机械系统虚拟样机平台建模技术与动力学求解研究
|
摘要
机械系统虚拟样机技术是计算机辅助分析的重要分支之一,对缩短产品设计周期,降低产品开发成本,提高产品设计质量均有着显著意义。借助这项技术,可通过建立机械系统数字模型,模拟现实环境下机械系统的运动学和动力学特性。本文从虚拟样机建模和动力学数值求解等方面对机械系统虚拟样机技术进行了深入系统的研究。
首先阐述了机械系统虚拟样机技术的基本概念和体系结构,提出一个支持模型数据共享和求解器兼容的软件平台框架。通过对模型元素表达和管理进行研究,归纳了模型元素关联关系和模型操作传播方式,并据此提出了模型元素更新机制,以实现模型编辑时的内部关系一致性维护与管理。
机械系统虚拟样机建模是样机动力学分析的基础。为了便于模型修改、融合领域工程设计知识并支持功能优化分析,提出了适用于机械系统建模的参数化技术。通过分析机械系统模型参数类型、参数特性和工程约束种类,结合元素关联关系,建立有向二分图表达的模型参数完整约束网络。根据约束网络描述的参数偏序关系,给出了模型参数推理求解序列生成方法,并结合模型元素更新机制,实现样机模型参数化驱动。
针对机械系统虚拟样机建模效率低、模型重用困难等问题,提出了面向复杂机械系统建模的子系统技术。基于机械系统模型结构特点,引入虚部件定义子系统外部拓扑连接关系,通过主控参数封装模型设计知识和内部参数信息,使用子系统坐标系解耦空间位姿关系,从而建立自顶向下的层次化子系统模型结构;根据层次结构特点和主控参数关联关系,提出了子系统装配算法和参数化求解算法,并在此基础上讨论了模型重用和子系统建模流程。
机械系统虚拟样机技术的主要功能是实现样机模型的运动特性仿真分析。为提高运动方程组装效率,在综合全局建模法和拓扑建模法优点的基础上,提出了运动方程混合建模方法。通过分析相邻构件的位姿关系,推导了系统运动方程递归关系式和约束雅可比矩阵;然后根据约束对运动方程求解效率的影响,建立了模型拓扑带权图,并研究了闭环系统最大求解效率派生树生成算法和无根开环系统基点选取算法。基于模型拓扑结构和递归关系式,推导了笛卡尔坐标空间到铰坐标空间的转换关系式,实现了递归组装运动方程的混合建模算法。
分析了机械系统动力学数值求解存在的主要问题。提出切空间扰动法甄别系统冗余与矛盾约束。通过扩展惩罚因子法,处理构形奇异和变拓扑情况的动力学数值求解,并伴随广义参数投影校正,避免约束违约。对于存在刚性特性的机械系统,为了提高数值算法稳定性,直接采用隐式积分格式离散运动方程,并推导了近似雅可比矩阵和方程残量计算公式,提高算法效率。考虑到整体求解算法效率低,求解并行差的问题,基于模型拓扑耦合关系,研究了子系统综合和分治算法。
最后,在上述理论研究成果的基础上,研制开发了机械系统虚拟样机软件平台—InteDyna,并给出了汽车建模和分析实例以验证本文研究内容的有效性和正确性。
As one of the important branches of computer aided engineering, mechanism system virtual prototyping (MSVP) is expected to reduce product design cycle with lower life-time cost, and has great significance to improve product quality. In virtue of this technology, engineers can simulate the characteristic of kinematics and dynamics of mechanical system on realistic condition by its digit model. In the dissertation, several key issues of developing an applicable MSVP including prototype modeling and dynamic numerical solution are addressed.
At first, the basis concept and main task of MSVP are discussed, an architecture of software platform is proposed which can be compatible with various numerical solvers and support data exchange with different software. Furthermore, the associated relationships of model elements and the operation spreading are also concluded according to the model representation, an event-driven update mechanism is presented to implement model management and element relationship maintenance.
Virtual prototype modeling is a basic problem in dynamic simulation of mechanism system. To facilitate model modification, integrate engineering design knowledge and support optimization analysis of model, a parametric modeling technique for MSVP is studied. According to the parameter trait, engineering constraint and associated relationship, a directed bi-partite graph is utilized to express parameter constraints. In terms of the partially ordered relationship of parameters, a solving sequence of reasoning is formulated. With the update mechanism, a parametric modeling method is proposed.
To improve modeling efficiency and reuse of models, subsystem modeling techniques for complicated mechanism systems are addressed. According to the characteristic of model structure, virtual parts are presented to define the topological relationship among the subsystems, main control parameters are introduced to encapsulate the design knowledge and the internal parameters, the reference frames of subsystem are used to position. Consequently, a top-down hierarchical architecture is constructed. In terms of the hierarchical architecture and main control parameters, the algorithms are also presented to assemble the subsystems and solve the parameter constraints. Based on these techniques, the complicated model can be decomposed into smaller and simpler subsystems to construct and reuse.
The kinematics and dynamics analysis is the essential function of MSVP. To improve the computationally efficiency of assembling equation of motion, a hybrid algorithm is presented by combination of global method and topological method. Firstly, the recursive formulations and Jacobian matrix are obtained by the kinematics relationship between reference frames of adjacent bodies, and then, according to the computational effect of cut joint, a weight graph is constructed to represent the topology of model. Based on this weight graph, the algorithms of the spanning tree generation with best efficiency and selection of base body are also proposed. Furthermore, the transformation formulation of Cartesian coordinates space to joint coordinates space is developed by model topology and recursive formulation, and an hybrid algorithm for assembling equation of motion is obtained.
The main problems of dynamic numerical solution of mechanism system are discussed. Firstly, a perturbation on tangent-plane algorithm is proposed to distinguish the redundant constraint, and then a modified penalty numerical method is applied to dynamic analysis of mechanism system with singular configuration and topology change. To eliminate the constraint violation, the project correction of general coordinates is utilized. For the system with stiffness characteristic, an implicit integration scheme is adopt to directly discrete the equation of motion. To improve the computational efficiency, the residual of equation and approximated Jacobian matrix are also computed by the recursive formulations. In the end, the subsystem synthesis algorithm and divide-and-conquer algorithm is also studied to improve the computational efficiency and parallel of dynamic analysis.
On the basis of the above proposed algorithms, a MSVP named InteDyna has been developed. Finally, the feasibility and validity for this research is testified using a whole vehicle modeling and simulation.
