Structural modeling of parachute dynamics

The dynamic behavior of parachute systems is an extremely complex phenomenon characterized by nonlinear, time-dependent coupling between the parachute and surrounding airflow, large shape changes in the parachute, and three-dimensional unconstrained motion of the parachute through the fluid medium. Because of these complexities, the design of parachutes has traditionally been performed using a semiempirical approach. This approach to design is time consuming and expensive. The ability to perform computer simulations of parachute dynamics would significantly improve the design process and ultimately reduce the cost of parachute system development. The finite element formulation for a structural model capable of simulating parachute dynamics is presented. Explicit expressions are given for structural mass and stiffness matrices and internal and external force vectors. Algorithms for solution of the nonlinear dynamic response are also given. The capabilities of the structural model are demonstrated by three example problems. In these examples, the effect of the surrounding airflow is approximated by prescribing the canopy pressure and by applying cable and payload drag forces on the structural model. The examples demonstrate the ability to simulate three-dimensional unconstrained dynamics beginning with an unstressed folded configuration corresponding to the parachute cut pattern. The examples include simulations of the inflation, terminal descent, and control phases.