Geometrically exact modeling and nonlinear mechanics of highly flexible structures

Large space structures must be designed to be stowed during launch and deployed once on orbit because the cargo space of a launch vehicle is always limited. The considerations about payload requirement, weight constraint, and ease of storage during launching make highly flexible deployable structures the main choice for NASA to build large space structures. However, highly flexible structures are usually made of thin-walled beams and shells and have small material dampings, and hence small loads may cause large deformations and maneuver may lead to destructive large vibrations. When a structure undergoes large displacements, various secondary effects may become significant, and its statics and dynamics may involve many nonlinear phenomena. Hence, nonlinear structural theories that can model large displacements and rotations are needed. Consequently, it is important to derive nonlinear structural theories that can model the large deformations of highly flexible structures and to analyze the static and dynamic behavior of such structures in order to design such structures without full scale testing.; In this thesis, we derive geometrically exact beam and shell theories, analyze large static deformations of beams and shells, and perform numerical and experimental studies on the nonlinear dynamics of highly flexible beams. A multiple shooting method and a nonlinear finite element method are used in numerical analyses, and a scanning laser vibrometer is used to perform dynamic testing to verify numerical results and to validate the derived total-Lagrangian beam and shell elements. All numerical and experimental results show that the derived nonlinear beam and shell theories are able to model very large displacements and rotations of beams and shells, and the developed nonlinear finite elements are accurate for performing large deformation analysis of highly flexible structures.