首先阐述了机械系统虚拟样机技术的基本概念和体系结构,提出一个支持模型数据共享和求解器兼容的软件平台框架。通过对模型元素表达和管理进行研究,归纳了模型元素关联关系和模型操作传播方式,并据此提出了模型元素更新机制,以实现模型编辑时的内部关系一致性维护与管理。
机械系统虚拟样机建模是样机动力学分析的基础。为了便于模型修改、融合领域工程设计知识并支持功能优化分析,提出了适用于机械系统建模的参数化技术。通过分析机械系统模型参数类型、参数特性和工程约束种类,结合元素关联关系,建立有向二分图表达的模型参数完整约束网络。根据约束网络描述的参数偏序关系,给出了模型参数推理求解序列生成方法,并结合模型元素更新机制,实现样机模型参数化驱动。
针对机械系统虚拟样机建模效率低、模型重用困难等问题,提出了面向复杂机械系统建模的子系统技术。基于机械系统模型结构特点,引入虚部件定义子系统外部拓扑连接关系,通过主控参数封装模型设计知识和内部参数信息,使用子系统坐标系解耦空间位姿关系,从而建立自顶向下的层次化子系统模型结构;根据层次结构特点和主控参数关联关系,提出了子系统装配算法和参数化求解算法,并在此基础上讨论了模型重用和子系统建模流程。
机械系统虚拟样机技术的主要功能是实现样机模型的运动特性仿真分析。为提高运动方程组装效率,在综合全局建模法和拓扑建模法优点的基础上,提出了运动方程混合建模方法。通过分析相邻构件的位姿关系,推导了系统运动方程递归关系式和约束雅可比矩阵;然后根据约束对运动方程求解效率的影响,建立了模型拓扑带权图,并研究了闭环系统最大求解效率派生树生成算法和无根开环系统基点选取算法。基于模型拓扑结构和递归关系式,推导了笛卡尔坐标空间到铰坐标空间的转换关系式,实现了递归组装运动方程的混合建模算法。
分析了机械系统动力学数值求解存在的主要问题。提出切空间扰动法甄别系统冗余与矛盾约束。通过扩展惩罚因子法,处理构形奇异和变拓扑情况的动力学数值求解,并伴随广义参数投影校正,避免约束违约。对于存在刚性特性的机械系统,为了提高数值算法稳定性,直接采用隐式积分格式离散运动方程,并推导了近似雅可比矩阵和方程残量计算公式,提高算法效率。考虑到整体求解算法效率低,求解并行差的问题,基于模型拓扑耦合关系,研究了子系统综合和分治算法。
最后,在上述理论研究成果的基础上,研制开发了机械系统虚拟样机软件平台—InteDyna,并给出了汽车建模和分析实例以验证本文研究内容的有效性和正确性。
As one of the important branches of computer aided engineering, mechanism system virtual prototyping (MSVP) is expected to reduce product design cycle with lower life-time cost, and has great significance to improve product quality. In virtue of this technology, engineers can simulate the characteristic of kinematics and dynamics of mechanical system on realistic condition by its digit model. In the dissertation, several key issues of developing an applicable MSVP including prototype modeling and dynamic numerical solution are addressed.
At first, the basis concept and main task of MSVP are discussed, an architecture of software platform is proposed which can be compatible with various numerical solvers and support data exchange with different software. Furthermore, the associated relationships of model elements and the operation spreading are also concluded according to the model representation, an event-driven update mechanism is presented to implement model management and element relationship maintenance.
Virtual prototype modeling is a basic problem in dynamic simulation of mechanism system. To facilitate model modification, integrate engineering design knowledge and support optimization analysis of model, a parametric modeling technique for MSVP is studied. According to the parameter trait, engineering constraint and associated relationship, a directed bi-partite graph is utilized to express parameter constraints. In terms of the partially ordered relationship of parameters, a solving sequence of reasoning is formulated. With the update mechanism, a parametric modeling method is proposed.
To improve modeling efficiency and reuse of models, subsystem modeling techniques for complicated mechanism systems are addressed. According to the characteristic of model structure, virtual parts are presented to define the topological relationship among the subsystems, main control parameters are introduced to encapsulate the design knowledge and the internal parameters, the reference frames of subsystem are used to position. Consequently, a top-down hierarchical architecture is constructed. In terms of the hierarchical architecture and main control parameters, the algorithms are also presented to assemble the subsystems and solve the parameter constraints. Based on these techniques, the complicated model can be decomposed into smaller and simpler subsystems to construct and reuse.
The kinematics and dynamics analysis is the essential function of MSVP. To improve the computationally efficiency of assembling equation of motion, a hybrid algorithm is presented by combination of global method and topological method. Firstly, the recursive formulations and Jacobian matrix are obtained by the kinematics relationship between reference frames of adjacent bodies, and then, according to the computational effect of cut joint, a weight graph is constructed to represent the topology of model. Based on this weight graph, the algorithms of the spanning tree generation with best efficiency and selection of base body are also proposed. Furthermore, the transformation formulation of Cartesian coordinates space to joint coordinates space is developed by model topology and recursive formulation, and an hybrid algorithm for assembling equation of motion is obtained.
The main problems of dynamic numerical solution of mechanism system are discussed. Firstly, a perturbation on tangent-plane algorithm is proposed to distinguish the redundant constraint, and then a modified penalty numerical method is applied to dynamic analysis of mechanism system with singular configuration and topology change. To eliminate the constraint violation, the project correction of general coordinates is utilized. For the system with stiffness characteristic, an implicit integration scheme is adopt to directly discrete the equation of motion. To improve the computational efficiency, the residual of equation and approximated Jacobian matrix are also computed by the recursive formulations. In the end, the subsystem synthesis algorithm and divide-and-conquer algorithm is also studied to improve the computational efficiency and parallel of dynamic analysis.
On the basis of the above proposed algorithms, a MSVP named InteDyna has been developed. Finally, the feasibility and validity for this research is testified using a whole vehicle modeling and simulation.
