Semi-analytical solution for static and quasi-static analysis of an inextensible cable

Abstract

The static and quasi-static analysis of cable structure and cable-driven systems is of significant interest to the researchers. In this paper, a semi-analytical solution for static equilibrium analysis of an inextensible cable is developed to know its initial configuration and tension. The analytical expression for the static equilibrium configuration of a cable, fixed at the two ends is generally available in the literature in terms of unknown reactions at the boundary nodes. Conventionally, researchers use numerical methods to solve for those unknown reactions at the boundary nodes, where a solution is sensitive to the initial guess. The proposed semi-analytical solution avoids such difficulty faced by an analyst or a designer of cable systems. The results obtained here were validated with a numerical solution for the static profile and cable tension. For the quasi-static analysis, these numerical methods are not suitable to compute the cable tension and its equilibrium profile due to the dependency of the solution on the initial guess and computation cost. To illustrate the need for a semi-analytical solution, the design problem for a cable support system and quasi-static analysis of an underwater tether connected between parent ship and a remotely operated vehicle (ROV) are presented. For the quasi-static analysis of the underwater tether, the proposed results are compared with those using the Newton-Raphson method in terms of computational cost and accuracy. In addition, guidelines are provided in this paper to choose an initial guess for the numerical approach so that a solution would be converged much faster.