Finite element formulation for modeling sliding cable elements

“Sliding cable elements” are developed to solve the general problem of constraining a string of cable elements to continuously pass through a prescribed moving node. These elements can be used for a wide variety of applications and in the current work are used to model various features in parachute systems. The principle of virtual work and total Lagrange formulation are used to derive the element internal force vector, tangent stiffness matrix, and time-dependent mass matrix and body forces. The element equations are implemented in a geometrically nonlinear, transient implicit finite element program. A searching algorithm is developed to track the relative movement of the elements, which is performed each iteration prior to formulation of the element equations. Two problems with analytical solutions are performed to validate the mechanical behavior of the new element and the searching algorithm. Several examples are presented where the sliding cable elements are used in parachute systems.