引文
[1]熊光楞,李伯虎,柴旭东.虚拟样机技术.系统仿真学报, 2001, 13(1): 114~117
[2]刘小平等.虚拟样机及其相关技术研究和实践.机械科学与技术, 2003, 22(1): 235~238
[3]王国强,张进平,马若丁编著.虚拟样机技术及其在ADAMS上的实践.西安:西北工业大学出版社, 2002
[4]陈立平,张云清等.机械系统动力学分析及ADAMS应用教程.北京:清华大学出版社, 2005
[5]吴洪涛,熊有伦.机械工程中的多体系统动力学问题.中国机械工程, 2000, 11(6):608~610
[6]刘贤喜.机械系统虚拟样机仿真软件的实用化研究: [博士学位论文].北京:中国农业大学, 2001
[7] Wang G Gary. Definition and Review of Virtual Prototyping. Journal of Computing and Information Science in Engineering, 2002, 2(3): 232~236
[8]熊光楞,范文慧. 21世纪制造业的建模与仿真技术.系统仿真学报, 2004,16(9):1884~1886
[9] Michael J. Pratt. Virtual Prototyping and product Models in Mechanical Engineering. Gaithersburg: National Institute of Standards and Technology, 1995
[10] National Bureau of Standards. Initial Graphics Exchange Specification (IGES) 30. Technical report, National Bureau of Standards, 1986
[11] ISO. Product Data Representation and Exchange-Part 42: Integrated Generic Resource: Geometric and Topological Representation Technical Report ISO CD 10303-42, International Organization for Standardization (ISO), 1992
[12] Krause F L, Rieger E and Ulbrich A. Feature Processing as Kernel for Integrated CAE Systems. In Feature Modeling and Recognition in Advanced CAD/CAM Systems Vol II IFIP, Valenciennes, France, 1994:693~716
[13] De Martino T, Falcidieno B and Habinger S. Design and Engineering Process Integration through a Multiple View Intermediate Modeller in a Distributed Object-Oriented System Environment. Computer-Aided Design, 1998,30(6):427~452
[14]尹周平.面向虚拟原型的产品特征建模和可接近性分析: [博士学位论文].武汉:华中科技大学, 2000
[15]刘振宇,谭建荣等.面向虚拟装配的产品层次信息表达研究.计算机辅助设计与图形学学报,2001,13(3): 223~228
[16] Burdea.G and Coifet.P. Virtual Reality Technology. New York: John Wiley&Sons, 1994
[17] J.D.Foley. Interface for Advanced Computing. Scientific American,1987,257(4): 127~135
[18]王政.基于交互驱动的虚拟样机动力学建模技术研究与应用: [博士学位论文].浙江:浙江大学, 2005
[19] Fang Y and Liou F W. Virtual Prototyping of Mechanical Assemblies with Deformable Components. Journal of Manufacturing Systems,1997,16(3):211~219
[20] Jayaram S, Connacher H I and Lyons K W. Virtual Assembly using Virtual Reality Techniques. Computer-Aided Design, 1997, 29(8): 575~584
[21] De Sa A G and Zachmann G. Virtual Reality as a Tool for Verification of Assembly and Maintenance Process. Computers & Graphics, 1999, 23:389~403
[22] Gupta R, Whitney D and Zelter D. Prototyping and Design for Assembly Analysis using Multimodal Virtual Environments. Computer-Aided Design, 1997, 29(8):585-597
[23] Wuerger D and Gadh R. Virtual Prototyping of Die Design Part One: Theory and Formulation. Concurrent Engineering: Research and Application, 1997, 5(4):307~315
[24] Buck M. Immersive User Interaction within Industrial Virtual Environments. In: Dai F, editor. Virtual Reality for Industrial Applications, Computer Graphics and Applications. Berlin: Springer,1998:39~59
[25] Lehner V D, Defanti T A. Projects in VP: Distributed Virtual Reality:Supporting Reomte Collabration in Vehicle Design. IEEE Computer Graphics and Appplications, 1997, 17(2):13~17
[26]汪成为.灵境技术的理论、实现及应用.北京:清华大学出版社;南宁:广西科学技术出版社, 1993:156~190
[27]鲍劲松,金烨,蒋祖华等.虚拟环紧下给予舒适性的客车内饰设计.计算机集成制造系统, 2001,7(7):36~40
[28]张云清,高斯,李凌阳等.基于多体力学的车辆动力学控制系统仿真及优化.动力学与控制学报, 2007,5(1):68~74
[29]张云清,项俊,陈立平,孙营.整车多体动力学模型的建立、验证及仿真分析.汽车工程, 2006,28(3):287~291
[30]张云清,马开献,田强等.基于ADAMS和MATLAB协同仿真的四轮转向模糊控制策略研究.计算机集成制造系统, 2007, 13(6):1234~1240
[31]王其东,方锡邦等.基于虚拟样机技术的汽车钢板弹簧设计与分析研究.机械工程学报, 2001,37(12):63~66
[32]丁国富,邹益胜等.基于虚拟原型的机械多体系统建模可视化.计算机辅助设计与图形学学报, 2006,18(6):793~799
[33] Haug E J. Computer Aided Kinematics and Dynamics of Mechanical Systems. Vol.1 Basic Methods, Boston: Allyn and Bacon, 1989
[34]谭建荣,王政,刘振宇.基于可视化外部力/力矩隐喻工具的虚拟样机动力学交互分析方法.计算机学报, 2004,27(11):1464~1470
[35]丁国富,闫开印,张卫华等.面向虚拟样机设计的产品属性提取研究.计算机集成制造系统, 2006,12(1):14~20
[36] Paredis C J J, Diaz-Calderon A, Sinha R, Khosla P K. Composable models for simulation-based design. Engineering with Computers, 2001,17(2):112~128
[37]金伟新,肖田元,胡晓峰等.多层多视多体建模方法研究.计算机仿真, 2004, 21(7), 39~42
[38] Diaz-Calderon A, Paredis C J J, Khosla P K. Organization and Selection of Reconfigurable Models. Proceedings of the Winter Simulation Conference. New York, NY, USA:WSC ACM Press, 2000:386~393
[39]洪嘉振.计算多体系统动力学.北京:高等教育出版社,1999
[40]陆佑方.柔性多体系统动力学.北京:高等教育出版社,1996
[41] Schiehlen.W. Multibody System Dynamics: Roots and Perspectives. Multibody System Dynamics, 1997,1,149~188
[42] Schiehlen W. Multi-Body Systems Handbook. Berlin:Springer, 1990
[43] Critcbley.J.H and Anderson K.S. A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics. International Journal for Multi-Scale Computational Engineering,2003,1:181~199
[44] Hooker Margulies.G. The Dynamical Attitude Equations for N-body Satellite. Journal on Astronomical Science, 1965,5(1):123~128
