多体系统动力学的常用积分器算法

本文将以单步法中的广义 α族积分器和多步法中的BDF族积分器为主要讨论对象,详细介绍大型多体系统动力学软件中常见类型的积分器的算法细节.每族积分器都给出了不止一套计算公式,而且其对应求解微分代数方程组(DAE)的index可以为1、2或者3.除此以外,本文还着重介绍了微分代数方程组的误差估计、变阶变步长策略等关键技术;...     

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.     

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。     

多体动力学优化的并行SQP方法

并行计算的发展大大提高计算机的计算效率,降低计算时间.针对多体动力学的优化问题,分析了求解灵敏度的三种方法的并行性,建立了有限差分法与直接微分法的并行算法.同时采用并行Armijo线性搜索,构成了完整的并行序列二次规划(SQP)算法.将上述算法应用到曲柄滑块的优化中,并与串行SQP算法进行了比较,证实了并行SQP算法可以大大降低计算时间.上述研究为多体动力学优化提供了一种并行求解思路.     

萤火虫算法求解多体系统动力学微分-代数方程

针对多体系统动力学微分-代数方程求解问题,研究基于萤火虫算法的求解方法.首先将广义坐标和广义速度进行Lagrange插值,结合Gauss数值积分方法,将微分-代数方程求解问题转化成求解最优化问题.然后用萤火虫算法对问题进行优化求解.最后,通过对平面双连杆机械臂的多体系统仿真实验,验证了萤火虫算法在求解动力学方程中既保持...     

基于隐式微分/代数方程的多体系统动力学设计灵敏度分析方法

基于一般性的积分型目标函数、隐式相容初始条件及终止时刻表达式,系统建立了含设计参数的用隐式微分／代数方程表达的多体系统动力学设计灵敏度分析的直接微分方法和伴随变量方法．为降低目标函数及其对设计变量导数的计算复杂性。将其积分形式的计算转化为微分形式．所得到的结果可方便地应用于高效的间接最优化设计方法．最后通过采用绝对坐标建模的平面两连杆机械臂模型对该方法进行了验证．     

非线性微分-代数系统的输出反馈镇定:基于线性采样控制

对满足指数1和线性增长条件的非线性微分-代数系统,本文证明其采样输出反馈镇 定控制问题可解.首先,给出一个线性显式非初始化状态观测器设计;然后,构造出线性的采样输出 反馈控制器,使得整个闭环系统渐近稳定.仿真结果表明了所提控制方法的有效性.     

指标约简中Gear算法的实现

基于组件的建模有时会产生高指标的微分代数方程(DAE),不能直接求解,需要进行指标约筒.Gear方法是一个经典的指标约简方法,对Gear方法从理论上进行了说明和分析.对于一类具有特殊结构的DAE,提出了Gear方法实现中的优化策略,以降低指标约简后得到的方程规模.把优化后的实现与未优化的实现进行了比对,实验结果表明,优化过的实现方法针对这类特殊的问题确实达到了更好的约简效果.     

微分代数系统的数值仿真算法

介绍了微分代数系统ＤＡＥ的基本概念及仿真算法,特别指出了用ＢＤＦ方法求解高指标常系数线性ＤＡＥ系统时的数值稳定性缺陷。最后,针对飞行器轨道约束实时控制问题,给出了３阶收敛的代数约束算法。     

求解非线性方程组系统的改进差分进化算法

针对基于邻域拥挤的差分进化算法求解非线性方程组系统时存在丢根、陷入局部最优等不足,提出一种改进的差分进化算法.首先,提出一种个体预判机制,判断当前群体的个体属于哪一类,并分别采取不同的操作;其次,设计一种新的混合差分变异算子,以增强算法跳出局部最优的能力;然后,改进外部存档策略,延长了父代优秀个体在种群的保存时间,有利于搜索该优秀个体附近的根.在所选测试函数集上的实验结果表明,所提出的算法能有效搜索到非线性方程组系统的多个根,并与当前5种算法进行对比,所提出算法在找根率和成功率上更具优越性.     

Simulation of Motion of Constrained Multibody Systems Based on Projection Operator

This paper presents an efficient dynamic formulation for solvingDifferential Algebraic Equations (DAE) by using the notion of orthogonalprojection. Firstly, the constraint equations are expressed explicitlyat acceleration level by using the notion of the orthogonal projection.Secondly, the Lagrangian multiplier is eliminated from the dynamicsequation by the projection operator. Then, the resultant equations areconsolidated into one equation which explicitly correlates theacceleration to the generalized force through a so-called constraint mass matrix. It is proved that the constraint mass matrix isalways invertible and hence the acceleration can be computed in aclosed-form manner even with the presence of redundant constraints or asingular configuration. The equation of motion is given explicitly in arelatively compact form, which can lead to computational efficiency. Italso has a useful physical interpretation, as the component of thegeneralized force contributing to motion dynamics is readily derivedform the formulation. Finally, results obtained from numericalsimulation of motion of a five-bar mechanism is documented.     

Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation

We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler-Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discuss a series of examples which utilize the explicit solutions to generate smooth surfaces that interpolate a given boundary configuration. We compare the speed of our explicit solution scheme with the solution arising from directly solving the associated linear system.     

An Implicit Runge–Kutta Method for Integration of Differential Algebraic Equations of Multibody Dynamics

When performing dynamic analysis of a constrained mechanical system, aset of index 3 Differential Algebraic Equations (DAE) describes the timeevolution of the model. This paper presents a state space DAE solutionframework that can embed an arbitrary implicit Ordinary DifferentialEquations (ODE) code for numerical integration of a reduced set of statespace ordinary differential equations. This solution framework isconstructed with the goal of leveraging with minimal effort establishedoff the shelf implicit ODE integrators for efficiently solving the DAEof multibody dynamics. This concept is demonstrated by embedding awell-known public domain singly diagonal implicit Runge–Kutta code inthe framework provided. The resulting L-stable, stiffly accurateimplicit algorithm is shown to be two orders of magnitude faster than astate of the art explicit algorithm when used to simulate a stiffvehicle model.     

Parallel Implementation of a Low Order Algorithm for Dynamics of Multibody Systems on a Distributed Memory Computing System

In this paper, a new hybrid parallelisable low order algorithm, developed by the authors for multibody dynamics analysis, is implemented numerically on a distributed memory parallel computing system. The presented implementation can currently accommodate the general spatial motion of chain systems, but key issues for its extension to general tree and closed loop systems are discussed. Explicit algebraic constraints are used to increase coarse grain parallelism, and to study the influence of the dimension of system constraint load equations on the computational efficiency of the algorithm for real parallel implementation using the Message Passing Interface (MPI). The equation formulation parallelism and linear system solution strategies which are used to reduce communication overhead are addressed. Numerical results indicate that the algorithm is scalable, that significant speed-up can be obtained, and that a quasi-logarithmic relation exists between time needed for a function call and numbers of processors used. This result agrees well with theoretical performance predictions. Numerical comparisons with results obtained from independently developed analysis codes have validated the correctness of the new hybrid parallelisable low order algorithm, and demonstrated certain computational advantages.