基于Lagrange法的刚体与柔体动力学对比研究

对于机器人、航天器和车辆悬架部件等一些多体系统来说,其中一些部件的大尺寸、轻型化趋势使得传统的刚性体建模已经难以准确地模拟实际的工况,将部件所具有的柔性特性加入到多体系统模型中进行柔体动力学仿真,由于考虑了部件弹性变形与大范围刚性运动之间的耦合,故可以得到部件更为真实的动力学行为.文中通过与基于Lagrange法的刚体动力学基本方程进行对比研究,详细说明了柔体动力学方程中上述的耦合作用.以某大型雷达可展开天线为例,分别在刚体和柔体的假设下对其展开运动进行动力学仿真,结果表明采用柔性体仿真更能真实反映其动力学特性.     

柔性航天器动力学建模及模型降阶研究

针对柔性航天器振动影响飞行器姿态稳定性和精度.为了解决上述问题,提出了多柔体航天器的动力学建模.首先,根据工程实现的假设振型法,采用拟坐标拉格朗日方程,推导出带有刚体模态的二阶系统刚柔耦合动力学模型,其中,为了减少模型计算量,通过坐标变换将刚体模态和柔性模态解耦,利用一种刚体模态解耦的二阶不稳定系统的模型降阶方法,并对航天器多柔体系统动力学方程进行了仿真分析,结果飞行姿态稳定,满足了精度要求,表明了动力学建模与模型降阶法的有效性和正确性.     

基于刚-柔混合模型的300T铁水车动力学仿真

为保证300t铁水车的安全运输,采用刚-柔混合动力学模型研究了该车的动力学性能.以I-DEAS软件为柔性体仿真平台,ADAMS/Rail软件为多刚体系统仿真平台,给出了创建刚-柔混合动力学模型的技术路线,采用在系统外将所关心的对象柔性化的建模方法建立了某公司研制的特种车辆-300t铁水运输车的刚-柔混合动力学模型.基于刚-柔混合模型的动力学仿真结果表明:弹性轨道对该车运行平稳性和曲线通过性能的影响大于柔性转向架对运行平稳性和曲线通过性能的影响.因此,对这类特种车辆进行动力学仿真应采用弹性轨道.当计算规模很大无法考虑转向架的柔性效应时,仅使用弹性轨道所获得的结果也能达到相当的精度.     

基于整体-局部高阶剪切理论的层合板多体系统的动静力学分析

基于高阶剪切理论,推导了整体-局部1,2-3高阶位移模式.在满足层间位移连续,层间剪应力连续,以及上下表面自由的条件下,层合板每个节点的独立变量变为13,并且不随层合板层数的增加而变化.在此基础上将整体-局部1,2-3高阶位移模式推广到刚-柔耦合层合板多体系统,利用混合坐标法,基于虚功原理,建立了考虑层合板层间应力连续的多体系统动力学方程.通过静力学算例,验证了整体-局部1,2-3高阶位移模式的准确性,得到了层合板层间应力沿着厚度的分布情况.通过多体系统动力学算例,对比了传统方法的计算结果,揭示了本文方法与传统方法在计算层合板多体系统中层间应力的差异,说明了刚-柔耦合层合板多体系统考虑层间剪应力连续的必要性.     

多体动力学与航天动力学及其控制进展

正多体系统动力学是研究由若干个物体通过各类约束方式连接组成的多体系统的运动规律的科学。多体系统动力学起源于上世纪六十年代,目前是应用力学方面最活跃的领域之一,并已成为动力学与控制学科的重要分支。多体系统动力学主要以复杂机械系统、航空航天、车辆船舶、机器人等多个工程领域为背景,研究内容涉及复杂系统的建模方法、求解策略、多场耦合动力学特性分析、实验研究等诸多方面,研究成果具体表现在为工程问题提     