[45] Featherstone.R. The Calculation of Robot Dynamics Using Articulated-Body Inertias, International Journal of Robotics Research, 1983,2:13~30
[46] E.J.Haug, M.McCullough. A Variational Vector Calculus Approach to Machine Dynamics. Journal of Mechanics Transimission and Automation in Design, 1986,108(1): 25~30
[47] Bae D S, Haug E J. Recursive Formulation for Constrained Mechanical System Dynamics. Part I. Open Loop Systems. Mechanics of Structures and Machines, 1987, 15(3): 359~382
[48] Bae D C, Haug E J A Recursive Formulation for Constrained Mechanical System Dynamics, Part II–Closed Loop Systems. Mechanics of Structures and Machines, 1987,15(4): 481~506
[49]王济勇,洪嘉振.柔性多体系统的递推组集建模与仿真软件的实现.应用力学学报, 1997,14(2):121~124
[50]洪嘉振,于清.柔性多体系统动力学的递推建模与算法.中国机械工程, 2000,11 (6):611~615
[51] Bae.D.S. Lee.J.K. Cho.H.J. Yae.H. An Explicit Integration Method for Real-Time Simulation of Multi-Body Vehicle Models. Computer Methods in Applied Mechanics andEngineering, 2000,187: 337~350
[52] J.Cuadrado, D.Dopico, M.Gonzalez, M.A.Naya. A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics. Journal of Mechanical Design, 2004,126(4): 602~608
[53]刘又午.多体动力学的休斯敦方法及其发展.中国机械工程, 2000, 11(6): 601~607
[54]员超,刘又午,宗光华.基于Huston多体系统逆动力学的主动控制方法分析.中国机械工程, 2000, 11(6): 647~649
[55]杨国来,陈运生.柔性多体系统动力学通用算法研究.应用力学学报, 2000, 17(2): 85~89
[56] Bayo E. An Efficient Computational Method for Real Time Multibody Dynamic Simulation in Fully Cartesian Coordinates. Computer Methods in Applied Mechanics and Engineering,1991,92,377~395
[57] Garcaude.J.J, Unda J,Avello. Natural Coordinates for the Computer Analysis of Multibody Systems. Computer Method in Applied Mechanics and Engineering,1986,56: 309-327
[58]刘延柱.完全笛卡尔坐标描述的多体系统动力学.力学学报, 1997,29(1): 84~94
[59] Vallejo D G, Escalona J L, Shababa A A. Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates. Nonlinear Dynamics, 2003, 34: 75~94
[60] Shabana A A. Finite Element Incremental Approach and Exact Rigid Body Inertia. ASME Journal of Mechanical Design. 1996,118(2): 171~178
[61] Shabana A A. Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics. Nonlinear Dynamics, 1998, 16: 293-306
[62] Escalona J L, Hussien H A, Shababa A A. Application of the Absolute Nodal Coordiante Formulation to Multibody System Dynamics. Journal of Sound and Vibration, 1998, 214(5): 833~851
[63] Sugiyama H, Escalona J L, Shababa A A. Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates. Nonlinear Dynamics, 2003, 31: 167~195
[64] R.Lot., M.Dalio. A Symbolic Approach for Automatic Generation of the Equations of Motion of Multibody Systems. Multibody System Dynamics, 2004,12,147~172
[65] A.Kecskemethy, T.Krupp, M.Hiller. Symbolic Processing of Multiloop Mechanism Dynamics Using Closed-Form Kinematics Solutions. Multibody System Dynamics, 1997,1: 23~45
[66] P.Fisette, D.A.Johnson, J.C.Samin. A Fully Symbolic Generation of the Equations of Motion of Multibody Systems Containing Flexible Beams. Computer Methods in Applied Mechanics and Engineering,1997,142,123~152
[67] J.J.Mcphee. Automatic Generation of Motion Equations for Planar Mechanical SystemsUsing the New Set of“Branch Coordinates”. Mechanics and Machine Theory, 1998, 33(6): 805~823
[68] J. J. McPhee, G.I. Milad, C.A.Gordon. Wittenburg’s Formulation of Multibody Dynamics Equations from a Graph-Theoretic Perspective. Mechanics and Machine Theory, 1996, 31(2): 201~213
[69] Sherman Y.T. Lang. H.K.Keavan. Graph Theoretic Modeling and Analysis of Multibody Planar Mechanical Systems. IEEE Transactions on Systems Man and Cybernetics-Part A: System and Humans, 2001,31(2):97~111
[70] Shi.P and McPhee.J. Dynamics of Flexible Multibody Systems Using Virtual Work and Linear Graph Theory. Multibody System Dynamics, 2000,4,355~381
[71]王琪,陆启韶.多体系统Lagrange方程数值算法的研究进展.力学进展, 2001, 31(1) :9-17
[72]潘振宽,赵维加,洪嘉振等.多体系统动力学微分/代数方程数值方法.力学进展, 1996, 26(1): 28~40
[73]于清,洪嘉振.受约束多体系统一种新的违约校正方法.力学学报,1998,30(3): 300~306
[74] Baumgarte J. Stabilization of Constraints and Integrals of Motion in Dynamical System. Computer Methods in Applied Mechanics and Engineering, 1972, 1: 1~16
[75] Ostermeyer G P. On Baumgarte Stabilization for Differential Algebraic Equations. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[76] Bae D S, Yang S M. A Stabilization Method for Kinematic and Kinetic Constraint Equation. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[77]赵维加,潘振宽,王艺兵.多体系统动力学微分/代数方程约束误差小扰动自我稳定方法.应用数学和力学, 2000,21(1):94~98
[78] Wu S D, Chiou J C, Lin Y C. Modified Adams-Moulton Predictor-Corrector Method in Solving Multibody Dynamical Systems. Mechanics of Structures and Machines, 2000, 28(2&3): 201~218
