Enhanced membrane elements for simulation of parachute dynamics

Parachute deployment problems are very complex. It is time-dependent, geometrically nonlinear. In addition, membranes are ‘tension only’ structures. It may undergo large scale dynamic wrinkling during deployment. ^ This thesis work develops robust finite element methods to simulate the nonlinear dynamic behavior of parachute deployment. Two classes of new finite elements are addressed: ^ A new class of elements is developed to facilitate opening a parachute model and stabilize the numerical solution during initial deployment. Two types of elements, called kink and fold elements, are developed that provide local bending stiffness and damping at predefined cable points and membrane edges, respectively. The pseudo-bending stiffness will facilitate the opening of models from a folded configuration. The damping will stabilize the solution without affecting the global motion. The ability to model real bending elements using a distribution of these discrete bending elements is also investigated. ^ A new curved anisotropic elastic membrane element undergoing large deformation with wrinkling is developed to predict the wrinkling phenomena that may occur in parachutes during deployment. Concise continuum level governing equations are derived in which singularities are eliminated. A simple and efficient algorithm which is guaranteed to converge is established to find the real strain and stress of the wrinkled membrane for elastic materials that obey the generalized Hooke\u27s law. The continuum theory is implemented into a finite element code. Explicit formulas for the internal force and tangent stiffness matrix are derived. Numerical examples are presented that demonstrate the effectiveness of the new theory for predicting wrinkling in membranes undergoing large deformation. ^ The two classes of new element are validated by numerical examples. Numerical results shows that the localized damping effect from the special elements was seen to be the principal contribution to that improvement. It was possible with the new elements to eliminate local high-frequency oscillations normal to the middle surfaces of the parachutes and to approach realistic terminal velocities using much larger time steps in the simulations. Numerical examples also show that the new membrane element with wrinkling can correctly and efficiently predict wrinkling in membranes undergoing large deformation.