Exact physics-based modeling and animation of highly flexible 1D mechanical systems
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this thesis, we present a geometrically exact beam theory and a corresponding displacement-based finite-element model for modeling, analysis and natural-looking animation of highly flexible beam components of multi-body systems undergoing huge static/dynamic rigid-elastic deformations. By using Jaumann strains, concepts of local displacements and orthogonal virtual rotations, and three Euler angles to exactly describe the coordinate transformation between the undeformed and deformed configurations, the beam theory can fully explain geometric nonlinearities and initial curvatures. In order to demonstrate the accuracy and capability of this nonlinear beam element, we perform nonlinear static and dynamic analysis of two highly flexible beams examples, which include the twisting of a circular ring into three small rings and the spinup of a flexible helicopter rotor blade. We use this method to analyze helicopter rotor blades' spinup dynamics and to simulate helicopter flight starting from takeoff, loiter, and then landing. These two numerical examples proved that the proposed nonlinear beam element is accurate and versatile for modeling, analysis and 3D rendering and animation of multi-body systems that contain highly flexible beam components.
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