[79] E. Bayo, A.Avello. Singularity-Free Augmented Lagrangian Algorithms for Constrained Multibody Dynamics. Nonlinear Dynamics, 1994,5:209~231
[80] Kurdila A J, Junkins J L, Hsu S. Lyapunov Stable Penalty Methods for Imposing Holonomic Constraints in Multibody System Dynamics. Nonlinear Dynamics, 1993,4: 51~82
[81] Petzold L R, Potra F A. ODAE Methods for the Numerical Solution of Euler-LagrangeEquation. Applied Numerical Mathematics, 1992, 10: 397~413
[82] Fuhrer C, Leimkuhler B. A New Class of Generalized Inverses for the Solution of Discretized Euler-Lagrange Equations. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[83] Potra F A. Implementation of Linear Multistep Methods for Solving Constrained Equations of Motion. SIAM Journal of Numerical Analysis, 1993, 30(3): 774~789
[84] Bae D S, Kim H W, Yoo H H. A Decoupling Solution Method for Implicit Numerical Integration of Constrained Mechanical Systems. Mechanics of Structures and Machines, 1999, 27(2): 129~141
[85] Haug E J, Yen J. Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[86] Park T. A Hybrid Constraint Stabilization-Generalized Coordinate Partitioning Method for Machine Dynamics. Journal of Mechanisms, Transmissions, and Automation in Design, 1986, 108(2): 211-216
[87] Ider S K, Amirouche F M C. Coordinate Reduction in the Dynamics of Constrained Systems - A New Approach. Journal of Applied Mechanics, 1988, 55: 889~904
[88]赵维加,潘振宽,洪嘉振等.多体系统动力学微分/代数方程组的一类缩并算法.纺织高校基础科学学报, 1995, 8(3): 234~239
[89]潘振宽,孙红旗,臧宏文等.多体系统动力学微分/代数方程组修正的QR分解法.青岛大学学报, 1996, 11(4): 37~42
[90] Singh R P, Likins P W. Singular Value Decomposition for Constrained Dynamic Systems. Journal of Applied Mechanics, 1985, 52(4): 943~948
[91] Yen J, Haug E J, Tak T O. Numerical Methods for Constrained Equations of Motion in Mechanical System Dynamics. Mechanics of Structures and Machines, 1991, 19(1): 41~76
[92]王艺兵,赵维加,潘振宽.多体系统动力学微分/代数方程组的一类新的数值分析方法.应用数学和力学, 1997, 18(9): 845~852
[93]张学胜,陈万吉.约束多体系统动力学正则方程的约束变尺度方法.计算力学学报, 1999, 16(3):314~319
[94]王琪,黄克累,陆启韶.具有奇异位置的多体系统动力学方程的隐式算法.计算力学学报, 1997, 14(4): 382~387
[95] Haug E J, Coroian D I, Serban R. Variable Fidelity Differential-Algebraic Equation Model Correlation. Mechanics of Structures and Machines, 1997, 25(1): 61~85
[96] ADAMS 11.0.0 Product Guides,2000
[97]梁崇高,阮平生.连杆机构的计算机辅助设计[M].北京:机械工业出版社, 1986
[98]张纪元,沈守范.计算机构学.北京:国防工业出版社, 1996
[99]戈新生,张涌.完全笛卡尔坐标描述的机械系统动力学分析及软件研究.机械科学与技术, 2000, 19(1): 22~24
[100]袁泉.非树型机械系统运动仿真模型和算法的研究: [博士学位论文].北京:中国农业大学, 2001
[101]洪嘉振,于清.柔性多体系统动力学的递推建模与算法.中国机械工程,2000,11 (6):611-615
[102] Wang.Z, Tan.J.R, Liu.ZY. Modeling Compliant Non-Penetration Constraint for VP Motion Simulation. 2005,18(2):163~168
[103] Tan.J.R, Wang.Z, Liu.Z.Y. Stable Programmed Manifold Solver for Virtual Prototyping Motion Simulation. Chinese Journal of Mechanical Engineering,2006,19(1): 76~80
[104] Robert M Cubert, Paul A Fishwick. OOPM: An Object-Oriented Multi-Modeling and Simulation Application Framework. Computer Simulation. 1998,70(6): 379~395
[105]王波兴,王波,张云清等.复杂机械系统仿真平台模型管理研究与实现.计算机辅助设计与图形学学报. 2004,16(6):819~825
[106]刘晓平,黄永红,金文华等.工程约束表示模型与求解算法研究.计算机学报. 1999,22(11):1153~1157
[107]刘忠途,王启付,陈立平.三维CAD系统的知识融合与驱动技术.计算机辅助设计与图形学学报,2005,17(5):1013~1018
[108]肖心枢.图论及其算法.北京:航空工业出版社, 1993
[109]陈立平.几何约束系统最大归约理论及应用研究: [博士学位论文],武汉:华中理工大学, 1995
[110]严蔚敏.吴伟民.数据结构.北京:清华大学出版社, 1993
[111] Robert W.Sebesta. Concepts of Programming Languages, Sixth Edition[M]. Addison Wesley/Pearson, 2006
[112]万昌江,谭建荣,刘振宇.基于语义的组件化样机建模技术研究.中国机械工程, 2005,16(16): 1142~1146
[113] Pogorelov D Y. On Numerical Methods of Modeling large multibody systems. Mechanism and Machine Theory, 1999,34:791-800
[114]张钹,张铃.问题求解理论及应用.北京:清华大学出版社,1990
[115]张钹,张铃.商空间理论与粒度计算.计算机科学, 2003,30(5):1~3
[116] Wittenburg J. Dynamics of Systems of Rigid Bodies. B.G.Teubner, Stuttgart, 1977
[117] Tsai FF, Haug E J. Real-Time Multibody Systems Dynamic Simulation: Part I. A Modified Recursive Formulation and Topological Analysis. Mechanics of Structures and Machines, 1991,19(1): 99~127
[118]吴永,胡继云,殷学纲.多体系统动力学方程在流行上的辛算法.力学进展,2002,32(2): 189~195
[119]李庆扬,王能超,易大义.数值分析.武汉:华中理工大学出版社,1982
[120]王颋.面向CAD设计模型的计算多体动力学虚拟原型: [博士学位论文].成都:西南交通大学, 2005
[121] E.Bayo, R Ledesma. Augmented Lagrangian and Mass-Orthogonal Projection Methods for Constrained Multibody Dynamics. Nonlinear Dynamics, 1996,9,113~130
[122]周凡利.约束机械系统动力学积分方法研究与系统实现: [硕士学位论文].武汉:华中科技大学, 2001
[123]袁兆鼎,费景高,刘德贵著.刚性常微分方程初值问题的数值解法.北京:科学出版社, 1987
[124] Wojciech Blajer. Augmented Lagrangian Formulation: Geometrical Interpretation and Application to Systems with Singularities and Redundancy. Multibody System Dynamics, 2002,8:141~159
[125] C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM press, 1995.
