Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.     

平面柔性多体系统正碰撞动力学建模理论研究

针对目前柔性多体系统碰撞动力学建模方法存在的不足,对影响碰撞动力学仿真的主要因素如柔性体建模和碰撞初始条件进行分析,建立起基于变约束的柔性体碰撞动力学方程。首先,为了解决子结构法在处理碰撞界面搜索时面临的难题,引入多体系统柔性体有限元描述方法,推导出凸形柔性体接触点间法向位移约束的二阶导数形式。其次,从碰撞引起的接触界面速度不连续机理出发,结合连续介质力学间断面理论,给出碰撞瞬时由物体本身物理性质决定的接触位置处速度跳跃公式。最后对两弹性圆盘低速碰撞问题进行数值仿真。结果表明本文提出的改进方法符合力学基本原理,仿真结果满足收敛性要求。     

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper,by defining new state vectors and developing new transfer matrices of various elements moving in space,the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space.Formulations and numerical example of a rigidflexible-body three pendulums system moving in space are given to validate the method.Using the new method to study the dynamics of multi-rigid-flexible-body system moving in space,the global dynamics equations of system are not needed,the orders of involved matrices of the system are very low and the computational speed is high,irrespective of the size of the system.The new method is simple,straightforward,practical,and provides a powerful tool for multi-rigid-flexible-body system dynamics.     

Fast simulation of flexible multibody dynamics with electric-hydraulic drive system

Hardware in the loop simulation (HILS) has been investigated in the field of the multibody dynamics (MBD), which combined the MBD simulation with the actual mechanical system. The fast simulation is necessary for the HILS system in order to require the real time simulation. This paper presents a fast simulation technique using the domain decomposition method with the iteration in the flexible multibody system in which flexible linkage system and electro-hydraulic drive system are coupled with each other.     

人体肌骨的多柔体系统动力学研究进展

人体肌肉骨骼系统简称肌骨系统, 包括骨骼、骨骼肌与关节连接, 其力学模型是典型的多柔体系统. 从多体动力学角度研究肌骨系统, 主要关注其在运动过程中的肌肉内力、关节力矩及产生的动力学影响, 属于动力学与生物力学的交叉融合. 肌骨系统的多体动力学模型已被广泛地应用于临床医学、竞技体育、军事训练、人机工程等诸多领域, 其仿真结果可为提高人体运动能力、降低关节载荷与能耗、避免运动损伤、加快康复进程等提供重要计算参考数据. 与此同时, 上述研究亦对肌骨动力学研究提出了许多新挑战. 本文综述了人体肌骨多柔体系统动力学相关研究进展, 包括骨骼肌功能解剖与生物力学建模、神经与肌肉控制理论、肌骨系统动力学问题与求解方法, 以及近年来肌骨多体动力学在步态分析、飞行员抗荷动作、口颌手术规划等领域的典型应用. 与工程领域的机械多体系统相比, 人体肌骨多体系统具有肌肉内力主动性与肌肉控制冗余性两大特征. 现有骨骼肌模型难以同时考虑肌肉的解剖结构、三维几何与肌力产生的生物化学机制. 已有大多数肌骨模型采用静态优化假设消除肌肉冗余性, 忽略了肌肉与肌腱内力平衡及兴奋收缩耦联机制. 此外, 目前仍缺乏实现肌骨模型个性化的无创在体测试手段. 未来, 人体肌骨多体动力学研究将会向更精确、智能、个性化的方向发展, 成为动力学与生物力学交叉的热点研究领域.      

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multi-body systems involving impact should consider the local plastic deformation and the strict requirements of the spa-tial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlin-ear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.     

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation. The project supported by the National Natural Science Foundation of China (10472066, 10372057). The English text was polished by Yunming Chen.     

A modified constraint force algorithm for flexible multibody dynamics with loop constraints

Nonlinear Dynamics - This paper presents a modified constraint force algorithm (m-CFA) for the dynamics of flexible multibody systems in arbitrary topologies. The m-CFA can efficiently calculate...     

Recent developments in multibody system dynamics

For the dynamical analysis of discrete mechanical systems the method of multibody systems is well qualified. The resulting equations of motion are solved by simulation codes and displayed by computer animation. The paper presents an approach for the efficient computation of motions and reactions.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

Screw-matrix method in dynamics of multibody systems

In the present paper the concept of screw in classical mechanics is expressed in matrix form, in order to formulate the dynamical equations of the multibody systems. The mentioned method can retain the advantages of the screw theory and avoid the shortcomings of the dual number notation. Combining the screw-matrix method with the tool of graph theory in Roberson/Wittenberg formalism. We can expand the application of the screw theory to the general case of multibody systems. For a tree system, the dynamical equations for eachj-th subsystem, composed of all the outboard bodies connected byj-th joint can be formulated without the constraint reaction forces in the joints. For a nontree system, the dynamical equations of subsystems and the kinematical consistency conditions of the joints can be derived using the loop matrix. The whole process of calculation is unified in matrix form. A three-segment manipulator is discussed as an example. This work is supported by the National Natural Science Fund.     

