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1.
刘铖  胡海岩 《力学学报》2021,53(1):213-233
多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group, LFLG),讨论如何发展一套新的多柔体系统动力学建模和计算方法体系, 具体内容包括:基于局部标架的梁、板壳单元,适用于长时间历程计算的多柔体系统碰撞动力学积分算法,结合区域分解技术的大规模多柔体系统动力学并行求解器, 以及若干验证性算例.上述基于李群局部标架的方法体系可在计算中消除刚体运动带来的几何非线性问题,使柔体系统的广义惯性力、广义弹性力及其雅可比矩阵满足刚体运动的不变性,使多柔体系统动力学与大变形结构力学相互统一,有望推动新一代多柔体系统动力学建模和计算软件的发展.   相似文献   

2.
多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group, LFLG),讨论如何发展一套新的多柔体系统动力学建模和计算方法体系,具体内容包括:基于局部标架的梁、板壳单元,适用于长时间历程计算的多柔体系统碰撞动力学积分算法,结合区域分解技术的大规模多柔体系统动力学并行求解器,以及若干验证性算例.上述基于李群局部标架的方法体系可在计算中消除刚体运动带来的几何非线性问题,使柔体系统的广义惯性力、广义弹性力及其雅可比矩阵满足刚体运动的不变性,使多柔体系统动力学与大变形结构力学相互统一,有望推动新一代多柔体系统动力学建模和计算软件的发展.  相似文献   

3.
带约束非线性多体系统动力学方程数值分析方法   总被引:1,自引:0,他引:1  
Lagrange方法是建立带约束多体系统动力学方程的普遍方法之一 ,其方程的形式为微分 代数方程组 ,数值计算与数值分析是研究多体系统动力学特性的重要方法。本文利用缩并法给出了带约束多体系统动力学方程的隐式数值计算方法和Lyapunov指数的计算方法。将数值仿真、Lya punov指数计算和Poincare映射有机结合 ,分析非线性多体系统动力学行为。通过一个算例 ,说明该方法的有效性  相似文献   

4.
富立  胡鸿奎  富腾 《力学学报》2017,49(5):1115-1125
基于非光滑动力学方法的多体系统接触碰撞分析是目前多体系统动力学的研究热点.本文采用牛顿-欧拉方法建立多体系统接触、碰撞问题的动力学模型,给出一种牛顿-欧拉型线性互补公式.该建模方法与目前一般采用的拉格朗日建模方法的不同之处是约束条件中除了库仑摩擦、单边约束之外还含有光滑等式约束.在建立系统动力学模型时,首先解除摩擦约束和单边约束得到原系统对应的基本系统.牛顿-欧拉方法采用最大数目坐标建立基本系统的动力学方程,由于坐标不相互独立,因此基本系统中带有等式约束,其数学模型为一组微分代数方程.借助约束雅可比矩阵,在基本系统微分代数方程中添加摩擦接触和单边约束对应的拉氏乘子,就可以得到系统全局运动的具有变拓扑结构特征的动力学方程,再结合非光滑约束互补条件便可构成完备的系统动力学模型.完备的动力学模型由动力学微分方程以及等式约束和不等式约束组成.线性互补公式采用分块矩阵形式进行推导,简化了推导过程.数值计算采用基于线性互补的时间步进算法.时间步进算法是目前流行的非光滑数值算法,其突出特点是可以免去数值积分中繁琐的事件检测过程,而数值积分过程中通过对线性互补问题的求解可以确定系统的触-离状态.通过对典型的曲柄滑块间隙机构进行数值分析,验证本文方法的有效性.  相似文献   

5.
可展桁架结构展开过程分析   总被引:2,自引:0,他引:2  
提出了一种分析构架式结构展开过程的有效算法。基于含多余广义坐标的动力学普遍方程 ,利用约束雅可比矩阵的零空间基引入一组准速率 ,得到独立的展开过程分析的动力学微分方程。为提高展开模拟的数值精度 ,文中提出了一种控制展开过程几何违约、速度违约和能量违约的数值稳定算法。该算法求解效率高 ,能和任意数值积分方法结合使用 ,能分析大型的构架式可展结构的展开过程  相似文献   