[126] Garcia de Jalon, J. and Bayo, E. Kinematic and Dynamic Simulation of Multibody systems, Spring-Verlag, Berlin, 1994
[127] Pogorelov D. Differential-Algebraic Equations in Multibody System Modeling. Numerical Algorithms, 1998,19: 183~194
[128] J.Z. Wang, Z.D.Ma, G.M.Hulbert. A Gluing Algorithm for Distributed Simulation of Multibody Systems. Nonlinear Dynamics, 2003,34: 159-188
[129]余志生.汽车理论.北京:机械工业出版社, 2000
[130]邓楚南等.轿车构造.北京:人民交通出版社, 2001
[2]刘小平等.虚拟样机及其相关技术研究和实践.机械科学与技术, 2003, 22(1): 235~238
[3]王国强,张进平,马若丁编著.虚拟样机技术及其在ADAMS上的实践.西安:西北工业大学出版社, 2002
[4]陈立平,张云清等.机械系统动力学分析及ADAMS应用教程.北京:清华大学出版社, 2005
[5]吴洪涛,熊有伦.机械工程中的多体系统动力学问题.中国机械工程, 2000, 11(6):608~610
[6]刘贤喜.机械系统虚拟样机仿真软件的实用化研究: [博士学位论文].北京:中国农业大学, 2001
[7] Wang G Gary. Definition and Review of Virtual Prototyping. Journal of Computing and Information Science in Engineering, 2002, 2(3): 232~236
[8]熊光楞,范文慧. 21世纪制造业的建模与仿真技术.系统仿真学报, 2004,16(9):1884~1886
[9] Michael J. Pratt. Virtual Prototyping and product Models in Mechanical Engineering. Gaithersburg: National Institute of Standards and Technology, 1995
[10] National Bureau of Standards. Initial Graphics Exchange Specification (IGES) 30. Technical report, National Bureau of Standards, 1986
[11] ISO. Product Data Representation and Exchange-Part 42: Integrated Generic Resource: Geometric and Topological Representation Technical Report ISO CD 10303-42, International Organization for Standardization (ISO), 1992
[12] Krause F L, Rieger E and Ulbrich A. Feature Processing as Kernel for Integrated CAE Systems. In Feature Modeling and Recognition in Advanced CAD/CAM Systems Vol II IFIP, Valenciennes, France, 1994:693~716
[13] De Martino T, Falcidieno B and Habinger S. Design and Engineering Process Integration through a Multiple View Intermediate Modeller in a Distributed Object-Oriented System Environment. Computer-Aided Design, 1998,30(6):427~452
[14]尹周平.面向虚拟原型的产品特征建模和可接近性分析: [博士学位论文].武汉:华中科技大学, 2000
[15]刘振宇,谭建荣等.面向虚拟装配的产品层次信息表达研究.计算机辅助设计与图形学学报,2001,13(3): 223~228
[16] Burdea.G and Coifet.P. Virtual Reality Technology. New York: John Wiley&Sons, 1994
[17] J.D.Foley. Interface for Advanced Computing. Scientific American,1987,257(4): 127~135
[18]王政.基于交互驱动的虚拟样机动力学建模技术研究与应用: [博士学位论文].浙江:浙江大学, 2005
[19] Fang Y and Liou F W. Virtual Prototyping of Mechanical Assemblies with Deformable Components. Journal of Manufacturing Systems,1997,16(3):211~219
[20] Jayaram S, Connacher H I and Lyons K W. Virtual Assembly using Virtual Reality Techniques. Computer-Aided Design, 1997, 29(8): 575~584
[21] De Sa A G and Zachmann G. Virtual Reality as a Tool for Verification of Assembly and Maintenance Process. Computers & Graphics, 1999, 23:389~403
[22] Gupta R, Whitney D and Zelter D. Prototyping and Design for Assembly Analysis using Multimodal Virtual Environments. Computer-Aided Design, 1997, 29(8):585-597
[23] Wuerger D and Gadh R. Virtual Prototyping of Die Design Part One: Theory and Formulation. Concurrent Engineering: Research and Application, 1997, 5(4):307~315
[24] Buck M. Immersive User Interaction within Industrial Virtual Environments. In: Dai F, editor. Virtual Reality for Industrial Applications, Computer Graphics and Applications. Berlin: Springer,1998:39~59
[25] Lehner V D, Defanti T A. Projects in VP: Distributed Virtual Reality:Supporting Reomte Collabration in Vehicle Design. IEEE Computer Graphics and Appplications, 1997, 17(2):13~17
[26]汪成为.灵境技术的理论、实现及应用.北京:清华大学出版社;南宁:广西科学技术出版社, 1993:156~190
[27]鲍劲松,金烨,蒋祖华等.虚拟环紧下给予舒适性的客车内饰设计.计算机集成制造系统, 2001,7(7):36~40
[28]张云清,高斯,李凌阳等.基于多体力学的车辆动力学控制系统仿真及优化.动力学与控制学报, 2007,5(1):68~74
[29]张云清,项俊,陈立平,孙营.整车多体动力学模型的建立、验证及仿真分析.汽车工程, 2006,28(3):287~291
[30]张云清,马开献,田强等.基于ADAMS和MATLAB协同仿真的四轮转向模糊控制策略研究.计算机集成制造系统, 2007, 13(6):1234~1240
[31]王其东,方锡邦等.基于虚拟样机技术的汽车钢板弹簧设计与分析研究.机械工程学报, 2001,37(12):63~66
[32]丁国富,邹益胜等.基于虚拟原型的机械多体系统建模可视化.计算机辅助设计与图形学学报, 2006,18(6):793~799
[33] Haug E J. Computer Aided Kinematics and Dynamics of Mechanical Systems. Vol.1 Basic Methods, Boston: Allyn and Bacon, 1989
[34]谭建荣,王政,刘振宇.基于可视化外部力/力矩隐喻工具的虚拟样机动力学交互分析方法.计算机学报, 2004,27(11):1464~1470
[35]丁国富,闫开印,张卫华等.面向虚拟样机设计的产品属性提取研究.计算机集成制造系统, 2006,12(1):14~20
[36] Paredis C J J, Diaz-Calderon A, Sinha R, Khosla P K. Composable models for simulation-based design. Engineering with Computers, 2001,17(2):112~128
[37]金伟新,肖田元,胡晓峰等.多层多视多体建模方法研究.计算机仿真, 2004, 21(7), 39~42
[38] Diaz-Calderon A, Paredis C J J, Khosla P K. Organization and Selection of Reconfigurable Models. Proceedings of the Winter Simulation Conference. New York, NY, USA:WSC ACM Press, 2000:386~393
[39]洪嘉振.计算多体系统动力学.北京:高等教育出版社,1999
[40]陆佑方.柔性多体系统动力学.北京:高等教育出版社,1996
[41] Schiehlen.W. Multibody System Dynamics: Roots and Perspectives. Multibody System Dynamics, 1997,1,149~188
[42] Schiehlen W. Multi-Body Systems Handbook. Berlin:Springer, 1990
[43] Critcbley.J.H and Anderson K.S. A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics. International Journal for Multi-Scale Computational Engineering,2003,1:181~199