The coupling dynamical modeling theory of flexible multibody system

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The “coupling matrix library” and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams. The project supported by the National Natural Science Foundation of China (No. 19832040).     

Modeling intermittent contact for flexible multibody systems

This paper consists of two parts. The first part presents a complementarity based recursive scheme to model intermittent contact for flexible multibody systems. A recursive divide-and-conquer framework is used to explicitly impose the bilateral constraints in the entire system. The presented approach is an extension of the hybrid scheme for rigid multibody systems to allow for small deformations in form of local mode shapes. The normal contact and frictional complementarity conditions are formulated at position and velocity level, respectively, for each body in the system. The recursive scheme preserves the essential characteristics of the contact model and formulates a minimal size linear complementarity problem at logarithmic cost for parallel implementation. For a certain class of contact problems in flexible multibody systems, the complementarity based time-stepping scheme requires prohibitively small time-steps to retain accuracy. Modeling intermittent contact for this class of contact problems motivated the development of an iterative scheme. The second part of the paper describes this iterative scheme to model unilateral constraints for a multibody system with relatively fewer contacts. The iterative scheme does not require a traditional complementarity formulation and allows the use of any higher order integration methods. A comparison is then made between the traditional complementarity formulation and the presented iterative scheme via numerical examples.     

A projective criterion to the coordinate partitioning method for multibody dynamics

Summary The paper discusses some developments in the coordinate partitioning method for the dynamic analysis of constrained/closed-loop multibody systems. First, the method is reformulated to a more compact form. Then, a simple and reliable projective criterion for choosing the best coordinates from the redundant ones is proposed, and some advantages are pointed out that may arise in the method by applying inverse kinematics algorithms. Finally, the problem of determination ofphysical reactions of constraints and closing conditions is discussed. A four-bar linkage mechanism serves for an illustration of some aspects of the paper.

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Ein Projektionskriterium zur Koordinatenwahl bei Mehrkörpersystemen mit kinematischen Schleifen

Übersicht Bei der Simulation der Bewegunsgleichungen von Mehrkörpersystemen mit kinematischen Schleifen in Minimalform stellt sich die Frage nach der Wahl günstiger verallgemeinerter Koordinaten. Hierfür wird ein Projektionskriterium vorgeschlagen, welches die Trennung der systembeschreibenden redundanten Koordinaten in die verallgemeinerten und davon abhängige Koordinaten gestattet. Durch Anwendung eines Verfahrens zur Rückwärtstransformation der kinematischen Beschreibung lassen sich in diesen explizite Schließbedingungen formulieren, was sich bei der Simulation vorteilhaft auswirkt; diese kann ohne Verletzung der Schließbedingungen erfolgen. Es wird auch gezeigt, wie auch bei Verwendung verallgemeinerter Koordinatenphysikalisch interpretierbare Reaktionen ermittelt werden können. Als Anwendungsbeispiel dient ein ebenes Viergelenk.

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On leave from the Department of Mechanics, Technical University of Radom, ul. Malczewskiego 29, 26-600 Radom, Poland     

Design and experimental validation of piecewise-linear state observers for flexible link mechanisms

The design of an observer estimating the state variables of a plant is an essential step towards the synthesis of high-performance model-based control schemes. In this paper, the problem of designing accurate state observers for flexible link mechanisms is tackled. The complexity of such a problem is considerable due to the nonlinear characteristics of flexible link mechanism dynamic models. Since nonlinear state observers have limited practical utility, in this work an investigation is made on the possibility of employing the Kalman filter theory together with suitable piecewise-linear truncated dynamic models. A general approach is developed and experimental results are given for the case of a four bar linkage with flexible links. Not only do these results confirm the theoretical and numerical results, but they also prove the practical effectiveness and efficiency of the proposed approach.     

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

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柔性多体系统产生动力刚化原因的研究

传统的柔性多体系统建模理论由于对柔性体的变形及其与大范围运动产生惯性力之间的耦合处理得过于简单,所以在分析存在高速大范围运动柔性多体系统的动力学性态时会得到完全错误的结论。本文将通过对作大范围运动弹性薄板的讨论来揭示产生这种错误的及探讨对传统性多体系统建模理论作出改进的对策