6.
在多体系统动力学正则方程的基础上建立了平面多体系统正则方程的隐式数值算法。利用平面运动的特性,对正则方程进行了简化,导出了该方程的Jacobi矩阵的一般表达式,给出了Runge-Kuta多体系统动力学方程隐式数值计算方法。算例表明,该方法是一种计算速度和精度均理想的数值方法。  相似文献   

7.
多体系统Lagrange方程数值算法的研究进展   总被引:1,自引:0,他引:1  
Lagrange方法是建立多体系统动力学方程的普遍方法之一,其方程的形式为常微分方程组或微分 - 代数方程组,数值计算与数值分析是研究多体系统动力学特性的重要方法.本文简要介绍了多体系统动力学方程的第一、二类Lagrange方程和修正的Lagrange方程的基本形式及这些方程的正则形式,着重介绍了正则方程在数值计算中的特点,就多体系统Lagrange方程的隐式算法、辛算法和多体系统动力学特性的数值分析方法(包括数值仿真、Poincar'e映射和Lyapunov指数的计算方法)的研究现状进行了综述.  相似文献   

8.
约束多体系统独立广义坐标的数值选取   总被引:1,自引:1,他引:0  
多体系统的完整约束定义了一个嵌入到欧氏空间的微分流型,多体系统独立的广义坐标选取问题等价于该流型的坐标选取问题。据此,本文提出了一种新的独立广义坐标数值选取理论,可将多体系统的微分-代数混合型运动方程转化为较易求解的纯微分方程,并且不以求解非线性方程组作为必须的手段。  相似文献   

9.
多柔体系统数值分析的模型降噪方法   总被引:2,自引:0,他引:2  
齐朝晖  曹艳  王刚 《力学学报》2018,50(4):863-870
多柔体系统的动力学方程通常是一组刚性微分方程, 目前普遍采用的刚性微分方程数值解法主要通过数值阻尼滤除系统响应中的高频分量, 其求解效率难以令人满意. 为了降低多柔体系统动力学方程的刚性, 从而可采用ODE45等常规微分方程求解器进行求解, 研究了在建模过程中滤除高频振荡分量的方法. 在以当前时刻为起点的短时间内对柔性体的应力进行均匀化, 用均匀化后的应力计算柔性体的变形虚功率, 由此得到的系统动力学方程的解中不含过高频率的弹性振动, 并且可以通过调节均匀化时间区间的长度参数控制滤波的范围. 数值算例表明: 这种模型降噪方法的计算效率和精度均不低于刚性微分方程求解器, 并且在刚性微分方程求解器失效的情况下模型降噪方法仍有良好的精度和效率. 本文所提的模型降噪方法可成为求解多柔体系统动力学方程的新途径.   相似文献   

10.
多柔体系统的动力学方程通常是一组刚性微分方程,目前普遍采用的刚性微分方程数值解法主要通过数值阻尼滤除系统响应中的高频分量,其求解效率难以令人满意.为了降低多柔体系统动力学方程的刚性,从而可采用ODE45等常规微分方程求解器进行求解,研究了在建模过程中滤除高频振荡分量的方法.在以当前时刻为起点的短时间内对柔性体的应力进行均匀化,用均匀化后的应力计算柔性体的变形虚功率,由此得到的系统动力学方程的解中不含过高频率的弹性振动,并且可以通过调节均匀化时间区间的长度参数控制滤波的范围.数值算例表明:这种模型降噪方法的计算效率和精度均不低于刚性微分方程求解器,并且在刚性微分方程求解器失效的情况下模型降噪方法仍有良好的精度和效率.本文所提的模型降噪方法可成为求解多柔体系统动力学方程的新途径.  相似文献   

