Object-oriented finite-element dynamic simulation of geometrically nonlinear space structures

The dynamics of space structures pose a unique combination of simulation challenges. They involve small strains but large rigid-body and strain-producing deformations, local and global instabilities, and often closely spaced equilibria. They are also strongly dependent on the behavior of various joints and deployment apparati, usually modeled as kinematic constraints. To be appropriate for simulating the geometrically nonlinear dynamics of space structures, finite element formulations for constraints, rods, cables, etc. must be geometrically exact, i.e., they must account correctly for the non-vectoral nature of finite rotations.This work reviews the theoretical development of existing geometrically exact formulations for rods, cables and constraints, corrects a few errors and omissions of the original publications, and derives a collection of nonlinear constraint formulations. It also employs analytical and numerical means in investigating the properties of numerically integrated, total-Lagrangian, CAll numerical investigations discussed in this work were carried out by means of a newly developed object-oriented nonlinear dynamics analysis platform (ONDAP). ONDAP's significance, in the context of many recent investigations of object-oriented finite element analysis, lies in its shallow, fine-grained class hierarchy and relative lack of simplifying assumptions, both motivated by the complexities of the target problem and of the numerical tools necessary for its solution. The discussion of ONDAP focuses on issues of wider relevance than the program itself, i.e., on its motivation, organization and conceptual underpinnings. Brief descriptions of ONDAP's implementation are provided where necessary.To assess the performance of geometrically exact formulations in simulating nonlinear dynamics of space structures, the stowage of a cable-controlled, hingeless, recoilable mast is modeled. This medium-sized problem with hundreds of structural elements and nodes, exhibits bifurcations and limit points, large rigid-body and intra-element deformations, bad numerical conditioning, closely spaced equilibria, and significant sensitivity to initial conditions. Good qualitative results are obtained using a single low-order finite element per structural element with a time step 0.5% of the fundamental period, and marked accuracy improvements are observed with discretization refinement.