多刚体动力学仿真的李群变分积分算法

刚体的构形可用其质心位置和姿态矩阵描述.刚体的位置可以在欧几里得空间中表示，但是其姿态矩阵是在李群上演化的.由于李群独特的非线性性质，基于欧氏空间的多体动力学建模与数值算法难以完全真实地描述系统的动力学特性，特别是长时间历程的动力学特性.本文基于几何力学理论，首先根据离散Hamilton变分原理与离散Legendre变换，建立了多刚体系统的Hamilton体系李群变分积分公式.其次，给出李群变分积分公式的两种离散格式：一般离散格式和RATTLie离散格式.最后，采用这两种不同离散格式构建的算法计算了重力作用下空间刚体双摆的动力学问题，对比研究了算法在保持系统群结构、系统能量等方面的性质.计算结果表明，RATTLie离散格式较一般格式精度更高，且能更好地保持系统群结构与能量.     

共线三球链问题的碰撞动力学研究

共线三球链的碰撞动力学问题能够展示多刚体系统碰撞问题的困难之一：非唯一解的问题.本文建立了三球链碰撞的Hertz接触模型,研究对其求解的数值算法,并用有限元模型（FEM）对其进行验证,研究表明：同线性模型比较,采用Hertz接触力模拟小球之间的接触力更接近有限元计算结果;在Hertz接触模型基础上,分析碰撞过程中接触力的变化过程;研究刚度比和质量比对于碰撞结束后各个小球运动状态的影响,并研究了两种刚体模型下碰撞次序假设成立的条件.     

多柔体系统动力学研究进展与挑战

首先回顾多体系统动力学的学科发展和学术交流情况,然后系统概述了多柔体系统动力学方程数值算法、多柔体系统接触/碰撞动力学与柔性空间结构展开动力学三个方面的研究进展及值得关注的若干问题,最后给出了开展多柔体系统动力学研究的若干建议.     

非线性动力学系统最优控制问题的保辛求解方法

基于对偶变量变分原理提出了求解非线性动力学系统最优控制问题的一种保辛数值方法.以时间区段一端状态和另一端协态作为混合独立变量,在时间区段内采用拉格朗日插值近似状态变量与协态变量,然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解,最终得到求解非线性动力学系统最优控制问题的保辛数值方法.数值实验验证了本文算法在求解精度与求解效率上的有效性.     

中心刚体-柔性梁应变反馈多目标优化控制

本文针对柔性结构在轨组装任务背景,将自动飞船和待运送部件分别简化为中心刚体和柔性梁附件,研究自由漂浮中心刚体-柔性梁系统的动力学与控制问题.首先基于小变形和低转速假设,将梁用假设模态法离散,采用Lagrange方程导出系统动力学方程.继而设计一种带有应变反馈的PD控制律用于完成中心刚体的状态镇定以及柔性梁振动抑制.此外,本文还使用遗传算法对控制器中的参数进行多目标优化.最后,通过数值算例验证了所设计控制器的有效性.     

多技术系统基于VHDL-AMS的统一建模与仿真技术研究

机电一体化系统设计要求跨领域的统一建模与仿真，多刚体动力学是其中的一个难点．通常的做法是采用动力学专用软件建模，求得DAEs形式的运动方程后再转化为集成环境中的统一建模语言．首先基于广义基尔霍夫网络理论，提出了基于端口的多技术系统集成组件，并采用VHDL—AMS混合系统建模语言进行描述．为了更有效的集成多刚体动力学，通过选取参考基作为端点，构造了计算多刚体系统动力学的广义基尔霍夫网络模型，具体阐述了基本组件的VHDL-AMS行为模型，从而将多刚体系统纳入基于VHDL—AMS的集成设计和仿真环境中．最后用一个实例进行了具体说明．     

变拓扑柔性多体系统接触碰撞动力学研究

在实际工程领域中存在着大量接触碰撞等非连续动力学问题,现有的解决柔性多体系统连续动力学过程的建模理论与方法,已经无法解决或无法很好解决这些问题.本文基于变拓扑思想,提出了附加接触约束的柔性多体系统碰撞动力学建模理论；通过设计柔性圆柱杆接触碰撞实验,验证了所提出附加约束接触碰撞模型的有效性；针对柔性多体系统全局动力学仿真面临时间和空间的多尺度问题,提出多变量的离散方法,从而提高了柔性多体系统非连续动力学的仿真效率.     