11.
In computational multibody algorithms, the kinematic constraintequations that describe mechanical joints and specified motiontrajectories must be satisfied at the position, velocity andacceleration levels. For most commonly used constraint equations, onlyfirst and second partial derivatives of position vectors with respect tothe generalized coordinates are required in order to define theconstraint Jacobian matrix and the first and second derivatives of theconstraints with respect to time. When the kinematic and dynamicequations of the multibody systems are formulated in terms of a mixedset of generalized and non-generalized coordinates, higher partialderivatives with respect to these non-generalized coordinates arerequired, and the neglect of these derivatives can lead to significanterrors. In this paper, the implementation of a contact model in generalmultibody algorithms is presented as an example of mechanical systemswith non-generalized coordinates. The kinematic equations that describethe contact between two surfaces of two bodies in the multibody systemare formulated in terms of the system generalized coordinates and thesurface parameters. Each contact surface is defined using twoindependent parameters that completely define the tangent and normalvectors at an arbitrary point on the body surface. In the contact modeldeveloped in this study, the points of contact are searched for on lineduring the dynamic simulation by solving the nonlinear differential andalgebraic equations of the constrained multibody system. It isdemonstrated in this paper that in the case of a point contact andregular surfaces, there is only one independent generalized contactconstraint force despite the fact that five constraint equations areused to enforce the contact conditions.  相似文献   

12.
基于可倾瓦径向滑动轴承瓦块的扰动特性,提出了计算轴承完整动力系数的数学解析模型。在由单块瓦和轴颈构成的子系统上建立局部动坐标参考系,全局广义位移向量可以通过简练的步骤转换为局部动坐标系下轴颈的位移向量,利用求解固定瓦轴承动力特性的方法求得的局部动坐标系下的油膜力又可以精确地转换为全局坐标系下的表达形式,全局坐标系下的油膜力向量关于广义位移和广义速度的Jocabian矩阵形成轴承的完整动力特性系数;利用Newton-Raphson方法同时求解瓦块和轴颈在给定的静态载荷下的平衡位置,其中所需用到的系数矩阵恰好为轴承油膜力关于广义位移的Jocabian矩阵的负值,在得到平衡位置的同时可以获得轴承完整的刚度和阻尼矩阵。数值算例证明了此方法的有效性。  相似文献   

13.
14.
Deformable components in multibody systems are subject to kinematic constraints that represent mechanical joints and specified motion trajectories. These constraints can, in general, be described using a set of nonlinear algebraic equations that depend on the system generalized coordinates and time. When the kinematic constraints are augmented to the differential equations of motion of the system, it is desirable to have a formulation that leads to a minimum number of non-zero coefficients for the unknown accelerations and constraint forces in order to be able to exploit efficient sparse matrix algorithms. This paper describes procedures for the computer implementation of the absolute nodal coordinate formulation' for flexible multibody applications. In the absolute nodal coordinate formulation, no infinitesimal or finite rotations are used as nodal coordinates. The configuration of the finite element is defined using global displacement coordinates and slopes. By using this mixed set of coordinates, beam and plate elements can be treated as isoparametric elements. As a consequence, the dynamic formulation of these widely used elements using the absolute nodal coordinate formulation leads to a constant mass matrix. It is the objective of this study to develop computational procedures that exploit this feature. In one of these procedures, an optimum sparse matrix structure is obtained for the deformable bodies using the QR decomposition. Using the fact that the element mass matrix is constant, a QR decomposition of a modified constant connectivity Jacobian matrix is obtained for the deformable body. A constant velocity transformation is used to obtain an identity generalized inertia matrix associated with the second derivatives of the generalized coordinates, thereby minimizing the number of non-zero entries of the coefficient matrix that appears in the augmented Lagrangian formulation of the equations of motion of the flexible multibody systems. An alternate computational procedure based on Cholesky decomposition is also presented in this paper. This alternate procedure, which has the same computational advantages as the one based on the QR decomposition, leads to a square velocity transformation matrix. The computational procedures proposed in this investigation can be used for the treatment of large deformation problems in flexible multibody systems. They have also the advantages of the algorithms based on the floating frame of reference formulations since they allow for easy addition of general nonlinear constraint and force functions.  相似文献   

