Development and implementation of model smoothing method in the framework of absolute nodal coordinate formulation

Abstract

A model smoothing formulation used to filter out the high-frequency components in the dynamical modeling process is developed and implemented in the framework of absolute nodal coordinate formulation (ANCF). Unlike the conventional method which employs stiff ordinary differential equation (ODE) solvers with numerical damping to calculate the dynamic responses of the ANCF model, a new formulation with the controlled high frequency is proposed in this paper. Using the average stress defined in a time interval to replace the instant stress in the virtual power of the internal force, the additional inertial and damping terms are introduced to the equations of motion of the ANCF element. It is proved that the highest frequency magnitude of the modified ANCF model can be adjusted by changing the length parameter of the time interval. As the high-frequency components are filtered out in the process of the model development, the traditional stiff problems of ANCF elements can be solved by using well-developed explicit integration algorithms, particularly in the very stiff and thin structures. Dynamic analysis of the classic examples including the pendulum beam and plate are performed to evaluate the performance of the model smoothing formulation of ANCF elements. Numerical results show that the proposed method can greatly improve the calculation efficiency of ANCF models, and the calculation accuracy can be also guaranteed.