Structural modeling of parachute dynamics

The dynamic behavior of parachute systems is an extremely complex phenomeno n characterized by nonlinear, time-dependent coupling between the parachute and surrounding airflow, large shape changes in the parachute, and three-d imensional unconstrained motion of the parachute through the fluid medium. Because of these complexities, the design of parachutes has traditionally b een performed using a semiempirical approach. This approach to design is ti me consuming and expensive. The ability to perform computer simulations of parachute dynamics would significantly improve the design process and ultim ately reduce the cost of parachute system development. The finite element f ormulation for a structural model capable of simulating parachute dynamics is presented. Explicit expressions are given for structural mass and stiffn ess matrices and internal and external force vectors. Algorithms for soluti on of the nonlinear dynamic response are also given. The capabilities of th e structural model are demonstrated by three example problems. In these exa mples, the effect of the surrounding airflow is approximated by prescribing the canopy pressure and by applying cable and payload drag forces on the s tructural model. The examples demonstrate the ability to simulate three-dim ensional unconstrained dynamics beginning with an unstressed folded configu ration corresponding to the parachute cut pattern. The examples include sim ulations of the inflation, terminal descent, and control phases.