Non-dimensional equation of motion of a two-dimensional beam using stiffness matrices based on structural mechanics in the absolute nodal coordinate formulation

The absolute nodal coordinate formulation is a technique for representing large rotations and deformations in flexible multibody dynamics. This technique has the advantage of representing large deformations; however, its disadvantage is the increased analysis time owing to the highly nonlinear stiffness matrix. In this study, a non-dimensional equation of motion is developed to reduce the analysis time. The two-dimensional equation of motion can be converted into a non-dimensional equation of motion by introducing variables that transform time, length, and force into non-dimensional variables. In particular, in this study, six stiffness matrix models are proposed. The analysis efficiency of the developed non-dimensional equation of motion is verified through a free-falling pendulum example, and proven through the straight avoidance behavior of a flexible hose. The results confirm that the developed equation of motion is more efficient than the dimensional equation of motion for solving two-dimensional problems.