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<p>Incorporating non-smooth problems, such as frictional contact and impact, into multibody systems via unilateral constraints poses a significant challenge in developing effective and precise numerical algorithms. This work presents an enhanced non-smooth adaptive time-stepping method for addressing the dynamics of multibody systems with friction and impact. The proposed non-smooth adaptive time-stepping method incorporates Richardson extrapolation and a step-dichotomy strategy during the smooth phase to dynamically adjust the time step and performs implicit contact prediction at the end of each smooth phase to approximate the instant of contact by refining the step before impact, thereby reducing errors in contact detection. In the non-smooth phase, the Gear-Gupta-Leimkuhler (GGL) projection equation is discretized via the trapezoidal rule, and a linear complementary contact model is established by combining it with the midpoint-discretized non-smooth measure-differential equations, which effectively suppresses unilateral constraint penetration. A novel unilateral velocity-constraint activation strategy is introduced to eliminate the velocity chattering phenomenon during persistent contact. The proposed method has been validated through the benchmark example, where compares to Moreau and non-smooth generalized-<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> <EquationSource Format="TEX">$\alpha $</EquationSource> </InlineEquation> methods demonstrate its superior accuracy. Under a prescribed position error threshold, the method reduces computational time while automatically enforcing constraint stabilization. Results from numerical examples confirm that the method is capable of accurately capturing and computing non-smooth events and exhibits robust long-term fidelity in simulating complex multi-contact systems with friction and impact.</p>

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An enhanced non-smooth adaptive time-stepping method for multibody systems with friction and impact

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Jie Yang,
  • Yan Li,
  • Zhiqiang Feng

摘要

Incorporating non-smooth problems, such as frictional contact and impact, into multibody systems via unilateral constraints poses a significant challenge in developing effective and precise numerical algorithms. This work presents an enhanced non-smooth adaptive time-stepping method for addressing the dynamics of multibody systems with friction and impact. The proposed non-smooth adaptive time-stepping method incorporates Richardson extrapolation and a step-dichotomy strategy during the smooth phase to dynamically adjust the time step and performs implicit contact prediction at the end of each smooth phase to approximate the instant of contact by refining the step before impact, thereby reducing errors in contact detection. In the non-smooth phase, the Gear-Gupta-Leimkuhler (GGL) projection equation is discretized via the trapezoidal rule, and a linear complementary contact model is established by combining it with the midpoint-discretized non-smooth measure-differential equations, which effectively suppresses unilateral constraint penetration. A novel unilateral velocity-constraint activation strategy is introduced to eliminate the velocity chattering phenomenon during persistent contact. The proposed method has been validated through the benchmark example, where compares to Moreau and non-smooth generalized- α $\alpha $ methods demonstrate its superior accuracy. Under a prescribed position error threshold, the method reduces computational time while automatically enforcing constraint stabilization. Results from numerical examples confirm that the method is capable of accurately capturing and computing non-smooth events and exhibits robust long-term fidelity in simulating complex multi-contact systems with friction and impact.