基于约束的刚体碰撞响应仿真研究与应用

为了解决虚拟场景中刚体碰撞与穿透问题,采用了一种基于约束的碰撞响应方法。根据刚体之间的穿透深度和在碰撞点处的相对速度,判定不同的碰撞状态。通过将多刚体碰撞和多点碰撞分割为单个碰撞,以刚体在碰撞点相对速度法向分量构建法向约束,切向分量构建切向摩擦约束。根据不同的碰撞状态以及牛顿恢复系数碰撞模型求取法向误差,并以碰撞点相对速度切向分量作为切向摩擦误差。结合约束与误差,得到碰撞的约束方程,联合刚体的动力学方程,迭代求解,计算碰撞之后刚体的速度,更新刚体的坐标与姿态,并计算刚体顶点在世界坐标系中的坐标。在虚拟矿山场景中进行了应用,仿真效果较好。     

基于十字链表的多刚体系统的数据存储

针对多刚体系统数据存储的不足,对多刚体系统的结构图与图论的有向图之间的关系进行了研究,提出了一种新的基于十字链表的链式存储模型.该存储模型不但较好地解决了复杂多刚体系统的存储问题,而且充分满足了在存储物理多刚体系统时的结构正确性和数据完备性要求,避免了非树形多刚体向树形多刚体的回路切除转换,使多刚体系统在数学建模与数据存储方面达到高度一致.     

具有奇异位置的多体系统动力学方程的改进算法

多体系统进行数值仿真时,很多选择了微分代数混合方程作为多体系统动力学数学模型.本文在现有的约束稳定化理论基础上,提出了针对具有奇异位置的多体系统动力学方程的改进算法.算法通过修正速度违约和控制稳定项,讨论了具有奇异位置的微分代数混合方程的数值仿真问题并给出了稳定项中相关系数的建议值,从而有效克服了求解混合方程时因为构型奇异给计算造成的困难.算例分别采用改进算法与ADAMS软件进行仿真,计算结果的比较表明了改进算法的有效性.本文给出的基于能量守恒的能量差曲线也证明了改进算法的有效性.     

New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite element analysis of 3D frictional contact problem

We propose a new second-order cone linear complementarity problem (SOCLCP) formulation for the numerical finite element analysis of three-dimensional (3D) frictional contact problems by the parametric variational principle. Specifically, we develop a regularization technique to resolve the multi-valued difficulty involved in the frictional contact law, and use a second-order cone complementarity condition to handle the regularized Coulomb friction law in contact analysis. The governing equations of the 3D frictional contact problem is represented by an SOCLCP via the parametric variational principle and the finite element method, which avoids the polyhedral approximation to the Coulomb friction cone so that the problem to be solved has much smaller size and the solution has better accuracy. In this paper, we reformulate the SOCLCP as a semi-smooth system of equations via a one-parametric class of second-order cone complementarity functions, and then apply the non-smooth Newton method for solving this system. Numerical results confirm the effectiveness and robustness of the SOCLCP approach developed.     

Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics

In this paper, we provide a full instruction on how to formulate and evaluate planar frictional contact problems in the spirit of non-smooth dynamics. By stating the equations of motion as an equality of measures, frictional contact reactions are taken into account by Lagrangian multipliers. Contact kinematics is formulated in terms of gap functions, and normal and tangential relative velocities. Associated frictional contact laws are stated as inclusions, incorporating impact behavior in form of Newtonian kinematic impacts. Based on this inequality formulation, a linear complementarity problem in standard form is presented, combined with Moreau’s time stepping method for numerical integration. This approach has been applied to the woodpecker toy, of which a complete parameter list and numerical results are given in the paper.     

Numerical treatment of the sea bed-long underwater cable dynamic interaction problem by an upper bounding algorithm

The numerical treatment of the dynamic response of an underwater cable, constrained by a frictionless rigid sea profile, by the use of an upper bounding algorithm is considered. By applying an appropriate discretization scheme with respect to time and space, the arising unilateral contact/impact problem is formulated as a sequence of variational inequality problems or as a sequence of quadratic programming problems that are equivalent to linear complementarity problems. The latter are numerically treated by applying an easy-to-use upper bounding Mangasarian algorithm leading to the solution of a linear programming problem which permits the treatment of large-scale problems.     

Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints

The main purpose of this paper is to present a modeling and simulation method for the rigid multibody system with frictional translational joints. The small clearance between a slider and guide is considered. The geometric constraints of the translational joints are treated as bilateral constraints and the impacts between sliders and guides are neglected when the clearance sizes of the translational joints are very small. The contact situations of the normal forces acting on the sliders are described by inequalities and complementarity conditions, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The dynamic equations of the multibody systems with normal and tangential contact forces are written on the acceleration-force level using the Lagrange multiplier technique. The problem of the transitions of the contact situation of the normal forces acting on sliders and the transitions of the stick-slip of the sliders in the system is formulated as a horizontal linear complementarity problem (HLCP), which is solved by event-driven method. Baumgarte’s stabilization method is used to decrease the constraint drift. Finally, two typical mechanisms are considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the systems with frictional translational joints and constraint stabilization effect.     

履带车多刚体建模与仿真分析

首先以车辆地面力学理论为基础,分析了典型的履带与地面相互作用关系及其在RecurDyn/Track(LM)程序中的处理,分别定义了两种典型地面土力学参数,从而建立了基于Bekker理论与Janosi & Hanamoto理论的循环动载荷作用下履带与地面相互作用力学模型;同时分析了履带系统各部件之间的接触力学模型,定义各接触参数及约束关系,从而准确合理地建立了履带车多刚体模型,通过施加运动函数,实现模型在典型地面参数下的行走特性仿真分析,仿真结果与理论分析及实际情况相符合,互为验证,从而为进一步深入研究提供了理论依据与有效分析手段.     

Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation

This article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a 42 degree-of-freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modeled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb’s friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time-stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Furthermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time-stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event-detecting time-stepping schemes, the event-capturing scheme enables us to perform the time-integration with a large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite-time accumulations with a reasonable time-step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical method deals with more than 70 contact points without any problems. Furthermore, the number of contact parameters is small—one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency, allows us to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data, showing a very good correlation.     

基于恢复系数的碰撞过程模型分析

论述了恢复系数的含义及作用,并在此基础上介绍了几种碰撞过程模型.通过详细推导恢复系数与模型参数之间的关系,使得不同的碰撞过程模型可统一用恢复系数表示能量损失,并用接触刚度表示变形.这也阐明了碰撞过程模型与刚性模型之间的区别和联系,把动态接触理论和古典碰撞理论统一了起来.通过对一个单球碰撞系统进行数值仿真,不仅验证了关系推导的正确性,而且对各种模型从精度、效率、微观接触过程等方面进行了比较.     

Discrete Time Transfer Matrix Method for Multibody System Dynamics

A new method for multibody system dynamics is proposed in this paper. This method, named as discrete time transfer matrix method of multibody system (MS-DT-TMM), combines and expands the advantages of the transfer matrix method (TMM), transfer matrix method of vibration of multibody system (MS-TMM), discrete time transfer matrix method (DT-TMM) and the numerical integration procedure. It does not need the global dynamics equations for the study of multibody system dynamics. It has the modeling flexibility and a small size of matrices, and can be applied to a wide range of problems including multi-rigid-body system dynamics and multi-flexible-body system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study of multibody system dynamics. Formulations of the method as well as some numerical examples of multi-rigid-body system dynamics and multi-flexible-body system dynamics to validate the method are given.     

A contact force solution for non-colliding contact dynamics simulation

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop an alternative approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for four test cases: (1) a thin rod sliding down a stationary wedge; (2) a cube pushed off a wedge by an applied force; (3) a cube rotating off the wedge under application of an external moment; and (4) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the new formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.     

Numerical modeling of wave processes in layered media in the Arctic region

The aim of this work is the numerical simulation of wave propagation in media with linear-elastic and acoustic layers as exemplified by the seismic prospecting problems in the Arctic region and the explosive impact on an iceberg. The complete system of equations describing the state of a linearly elastic body and the system of equations describing the acoustic field are solved. The grid-characteristic method is used to provide the contact and boundary conditions, including the contact condition between acoustic and linear-elastic layers, to be correctly described.