Unilateral contact problems for cables: Fid-Bau Portal

Unilateral contact problems for cables

Binda, Luigia / Contro, Roberto

Abstract A cable (such as in a submarine energy-transmission line) is supposed to be subjected to given transversal loads and a given tension force, in the vicinity of a frictionless rigid ground of known profile. The search for its equilibrium configuration is a contact (unilateral support) problem of a special kind. The problem is studied here with reference to a finite difference discretization of the system, under the small deformation hypothesis. On this basis its formulation becomes a linear complementarity problem or, alternatively, a quadratic, strictly convex program. Extremum properties of the solution are established and interpreted in mechanical terms. A general monotonicity property of the equilibrium configuration under proportional loading is pointed out; precisely, it is proved that, despite the nonlinearity of the system, whatever the load distribution, as the load factor increases, in any point of the cable the possible contact reaction and the vertical distance from the obstacle will never decrease. Among the mathematical programming algorithms presently available, Cryer's systematic overrelaxation is found to be efficient for the numerical solution of large-size problems of the type in question. Some numerical experience is presented.