[44] Hooker Margulies.G. The Dynamical Attitude Equations for N-body Satellite. Journal on Astronomical Science, 1965,5(1):123~128
[45] Featherstone.R. The Calculation of Robot Dynamics Using Articulated-Body Inertias, International Journal of Robotics Research, 1983,2:13~30
[46] E.J.Haug, M.McCullough. A Variational Vector Calculus Approach to Machine Dynamics. Journal of Mechanics Transimission and Automation in Design, 1986,108(1): 25~30
[47] Bae D S, Haug E J. Recursive Formulation for Constrained Mechanical System Dynamics. Part I. Open Loop Systems. Mechanics of Structures and Machines, 1987, 15(3): 359~382
[48] Bae D C, Haug E J A Recursive Formulation for Constrained Mechanical System Dynamics, Part II–Closed Loop Systems. Mechanics of Structures and Machines, 1987,15(4): 481~506
[49]王济勇,洪嘉振.柔性多体系统的递推组集建模与仿真软件的实现.应用力学学报, 1997,14(2):121~124
[50]洪嘉振,于清.柔性多体系统动力学的递推建模与算法.中国机械工程, 2000,11 (6):611~615
[51] Bae.D.S. Lee.J.K. Cho.H.J. Yae.H. An Explicit Integration Method for Real-Time Simulation of Multi-Body Vehicle Models. Computer Methods in Applied Mechanics andEngineering, 2000,187: 337~350
[52] J.Cuadrado, D.Dopico, M.Gonzalez, M.A.Naya. A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics. Journal of Mechanical Design, 2004,126(4): 602~608
[53]刘又午.多体动力学的休斯敦方法及其发展.中国机械工程, 2000, 11(6): 601~607
[54]员超,刘又午,宗光华.基于Huston多体系统逆动力学的主动控制方法分析.中国机械工程, 2000, 11(6): 647~649
[55]杨国来,陈运生.柔性多体系统动力学通用算法研究.应用力学学报, 2000, 17(2): 85~89
[56] Bayo E. An Efficient Computational Method for Real Time Multibody Dynamic Simulation in Fully Cartesian Coordinates. Computer Methods in Applied Mechanics and Engineering,1991,92,377~395
[57] Garcaude.J.J, Unda J,Avello. Natural Coordinates for the Computer Analysis of Multibody Systems. Computer Method in Applied Mechanics and Engineering,1986,56: 309-327
[58]刘延柱.完全笛卡尔坐标描述的多体系统动力学.力学学报, 1997,29(1): 84~94
[59] Vallejo D G, Escalona J L, Shababa A A. Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates. Nonlinear Dynamics, 2003, 34: 75~94
[60] Shabana A A. Finite Element Incremental Approach and Exact Rigid Body Inertia. ASME Journal of Mechanical Design. 1996,118(2): 171~178
[61] Shabana A A. Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics. Nonlinear Dynamics, 1998, 16: 293-306
[62] Escalona J L, Hussien H A, Shababa A A. Application of the Absolute Nodal Coordiante Formulation to Multibody System Dynamics. Journal of Sound and Vibration, 1998, 214(5): 833~851
[63] Sugiyama H, Escalona J L, Shababa A A. Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates. Nonlinear Dynamics, 2003, 31: 167~195
[64] R.Lot., M.Dalio. A Symbolic Approach for Automatic Generation of the Equations of Motion of Multibody Systems. Multibody System Dynamics, 2004,12,147~172
[65] A.Kecskemethy, T.Krupp, M.Hiller. Symbolic Processing of Multiloop Mechanism Dynamics Using Closed-Form Kinematics Solutions. Multibody System Dynamics, 1997,1: 23~45
[66] P.Fisette, D.A.Johnson, J.C.Samin. A Fully Symbolic Generation of the Equations of Motion of Multibody Systems Containing Flexible Beams. Computer Methods in Applied Mechanics and Engineering,1997,142,123~152
[67] J.J.Mcphee. Automatic Generation of Motion Equations for Planar Mechanical SystemsUsing the New Set of“Branch Coordinates”. Mechanics and Machine Theory, 1998, 33(6): 805~823
[68] J. J. McPhee, G.I. Milad, C.A.Gordon. Wittenburg’s Formulation of Multibody Dynamics Equations from a Graph-Theoretic Perspective. Mechanics and Machine Theory, 1996, 31(2): 201~213
[69] Sherman Y.T. Lang. H.K.Keavan. Graph Theoretic Modeling and Analysis of Multibody Planar Mechanical Systems. IEEE Transactions on Systems Man and Cybernetics-Part A: System and Humans, 2001,31(2):97~111
[70] Shi.P and McPhee.J. Dynamics of Flexible Multibody Systems Using Virtual Work and Linear Graph Theory. Multibody System Dynamics, 2000,4,355~381
[71]王琪,陆启韶.多体系统Lagrange方程数值算法的研究进展.力学进展, 2001, 31(1) :9-17
[72]潘振宽,赵维加,洪嘉振等.多体系统动力学微分/代数方程数值方法.力学进展, 1996, 26(1): 28~40
[73]于清,洪嘉振.受约束多体系统一种新的违约校正方法.力学学报,1998,30(3): 300~306
[74] Baumgarte J. Stabilization of Constraints and Integrals of Motion in Dynamical System. Computer Methods in Applied Mechanics and Engineering, 1972, 1: 1~16
[75] Ostermeyer G P. On Baumgarte Stabilization for Differential Algebraic Equations. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[76] Bae D S, Yang S M. A Stabilization Method for Kinematic and Kinetic Constraint Equation. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[77]赵维加,潘振宽,王艺兵.多体系统动力学微分/代数方程约束误差小扰动自我稳定方法.应用数学和力学, 2000,21(1):94~98
[78] Wu S D, Chiou J C, Lin Y C. Modified Adams-Moulton Predictor-Corrector Method in Solving Multibody Dynamical Systems. Mechanics of Structures and Machines, 2000, 28(2&3): 201~218
[79] E. Bayo, A.Avello. Singularity-Free Augmented Lagrangian Algorithms for Constrained Multibody Dynamics. Nonlinear Dynamics, 1994,5:209~231
[80] Kurdila A J, Junkins J L, Hsu S. Lyapunov Stable Penalty Methods for Imposing Holonomic Constraints in Multibody System Dynamics. Nonlinear Dynamics, 1993,4: 51~82
