Catenary Solutions for Inextensible Cables: A Perturbation-Based High-Order Approximation

Cable structures are structurally efficient and architecturally elegant solutions for bearing and transferring loads across medium and large spans. The shape-finding problem related to the equilibrium configuration of suspended cables may present some algorithmic hurdles, related to the coexistence of analytical catenary solutions with nonlinear compatibility equations that need to be solved numerically. The catenary function describing the static equilibrium configuration for an inextensible cable suspended between displaceable supports is asymptotically expressed, using a proper perturbation method. The asymptotic configuration solution is described by an explicit polynomial function of the mechanical parameters and support displacements, automatically satisfying the compatibility condition. Fine approximation accuracy is achieved by extending the perturbation solution to high orders.