Nonlinear Analysis of Cable Structures with Geometric Constraints

The purpose of this paper is the modelling in large displacement of systems composed of a rigid platform suspended by flexible cables, as can be observed in lifting systems of a construction crane or in cable-driven parallel robots (CDPRs). A recent approach has been proposed in the literature to model the nonlinear behavior of a cable element based on three dimensional catenary elastic modelling and the general displacement control method (GDCM) as solver. In this paper, two modifications of this method are proposed to take into account the geometric constraints coupling the large displacements of the cable extremities. The first approach is to consider these constraints using penalty functions thus modifying the tangent stiffness matrix and the second method by adding external explicit elastic forces. These two methods are tested and compared by using numerical examples. The first method is numerically safer because it is not dependent on the poor numerical conditioning of the cable’stiffness matrix encountered when internal cable’s tension cannot balance the external forces.