[81] Petzold L R, Potra F A. ODAE Methods for the Numerical Solution of Euler-LagrangeEquation. Applied Numerical Mathematics, 1992, 10: 397~413
[82] Fuhrer C, Leimkuhler B. A New Class of Generalized Inverses for the Solution of Discretized Euler-Lagrange Equations. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[83] Potra F A. Implementation of Linear Multistep Methods for Solving Constrained Equations of Motion. SIAM Journal of Numerical Analysis, 1993, 30(3): 774~789
[84] Bae D S, Kim H W, Yoo H H. A Decoupling Solution Method for Implicit Numerical Integration of Constrained Mechanical Systems. Mechanics of Structures and Machines, 1999, 27(2): 129~141
[85] Haug E J, Yen J. Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics. Haug E J, Deyo R C, ed, Proceedings of the NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Snowbird, 1989. Berlin: Springer-Verlag, 1990
[86] Park T. A Hybrid Constraint Stabilization-Generalized Coordinate Partitioning Method for Machine Dynamics. Journal of Mechanisms, Transmissions, and Automation in Design, 1986, 108(2): 211-216
[87] Ider S K, Amirouche F M C. Coordinate Reduction in the Dynamics of Constrained Systems - A New Approach. Journal of Applied Mechanics, 1988, 55: 889~904
[88]赵维加,潘振宽,洪嘉振等.多体系统动力学微分/代数方程组的一类缩并算法.纺织高校基础科学学报, 1995, 8(3): 234~239
[89]潘振宽,孙红旗,臧宏文等.多体系统动力学微分/代数方程组修正的QR分解法.青岛大学学报, 1996, 11(4): 37~42
[90] Singh R P, Likins P W. Singular Value Decomposition for Constrained Dynamic Systems. Journal of Applied Mechanics, 1985, 52(4): 943~948
[91] Yen J, Haug E J, Tak T O. Numerical Methods for Constrained Equations of Motion in Mechanical System Dynamics. Mechanics of Structures and Machines, 1991, 19(1): 41~76
[92]王艺兵,赵维加,潘振宽.多体系统动力学微分/代数方程组的一类新的数值分析方法.应用数学和力学, 1997, 18(9): 845~852
[93]张学胜,陈万吉.约束多体系统动力学正则方程的约束变尺度方法.计算力学学报, 1999, 16(3):314~319
[94]王琪,黄克累,陆启韶.具有奇异位置的多体系统动力学方程的隐式算法.计算力学学报, 1997, 14(4): 382~387
[95] Haug E J, Coroian D I, Serban R. Variable Fidelity Differential-Algebraic Equation Model Correlation. Mechanics of Structures and Machines, 1997, 25(1): 61~85
[96] ADAMS 11.0.0 Product Guides,2000
[97]梁崇高,阮平生.连杆机构的计算机辅助设计[M].北京:机械工业出版社, 1986
[98]张纪元,沈守范.计算机构学.北京:国防工业出版社, 1996
[99]戈新生,张涌.完全笛卡尔坐标描述的机械系统动力学分析及软件研究.机械科学与技术, 2000, 19(1): 22~24
[100]袁泉.非树型机械系统运动仿真模型和算法的研究: [博士学位论文].北京:中国农业大学, 2001
[101]洪嘉振,于清.柔性多体系统动力学的递推建模与算法.中国机械工程,2000,11 (6):611-615
[102] Wang.Z, Tan.J.R, Liu.ZY. Modeling Compliant Non-Penetration Constraint for VP Motion Simulation. 2005,18(2):163~168
[103] Tan.J.R, Wang.Z, Liu.Z.Y. Stable Programmed Manifold Solver for Virtual Prototyping Motion Simulation. Chinese Journal of Mechanical Engineering,2006,19(1): 76~80
[104] Robert M Cubert, Paul A Fishwick. OOPM: An Object-Oriented Multi-Modeling and Simulation Application Framework. Computer Simulation. 1998,70(6): 379~395
[105]王波兴,王波,张云清等.复杂机械系统仿真平台模型管理研究与实现.计算机辅助设计与图形学学报. 2004,16(6):819~825
[106]刘晓平,黄永红,金文华等.工程约束表示模型与求解算法研究.计算机学报. 1999,22(11):1153~1157
[107]刘忠途,王启付,陈立平.三维CAD系统的知识融合与驱动技术.计算机辅助设计与图形学学报,2005,17(5):1013~1018
[108]肖心枢.图论及其算法.北京:航空工业出版社, 1993
[109]陈立平.几何约束系统最大归约理论及应用研究: [博士学位论文],武汉:华中理工大学, 1995
[110]严蔚敏.吴伟民.数据结构.北京:清华大学出版社, 1993
[111] Robert W.Sebesta. Concepts of Programming Languages, Sixth Edition[M]. Addison Wesley/Pearson, 2006
[112]万昌江,谭建荣,刘振宇.基于语义的组件化样机建模技术研究.中国机械工程, 2005,16(16): 1142~1146
[113] Pogorelov D Y. On Numerical Methods of Modeling large multibody systems. Mechanism and Machine Theory, 1999,34:791-800
[114]张钹,张铃.问题求解理论及应用.北京:清华大学出版社,1990
[115]张钹,张铃.商空间理论与粒度计算.计算机科学, 2003,30(5):1~3
[116] Wittenburg J. Dynamics of Systems of Rigid Bodies. B.G.Teubner, Stuttgart, 1977
[117] Tsai FF, Haug E J. Real-Time Multibody Systems Dynamic Simulation: Part I. A Modified Recursive Formulation and Topological Analysis. Mechanics of Structures and Machines, 1991,19(1): 99~127
[118]吴永,胡继云,殷学纲.多体系统动力学方程在流行上的辛算法.力学进展,2002,32(2): 189~195
[119]李庆扬,王能超,易大义.数值分析.武汉:华中理工大学出版社,1982
[120]王颋.面向CAD设计模型的计算多体动力学虚拟原型: [博士学位论文].成都:西南交通大学, 2005
[121] E.Bayo, R Ledesma. Augmented Lagrangian and Mass-Orthogonal Projection Methods for Constrained Multibody Dynamics. Nonlinear Dynamics, 1996,9,113~130
[122]周凡利.约束机械系统动力学积分方法研究与系统实现: [硕士学位论文].武汉:华中科技大学, 2001
[123]袁兆鼎,费景高,刘德贵著.刚性常微分方程初值问题的数值解法.北京:科学出版社, 1987
[124] Wojciech Blajer. Augmented Lagrangian Formulation: Geometrical Interpretation and Application to Systems with Singularities and Redundancy. Multibody System Dynamics, 2002,8:141~159
[125] C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM press, 1995.
[126] Garcia de Jalon, J. and Bayo, E. Kinematic and Dynamic Simulation of Multibody systems, Spring-Verlag, Berlin, 1994
[127] Pogorelov D. Differential-Algebraic Equations in Multibody System Modeling. Numerical Algorithms, 1998,19: 183~194
[128] J.Z. Wang, Z.D.Ma, G.M.Hulbert. A Gluing Algorithm for Distributed Simulation of Multibody Systems. Nonlinear Dynamics, 2003,34: 159-188
[129]余志生.汽车理论.北京:机械工业出版社, 2000
[130]邓楚南等.轿车构造.北京:人民交通出版社, 2001