Projective geometric algebra for flexible multibody dynamics: implementation and validation through benchmark problems

Abstract This paper presents the validation of a novel code for the dynamic analysis of flexible multibody systems, which leverages projective geometric algebra for the kinematic description of the system. The theoretical foundations of geometric algebra are introduced briefly. A closed-form solution for the interpolation of motion is derived within the proposed framework and a finite element formulation of geometrically exact beams is developed. The accuracy of this code is assessed by comparing its prediction with those of eight multibody dynamics codes developed by independent researchers. Results are presented for three benchmark problems: the flexible four-bar mechanism, the lateral buckling of a thin beam, and the stability of a rotating shaft. Excellent agreement is found between the predictions of the proposed code and the previously published results, confirming the accuracy of the PGA-based approach. These findings demonstrate the potential of geometric algebra as a robust and elegant basis for the analysis of complex multibody systems.