15.
A method is presented for formulating and numerically integrating index 0 differential-algebraic equations of motion for multibody systems with holonomic and nonholonomic constraints. Tangent space coordinates are defined in configuration and velocity spaces as independent generalized coordinates that serve as state variables in the formulation. Orthogonal dependent coordinates and velocities are used to enforce position, velocity, and acceleration constraints to within specified error tolerances. Explicit and implicit numerical integration algorithms are presented and used in solution of three examples: one planar and two spatial. Numerical results verify that accurate results are obtained, satisfying all three forms of kinematic constraint to within error tolerances embedded in the formulation.  相似文献   

16.
The solution of the constrained multibody system equations of motion using the generalized coordinate partitioning method requires the identification of the dependent and independent coordinates. Using this approach, only the independent accelerations are integrated forward in time in order to determine the independent coordinates and velocities. Dependent coordinates are determined by solving the nonlinear constraint equations at the position level. If the constraint equations are highly nonlinear, numerical difficulties can be encountered or more Newton–Raphson iterations may be required in order to achieve convergence for the dependent variables. In this paper, a velocity transformation method is proposed for railroad vehicle systems in order to deal with the nonlinearity of the constraint equations when the vehicles negotiate curved tracks. In this formulation, two different sets of coordinates are simultaneously used. The first set is the absolute Cartesian coordinates which are widely used in general multibody system computer formulations. These coordinates lead to a simple form of the equations of motion which has a sparse matrix structure. The second set is the trajectory coordinates which are widely used in specialized railroad vehicle system formulations. The trajectory coordinates can be used to obtain simple formulations of the specified motion trajectory constraint equations in the case of railroad vehicle systems. While the equations of motion are formulated in terms of the absolute Cartesian coordinates, the trajectory accelerations are the ones which are integrated forward in time. The problems associated with the higher degree of differentiability required when the trajectory coordinates are used are discussed. Numerical examples are presented in order to examine the performance of the hybrid coordinate formulation proposed in this paper in the analysis of multibody railroad vehicle systems.  相似文献   

17.
In this paper, a new approach for dynamic analysis of the flexible multibody manipulator systems is described. The organization of the computer implementations which are used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute, joint and elastic coordinates is discussed. The main processor source code consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic coordinates. At the same time, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The absolute, joint and elastic accelerations are integrated forward in time using direct numerical integration methods. The absolute positions and velocities can then be determined using the kinematic relationships. The flexible 2-DOF double-pendulum and spatial manipulator systems are used as illustrated examples to demonstrate and verify the application of the computational procedures discussed in this paper.  相似文献   

18.
带约束多体系统动力学方程的隐式算法   总被引:3,自引:0,他引:3  
研究了带约束多体系统隐式算法,用子矩阵的形式推导出了多体系统正则方程的Jacobi矩阵,它适用于多种隐式算法并给出了隐式Runge-Kutta算法,最后用一算例表明了隐式算法的计算效率和精度明显优于算法。  相似文献   

19.
This paper presents a?new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a?uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations.  相似文献   

20.
多体系统Lagrange方程数值算法的研究进展   总被引:7,自引:3,他引:4  
王琪  陆启韶 《力学进展》2001,31(1):9-17
Lagrange方法是建立多体系统动力学方程的普遍方法之一, 其方程的形式为常微分方程组或微分-代数方程组,数值计算与数 值分析是研究多体系统动力学特性的重要方法。本文简要介绍了多 体系统动 力学方程的第一、二类Lagrange方程和修正的Lagrange方 程的基本形式及这些方程的正则形式,着重介绍了正则方程在数值 计算中的特点,就多体系统Lagrange方程的隐式算法、辛算法和多 体系统动力学特性的数值分析方法(包括数值仿真、 Poincarè映射 和Lyapunov指数的计算方法)的研究现状进行了综述。  相似文献   

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