Multibody Constraints in the Geometrically Nonlinear Intrinsic Formulation

The intrinsic formulation for geometrically nonlinear beam dynamics provides a compact and versatile description of slender beam-like structures. With nonlinearities limited to second-order couplings in the formulation, it has been an attractive choice in formulating nonlinear reduced-order models for dynamic analysis and control design in aeroelasticity problems involving large displacements and rotations. Owing to its rotation-free formalism, the intrinsic formulation has not been formulated to accommodate multibody constraints, limiting its use against multibody structures with kinematic constraints. This work aims to address such weakness as we present developments in introducing multibody constraints into the full and reduced-order intrinsic equations while still preserving the beneficial traits of the method. We describe the resolution of displacement-level constraints using index-1 approach and adaptation of constraint stabilization strategies to the intrinsic formulation using state projection. The numerical behavior of the full- and reduced-order implementations are assessed using test cases with large static and dynamic deformations with time-domain simulations to demonstrate validity of the approach.