Geometrically Exact Total-Lagrangian Modeling and Nonlinear Finite Element Analysis of Highly Flexible Multibody Systems

Presented here is a new displacement-based total-Lagrangian modeling and finite element formulation of multibody systems with highly flexible beams undergoing arbitrary large rigid-elastic deformation. The theory uses three Euler angles to describe the coordinate tranformation of the undeformed and deformed coordinate systems, and accurately accounts for geometric nonlinearities and initial curvatures of beams by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. Nonlinear dynamic analysis of a slider crank mechanism in different situations is carried out to demonstrate the proposed methodology and its accuracy, and the accuracy of numerical results is checked against available numerical results from the literature. All the numerical results and comparisons reveal that the proposed methodology is accurate and versatile.