The computational procedures of higher-order implicit integrators for mechanical systems with friction are provided in this paper. The dynamic equations are established using the augmented Lagrangian formulation, and set-valued friction forces are described by projection functions. To reduce the accuracy loss caused by event transitions and to eliminate spurious oscillations in the acceleration, a new robust event-driven scheme, which accurately detects event transitions and corrects the friction forces and accelerations at switching points, is proposed. The numerical performance of the proposed scheme is demonstrated by solving several benchmark problems. Numerical results show that the newly developed scheme can approximately achieve second-order accuracy, and they are more accurate than the classical Moreau time-stepping scheme under close computational efforts. Finally, a slider-crank system is simulated to prove the validity of the developed method for nonlinear mechanical systems with friction.

中文翻译：

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具有设定值摩擦力的机械系统的一种改进的隐式方法

本文提供了具有摩擦力的机械系统的高阶隐式积分器的计算程序。使用增强的拉格朗日公式建立动力学方程，并通过投影函数描述设定值的摩擦力。为了减少事件过渡引起的精度损失并消除加速度中的虚假振荡，提出了一种新的鲁棒事件驱动方案，该方案可准确检测事件过渡并校正切换点处的摩擦力和加速度。通过解决几个基准问题证明了所提出方案的数值性能。数值结果表明，新开发的方案可以近似实现二阶精度，在经过严格的计算之后，它们比经典的Moreau时间步长方案更准确。最后，对曲柄滑块系统进行了仿真，以证明所开发方法对带有摩擦力的非线性机械系统的有效性。