Geometrically exact physics-based modeling and computer animation of highly flexible 1D mechanical systems

This paper presents 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 multibody systems undergoing huge static/dynamic rigid-elastic deformations. The beam theory fully accounts for geometric nonlinearities and initial curvatures 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. To demonstrate the accuracy and capability of this nonlinear beam element, nonlinear static and dynamic analysis of two highly flexible beams are performed, including the twisting a circular ring into three small rings and the spinup of a flexible helicopter rotor blade (Graphical abstract). These numerical results reveal that the proposed nonlinear beam element is accurate and versatile for modeling, analysis and 3D rendering and animation of multibody systems with highly flexible beam components.

Graphical abstractSimulated helicopter take-off with blade rotations (left to right, top to bottom) computed using the proposed geometrically exact 1D beam theory.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Present a geometrically exact theory for modeling highly flexible beams. ► Present the corresponding finite-element formulation. ► Present the corresponding multiple shooting formulation for static analysis. ► Present two advanced numerical examples to verify the proposed beam theory.