Design of a planar multibody dynamic system with ANCF beam elements based on an element-wise stiffness evaluation procedure

The absolute nodal coordinate formulation (ANCF) has been widely applied for large deformation analysis in flexible multibody dynamics. Although the formulation led to stable solutions for time integration under large rotations and deformations, excessive time consumption was recorded. The nonlinear relationship between the deformation and the internal force accounted for repeated adjustment to the force equilibrium state as the structure deformed. In this research, an equivalent model of the ANCF beam structure was constructed. The stiffness evaluation method was applied in an element-wise manner. In this model, the irrelevant parts were separated from those that relate to the displacements and design parameters enabling efficient updates of internal forces to achieve force equilibrium. Therefore, by using this model, optimization problems, in which displacements as well as design parameters keep changing can be efficiently approached. To verify the proposed method, two examples of optimization problems related to a free-falling pendulum and a slider-crank mechanism are demonstrated.