Two-dimensional higher-order deformation gradient element for flexible beams with large deformation in a floating frame of reference

This study proposes a two-dimensional higher-order deformation gradient element based on the floating frame of reference formulation to meet the dynamics control requirements of systems with large deformations/rotations. The proposed model can be regarded as an equivalent element of absolute nodal coordinate formulation, since its derivation process only involves the transformation relationships between coordinate systems without the small deformation assumption. Furthermore, a dynamics model of flexible hub-beam system is derived using the Green-Lagrange strain tensor and the Lagrange’s equation of the second kind, which can precisely describe dynamic behavior undergoing large deformation. Ultimately, several traditional numerical examples, such as a cantilever beam subjected to a vertical tip force, are shown to verify the performance of the proposed model. The results are then compared with existing model