多体系统动力学数值解法

多体系统动力学研究的主要内容动力学建模与数值解法是多体系统动力学研究的主要内容之一。对多体系统动力学方程及其动力学数值解法的研究成果进行了较为全面的阐述。多体系统动力学及动力学方程进行了简单的归纳和总结,多体系统动力学数值求解,特别是刚柔耦合多体系统微分／代数方程的数值解法等研究热点进行了详细的阐述,并简要展望了多体系统动力学数值解法今后的发展趋势,为多体系统动力学计算机仿真奠定了基础。     

柔性多体系统动力学在直升机旋翼桨叶上的应用

提出了一种全新的计算旋翼桨叶动力响应的方法。以柔性多体系统动力学为基础，结合有限单元法和拉格朗日方程，推导出绕动轴转动的多柔体动力学质量矩阵，建立了直升机旋翼桨叶的动力学控制方程及其系数矩阵的解析表达式，采用Rung-Kutta法进行数值积分．分析了挥舞运动在强耦合状态下的运动规律。仿真结果表明采用此方法建立旋翼桨叶的动力学控制方程。可以更真实的反映桨叶的实际运动状态。     

考虑刚-柔-热耦合的板结构多体系统的动力学建模

对热载荷作用下中心刚体与大变形薄板多体系统的动力学建模问题进行研究.基于Kirchhoff假设,从格林应变和曲率与绝对位移的非线性关系式出发,推导了非线性广义弹性力阵,用绝对节点坐标法建立了大变形矩形薄板的有限元离散的动力学变分方程.为了考虑刚体姿态运动、弹性变形和温度变化的相互耦合作用,推导了热流密度与绝对节点坐标之间的关系式.引入系统的运动学约束方程,建立了中心刚体-矩形板多体系统的考虑刚-柔-热耦合的热传导方程和带拉格朗日乘子的第一类拉格朗日动力学方程.为了有效地提高计算效率,将改进的中心差分法和广义-α法相结合,求解热传导方程和动力学方程,差分后的方程通过牛顿迭代法耦合求解.对刚-柔耦合和刚-柔-热三者耦合两种模型的仿真结果进行比较表明,刚体运动对温度梯度和热变形的影响显著.此外,本文建模方法考虑了几何非线性项,因此也考虑了热膨胀引起的轴向变形对横向变形的影响.     

计及环境特征的刚-柔机械臂动力学建模方法与理论研究

基于Kane方程推导建立了在惯性参考坐标系中的刚—柔机械臂的非线性动力学模型 ,并利用假设模态的方法对方程进行离散 .在对刚—柔机械臂进行主动柔顺控制时 ,柔性机械臂要受到未确知外部环境的约束 .本文建立了计及环境特征的一般柔性多体系统动力学模型以及计及环境特征的刚—柔机械臂动力学模型 .     

MSC软件在单缸柴油机设计中的应用

对某单缸柴油机曲轴、曲轴箱、机座等构件系统进行多柔体动力学仿真,着重对机座进行强度校核和疲劳安全系数计算. 通过分析,得到机座强度储备较高、符合安全运行要求的结论.     

Erratum to: New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

Flexible Multibody Dynamics: Review of Past and Recent Developments

In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynamics, control-structure interaction, use of modal identification and experimental methods in flexible multibody simulations, application of flexible multibody techniques to computer graphics, numerical issues, and large deformation problem. Establishing the relationship between different flexible multibody formulations is an important issue since there is a need to clearly define the assumptions and approximations underlying each formulation. This will allow us to establish guidelines and criteria that define the limitations of each approach used in flexible multibody dynamics. This task can now be accomplished by using the absolute nodal coordinate formulation which was recently introduced for the large deformation analysis of flexible multibody systems.     

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.     

Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes

In this work we discuss an application of the finite elementmethod to modeling of flexible multibody systems employing geometricallyexact structural elements. Two different approaches to handleconstraints, one based on the Lagrange multiplier procedure and anotherbased on the use of release degrees of freedom, are examined in detail.The energy conserving time stepping scheme, which is proved to be wellsuited for integrating stiff differential equations, gouverning themotion of a single flexible link is appropriately modified and extendedto nonlinear dynamics of multibody systems.     

