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.

在绝对节点坐标公式 (ANCF) 的框架中开发并实现了用于滤除动力学建模过程中的高频分量的模型平滑公式。与使用具有数值阻尼的刚性常微分方程 (ODE) 求解器来计算 ANCF 模型动态响应的传统方法不同，本文提出了一种具有受控高频的新公式。使用时间间隔内定义的平均应力代替内力虚幂中的瞬时应力，将附加惯性项和阻尼项引入到 ANCF 单元的运动方程中。证明修改后的ANCF模型的最高频率幅度可以通过改变时间间隔的长度参数来调整。由于在模型开发过程中过滤掉了高频分量，ANCF 单元的传统刚性问题可以通过使用成熟的显式积分算法来解决，特别是在非常刚性和薄的结构中。对包括摆梁和板在内的经典示例进行动态分析，以评估 ANCF 元素的模型平滑公式的性能。数值结果表明，提出的方法可以大大提高ANCF模型的计算效率，同时也保证了计算精度。对包括摆梁和板在内的经典示例进行动态分析，以评估 ANCF 元素的模型平滑公式的性能。数值结果表明，提出的方法可以大大提高ANCF模型的计算效率，同时也保证了计算精度。对包括摆梁和板在内的经典示例进行动态分析，以评估 ANCF 元素的模型平滑公式的性能。数值结果表明，所提出的方法可以大大提高ANCF模型的计算效率，同时也保证了计算精度。