BAT子弹药折叠翼展开冲击非光滑模型的隐式积分算法

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摘要非光滑动力学模型能有效处理多体系统内的单边约束，是弹性接触/碰撞分析的主要研究方法，但其复杂的数学形式难以进行工程应用。为了降低非光滑模型的应用难度并提高模型计算精度，以BAT子弹药折叠翼的展开冲击过程为研究对象，建立了速度-冲量形式的完备非光滑动力学方程组，并基于互补接触定律，推导了方程组较为简洁的线型互补形式；提出了一种新型隐式积分算法，用于提高碰撞力的计算精度和效率。通过构造下一时刻的近似速度，由该近似速度和当前速度来加权构造下一时刻的位移，并更新下一时刻各状态量。工程算例中，对包含碰撞冲击的BAT子弹药折叠翼展开过程进行计算，将提出的隐式积分算法与已有算法进行对比分析，结果表明：相较于Moreau中点算法，隐式积分算法对碰撞力的计算精度更高，基于所提隐式积分算法的非光滑动力学模型能够严格遵从单边约束，计算的相对误差在10-8量级，能够为小载荷、高精度的多体碰撞系统提供更为准确的数值计算方法。
关键词：非光滑动力学；线性互补问题；多体动力学；折叠翼；碰撞冲击

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	张洪铭1
	顾晓辉1
	孙丽2

关键词 ：非光滑动力学, 线性互补问题, 多体动力学, 折叠翼, 碰撞冲击

Abstract：Non-smooth dynamic model can effectively deal with unilateral constraints in multibody systems and is the main research method of elastic contact / collision analysis, but its complex mathematical form is difficult to be applied in engineering. In order to reduce the difficulty of the application of the non-smooth model and improve the calculation accuracy of the model, taking the unfolding impact process of the BAT submunition as the research object, the complete non-smooth dynamic equations in the form of velocity-impulse are established, and the linear complementary form of the equations is derived based on the complementary contact law. A new implicit integration algorithm is proposed in this paper to improve the accuracy and efficiency of collision force calculation. By constructing the approximate velocity of the next time point, using the approximate velocity and the current velocity, the displacement of the next time point is constructed by weighted summation, and the state variables of the next time are updated. Through the calculation of the folding wing deployment process of BAT submunitions including collision impact, the proposed implicit integration algorithm is compared with the existing algorithm. The results show that the implicit integration algorithm proposed in this paper is more accurate in calculating the collision force than the Moreau midpoint algorithm. The non-smooth dynamic model based on the proposed implicit integration algorithm can strictly comply with unilateral constraints, and the relative error is of the order of 10-8 level, which can provide a more accurate numerical calculation method for multi-body collision systems with small loads and high precision.

Key words： non-smooth dynamics LCP multibody dynamics folding wings impact

收稿日期: 2021-05-19 出版日期: 2022-09-15

引用本文:

张洪铭1，顾晓辉1，孙丽2. BAT子弹药折叠翼展开冲击非光滑模型的隐式积分算法[J]. 振动与冲击, 2022, 41(17): 1-8.
ZHANG Hongming1, GU Xiaohui1, SUN Li2. Implicit integration algorithm for impact non-smooth model of BAT submunition folded wing unfolding. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(17): 1-8.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I17/1

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