Analysis of Nonlinear Multibody Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of nonlinear multibody systems involving elastic members made of laminated, anisotropic composite materials. The analysis methodology can be viewed as a three-step procedure. First, the sectional properties of beams made of composite materials are determined based on an asymptotic procedure that involves a two-dimensional finite element analysis of the cross-section. Second, the dynamic response of nonlinear, flexible multibody systems is simulated within the framework of energy-preserving and energy-decaying time-integration schemes that provide unconditional stability for nonlinear systems. Finally, local three-dimensional stresses in the beams are recovered, based on the stress resultants predicted in the previous step. Numerical examples are presented and focus on the behavior of multibody systems involving members with elastic couplings.     

Optimization of flexible components of multibody systems via equivalent static loads

An optimization methodology that iteratively links the results of multibody dynamics and structural analysis software to an optimization method is presented to design flexible multibody systems under dynamic loading conditions. In particular, rigid multibody dynamic analysis is utilized to calculate dynamic loads of a multibody system and a structural optimization algorithm using equivalent static loads transformed from the dynamic loads are used to design the flexible components in the multibody dynamic system. The equivalent static loads, which are derived from equations of motion, are used as multiple loading conditions of linear structural optimization. A simple example is solved to verify the proposed methodology and the pelvis part of the biped humanoid, a complex multibody system which consists of many bodies and joints, is redesigned using the proposed methodology.     

First order sensitivity analysis of flexible multibody systems using absolute nodal coordinate formulation

Design sensitivity analysis of flexible multibody systems is important in optimizing the performance of mechanical systems. The choice of coordinates to describe the motion of multibody systems has a great influence on the efficiency and accuracy of both the dynamic and sensitivity analysis. In the flexible multibody system dynamics, both the floating frame of reference formulation (FFRF) and absolute nodal coordinate formulation (ANCF) are frequently utilized to describe flexibility, however, only the former has been used in design sensitivity analysis. In this article, ANCF, which has been recently developed and focuses on modeling of beams and plates in large deformation problems, is extended into design sensitivity analysis of flexible multibody systems. The Motion equations of a constrained flexible multibody system are expressed as a set of index-3 differential algebraic equations (DAEs), in which the element elastic forces are defined using nonlinear strain-displacement relations. Both the direct differentiation method and adjoint variable method are performed to do sensitivity analysis and the related dynamic and sensitivity equations are integrated with HHT-I3 algorithm. In this paper, a new method to deduce system sensitivity equations is proposed. With this approach, the system sensitivity equations are constructed by assembling the element sensitivity equations with the help of invariant matrices, which results in the advantage that the complex symbolic differentiation of the dynamic equations is avoided when the flexible multibody system model is changed. Besides that, the dynamic and sensitivity equations formed with the proposed method can be efficiently integrated using HHT-I3 method, which makes the efficiency of the direct differentiation method comparable to that of the adjoint variable method when the number of design variables is not extremely large. All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based flexible multibody systems.     

Flexible Multibody Systems Models Using Composite Materials Components

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method.     

Analysis of Flexible Multibody Systems with Intermittent Contacts

This paper is concerned with the dynamic analysis of flexible,nonlinear multibody systems undergoing intermittent contacts. Contact isassumed to be of finite duration, and the forces acting between thecontacting bodies which can be either rigid or deformable are explicitlycomputed during simulation. The modeling of contact consists of threeparts: a number of holonomic constraints that define the candidatecontact points on the bodies, a unilateral contact condition which istransformed into a holonomic constraint by the addition of a slackvariable, and a contact model which describes the relationship betweenthe contact force and the local deformation of the contacting bodies.This work is developed within the framework of energy preserving anddecaying time integration schemes that provide unconditional stabilityfor nonlinear, flexible multibody systems undergoing intermittentcontacts.