be calculated through numerically by the Simpson method. In the calculation, the submarine cable is divided into N segments.…”

“…The mooring cables are simulated by hybrid beam elements, while the seabed is simulated by different soil constitutive models. Chucheepsakul et al [13] presented a variational model to analyze the three-dimensional steady state behavior of an extensible marine cable. Meanwhile, the finite element method and the shooting-optimization technique are employed to solve and evaluate the problem.…”

Geometrical nonlinearities on the static analysis of highly flexible steel cable-stayed bridges

“…In the last decades, several finite elements have been proposed for cable modelling (see e.g. [4][5][6][7][8][9][10][11]), though not specifically for the analysis of cable-stayed bridges. Nevertheless, some such elements have been extensively used in these structures (e.g.…”

“…Vertical and horizontal components of an infinitesimal portion of an elastic catenary. 6. Implicit plotting of F h vs. L 0 .…”

Semiclosed-form solution for static nonlinear analysis of extensible cables

“…Therefore, there has been a number of modern analytical and semi-analytical studies as well [30,[43][44][45][46][47][48][49]. This paper attempts to present a technique which is mostly analytical but employs a limited amount of numerical techniques to evaluate a portion of the static analysis problem for an extensible cable.…”