多柔性体系统动力学的有限元方法(MUFEM)

本文探讨多柔性体系统动力学的一种新的数值仿真方法一多体有限元方法（MultibodyFiniteElementMethod,MUFEM）。MUFEM以有限元方法为基础,综合区域分解法（DDM）和非连续体变形分析方法（DDA）的主要优点。MUFEM的主要特点是：1）构造边界网格描述系统动态变化的拓扑几何关系;2）采用FEM模型和类似子结构的方法分析多柔性体系统的动力学特性;3）各子块之间可能接触边界的非连续性用Lagrange乘子处理;4）摩擦接触问题用非线性数学规划方法求解。算例表明,MUFEM能很好模拟多柔性体系统的运动以及相互之间的作用,有良好的发展前景。     

A TORSIONAL SPRING-LIKE BEAM ELEMENT FOR THE DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS

A new finite element beam formulation for modelling flexible multibody systems undergoing large rigid-body motion and large deflections is developed. In this formulation, the motion of the ‘nodes’ is referred to a global inertial reference frame. Only Cartesian position co-ordinates are used as degrees of freedom. The beam element is divided into two subelements. The first element is a truss element which gives the axial response. The second element is a torsional spring-like bending element which gives the transverse bending response. D'Alembert principle is directly used to derive the system's equations of motion by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to determine the flexible deformations of the element and to extract those deformations from the total element motion. The equations of motion are solved along with constraint equations using a direct iterative integration scheme. Two numerical examples which were presented in earlier literature are solved to demonstrate the features and accuracy of the new method.     

火炮多柔体系统动力学的自动建模技术

本文介绍了火炮多柔体系统动力学的自动建模技术,包括火炮多体系统拓扑结构的自动识别、坐标系及自由度的自动确定、运动学公式的自动推导、载荷的自动施加、运动微分方程的自动组集和自动求解等。建模过程的自动化避免了繁琐的人工推导,并且可实现模型的通用性,从而可在计算机上方便地对任意类型火炮的发射过程进行仿真,有效地用于火炮设计。     

APPLICATION OF TOPOLOGICAL OPTIMIZATION TECHNIQUES TO STRUCTURAL CRASHWORTHINESS

The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density. Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored. The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.     

基于绝对坐标法的柴油机曲轴柔性多体系统的动力学仿真

该文基于柔性多体动力学理论,在自主研发的多体系统程序中,建立了某大型船用柴油机曲轴的柔性多体动力学仿真模型。其中采用基于绝对节点坐标的三维实体单元和基于有限段法的梁单元分别对曲柄和主轴颈进行建模,利用约束方程将发动机曲柄连杆机构的各部件进行组装,并考虑了轴承的弹性和非线性。对曲轴进行了约束模态分析和动力学仿真分析,计算了主轴承的载荷和轴颈的位移,得到了曲轴的动应力分布规律并进行了其强度校核。结果表明基于绝对节点坐标法的柔性多体系统的动力学建模和仿真计算的实现为柴油机的改进和设计提供了理论依据。     

基于二阶常微分方程的多体系统动力学设计灵敏度分析的伴随变量方法

针对二阶常微分方程描述的多体动力学模型和通用积分形式的目标函数,通过引入伴随变量,系统地推导了多体系统动力学设计灵敏度分析计算公式,避免了直接微分方法中广义坐标及其各阶导数对设计参数偏微分的计算,在设计参数较多的情况下提高了计算效率。又将目标函数及其导数积分形式的计算转化为微分方程的初值问题,进一步提高了计算效率和精度。文末给出一个平面机械臂模型算例。     

多体动力学热-结构耦合圆管单元及其应用

航天器柔性附件在突加太阳辐射热载荷作用下的热诱发振动会严重影响航天器的正常工作。航天器是典型的多体系统;部件间的相互作用会严重影响航天器的热诱发振动响应,因而有必要使用多体系统动力学的方法对此进行研究。该文在柔性多体系统动力学框架内,推导建立了一种考虑辐射换热的热-结构耦合圆管单元。温度变化会使圆管单元产生轴向伸缩和横向弯曲;同时,在给定辐射热流作用下,圆管单元受热条件与其姿态和变形相关。使用该圆管单元、刚体单元和柔性体单元可以实现多体系统动力学热-结构耦合分析。该文的方法首先用于哈勃太空望远镜太阳能电池板简化模型的热诱发振动分析,所得结果与文献结果吻合良好。然后,该文研究了由本体、动量轮、柔性支撑杆和端部质量组成的航天器在突加辐射热流作用下的振动响应。结果表明：各部件间的相互作用会对航天器的热诱发振动响应产生显著影响。     

A NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF VEHICLES MOVING ON FLEXIBLE STRUCTURES HAVING GAPS

A numerical method is presented for the dynamic analysis of vehicles moving on flexible structures which contain gaps. The Lagrange multipliers associated with the kinematic constraints of the vehicle components and the contact forces between the rigid wheels of the vehicle and the flexible structures are simultaneously computed with the solutions of the equations of motion by using the iterative schemes. On the kinematic joints and on the possible contact points the velocity and acceleration constraints as well as the displacement constraints are satisfied by the monotone reductions of the corresponding error vectors. And a well-developed simple one-step time integration of ordinary differential equation is employed for the solution of the equations of motion. Convergences of the iterative schemes are analysed and numerical simulations are conducted. © 1997 by John Wiley & Sons, Ltd.     

HT120点焊机器人柔性臂动力学和强度分析

利用多体动力学分析软件ADAMS,直接从三维CAD模型中获取HT120点焊机器人的几何形状、质量分布和转动惯量等重要信息。在此基础上,适当添加约束、力和运动关系,建立了HT120点焊机器人的数字虚拟样机模型。然后进行了动力学仿真,并将机器人小臂等关键部件设为柔性体,利用有限元软件研究小臂动力学仿真过程中的应力分布情况,对造型设计,结构优化以及疲劳分析提供了参考。     

鲁棒优化设计方法在结构动力学中的应用

在传统的静力学鲁棒优化设计基础上,考虑时间t参数,通过优化系统目标函数和约束条件的鲁棒性,将鲁棒优化设计方法运用在动力学问题中。通过一个主系统的质量和刚度均有微小波动的二自由度模型减振器设计算例,与传统的优化设计方法相比,显示了鲁棒优化设计的优越性,能使结构具有更稳定的性能。     

带有可伸展平动附件多柔体簇系统动力学拟变分原理及其应用

应用混合坐标法对多柔体簇系统进行运动学描述,得到附件和根体的动能,建立带有可伸展平动附件多柔体簇系统动力学拟变分原理。应用对合变换,得到两类变量的多柔体簇系统动力学拟变分原理。并推导其拟驻值条件对变分原理进行检验。最后,应用多柔体簇系统动力学拟Hamilton原理的拟驻值条件建立空间飞行器附件振动偏微分方程。     

FLEXIBLE MECHANISMS THROUGH NATURAL COORDINATES AND COMPONENT SYNTHESIS: AN APPROACH FULLY COMPATIBLE WITH THE RIGID CASE

In this paper, a new method for the dynamic simulation of mechanisms with flexible bodies is presented. The principal object of this work is to define the flexible bodies based on the modelization technique developed for rigid bodies using ‘natural co-ordinates’. In the rigid case, each body is defined by means of the Cartesian co-ordinates of some of its points and the Cartesian components of some of its unit vectors, which are pointed in the direction of the pairs axis that connect the body to its neighbours. In the flexible case, more variables are needed to define each body: on the one hand, two additional unit vectors are considered, rigidly attached to an already existing one, constituting a rigid orthogonal triedron, that will become the local reference frame of the body and on the other, amplitudes of static and dynamic modes, corresponding to component synthesis with fixed boundaries, are considered. There are an infinite number of dynamic modes, so that the analyst should make a selection of the most relevant ones for each problem; their amplitudes will be added to the body variables. However, there are a finite number of static modes: three for each point, except for the local frame origin, and two for each unit vector, except for the three that define the local frame; static modes amplitudes will not increase the number of body variables, since they may be expressed as the difference between the values of the points in local co-ordinates (respectively, the values of the unit vectors) in a body deformed configuration and their values in the undeformed one, that is, they may be expressed in terms of the co-ordinates of points and components of unit vectors that already define the body. This idea leads to a totally new dynamic formulation.     

AN OPTIMAL DESIGN SCHEME WITH APPLICATION TO TANKER TRANSVERSE STRUCTURE

There is considerable interest at the present time in the development of rational approaches to the design of ship structure. Particularly important is the design of structure for large oil tankers. These ships now represent about half the world's demand for tonnage and the increase in their size rapidly outstrips traditional evolutionary design methods. In Section 2 of the paper the development of a design scheme for ship structure is described. Broadly the system consists of a finite element analysis routine linked to an optimization algorithm. In Section 3 detailed results are presented for an application of the scheme to a particular tanker transverse problem. In Section 4 the sensitivity of the optimum design with respect to changes in certain key parameters of the design problem is investigated. In Section 5 some alternative ways of using the design scheme are discussed.     

LAGRANGEAN RELAXATION AND SUBGRADIENT OPTIMIZATION APPLIED TO OPTIMAL DESIGN WITH DISCRETE SIZING

The discrete sizing problem in optimal design is adressed. Lagrangean dual approaches earlier published are briefly reviewed and it is noted that quite sophisticated procedures have been used to solve the dual problems. The simple concept of Lagrangean relaxation combined with subgradient optimization and Lagrangean heuristics has, however, not been applied to the discrete sizing problem. In this paper a scheme based on this concept is described and tested on some small problems. The results indicate that subgradient optimization is completely capable of solving the dual problem. Moreover it is possible to devise heuristics that construct feasible solutions to the original problem, using the Lagrangean subproblem solution.     

具有形状和应力约束的连续体结构拓扑优化及其在框架结构设计中的应用

本文研究了在形状和应力约束下的连续体结构拓扑优化问题,采用满应力法求解保证了应力约束的满足;根据对形状的要求,固定部分单元不被删除,强迫最优拓扑满足设计要求。对框架结构进行了计算,结果表明了算法的正确性。     

基于分层设计变量的复合材料层合板优化设计及灵敏度分析

在复合材料层合板的结构优化设计中,提出分层设计变量的优化方法以满足实际工程需要。在结构位移、自振频率和屈曲临界荷载灵敏度分析中,给出了刚度矩阵对分层厚度和分层角度设计变量的灵敏度计算公式,考虑了分层厚度变化引起层合板对称中心的改变,保证了计算准确性。数值算例验证了灵敏度算法的精度,应用实例显示了分层设计变量方法的实用性。