柔性多体系统动力学及其设计灵敏度分析
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摘要
本文研究了基于等几何分析和绝对节点坐标的柔性多体系统动力学及其设计灵敏度分析。
等几何分析是一种新型的有限元分析方法。不同于传统有限元分析,这种方法将几何建模与有限元分析统一于同一种几何描述框架下,能够直接在NURBS几何体上进行有限元网格划分,得到精确的有限元分析模型,有着传统有限元方法难以比拟的优势。为了将这种方法扩展至柔性多体系统动力学研究领域,本文提出了一种基于Green-Lagrange应变张量方法,使等几何分析方法适用于解决柔性系统大转动、大变形相耦合的问题。在此基础上,提出了一套基于连续介质力学的柔性多体系统等几何分析方法,研究了方程组中各部分的具体形式及计算方法,并通过数值算例验证了所提出方法的可行性。这套方法对于扩展柔性多体系统动力学分析的建模方式,改善前、后处理过程的效率以及提高动力学分析计算的精度有着重要的意义。
绝对节点坐标也是一种新型的有限元分析方法,这种方法的最大特点就是采用全局斜率作为节点变量。本文运用这种方法研究了柔性多体系统动力学,尤其是研究了大范围运动与变形相耦合的问题,通过算例验证了这种方法的可行性。并与等几何分析进行了比较,分析了两种方法在进行有限元分析时的异同,这对于在不同情况下选择适当的几何描述方法有着重要的意义。
在动力学分析的基础上,研究了与系统优化相关的柔性多体系统设计灵敏度分析。系统研究了有限差分法,直接微分法和伴随变量法等设计灵敏度分析方法,并分析了其各自优缺点。重点研究了柔性多体系统的设计灵敏度分析,提出了一种基于绝对节点坐标和连续介质力学的柔性系统灵敏度方程的组装方法。避免了使用符号微分方法推导系统灵敏度方程的繁琐过程,大幅提升了构建及求解系统灵敏度方程的效率。通过数值算例,对比了有限差分法以及运用所提出方法修改后的直接微分与伴随变量法。结果表明,直接微分法在系统方程构成、数值计算效率和精度等方面均优于其他两种方法,大大增强了直接微分法在基于绝对节点坐标的柔性多体系统灵敏度分析及优化过程中的应用价值。
此外,本文也对多体系统动力学方程组形式及其数值积分方法进行了研究。对常见的六种隐式积分方法从全局收敛性、能量耗散、违约稳定以及计算效率等方面进行了综合对比分析。研究结果对于在不同情况下选择适当的数值积分方法十分有益。
In this paper, the flexible multibody system (FMS) dynamics and its design sensitivity analysis are investigated based on the Isogeometric Analysis (IGA) and Absolute Nodal Coordinate Formulation (ANCF).
IGA is a newly proposed finite element method (FEM). Different from traditional FEMs, IGA employs the same discription framework for geometric modeling and finite element analysis (FEA). It can obtain the exact FEA model by directly meshing the NURBS geometry, which is hard to be done by traditional FEMs. To extend IGA into FMS, a Green-Lagrange strain tensor based method is proposed to solve the large rotation and deformation coupled problems. Furthermore, this thesis also proposes a continuum mechanics based IGA method to analyze FMS. All the components of the dynamic equations are deduced in detail and their numerical evaluation methods are reviewed. The feasibility of this formula-tion is verified by numerical example studies. The proposed approach has great importance in the extension of FMS modeling methods, improvements of the pre and post processing efficiency and the numerical calculation precision.
ANCF is another new FEM, whose most distinguished feature is the use of global slopes as nodal variables. In this thesis, ANCF is extended into FMS, especially in large rotation and deformation problems. The results are verified by numerical experiments and a comparison between ANCF and IGA is made. Differences between these two methods are featured out, which is valuable for the selection of appropriate geometric modeling method in different cases for FEA.
Design sensitivity analysis of FMS is investigated based on dynamic analysis of FMS. Finite difference method, direct differentiation method and adjoint variable method are systematically studied and their characteristics are analysed. An ANCF and continuum mechanics based method is proposed to assemble the system sensitivity equations, which avoids the sophisticated symbolic differentiation process and greatly improves the efficiency of construction and numerical integration of system sensitivity equations. Finite difference method and the revised direct differentiation and adjoint variable methods are compared through numerical examples. Results show that the revised direct differentiation method is better than the other two methods in the aspects of system equation construction, numerical integration and accuracy.All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based FMS.
In addition, the system dynamic equations and numerical integration methods are researched in detail. Six kinds of implicit integration methods are compared from the aspects of global convergence, energy preservation, kinematic constraint drift and numerical efficiency, which is valuable for the choice of integration methods in different circumstances.
等几何分析是一种新型的有限元分析方法。不同于传统有限元分析,这种方法将几何建模与有限元分析统一于同一种几何描述框架下,能够直接在NURBS几何体上进行有限元网格划分,得到精确的有限元分析模型,有着传统有限元方法难以比拟的优势。为了将这种方法扩展至柔性多体系统动力学研究领域,本文提出了一种基于Green-Lagrange应变张量方法,使等几何分析方法适用于解决柔性系统大转动、大变形相耦合的问题。在此基础上,提出了一套基于连续介质力学的柔性多体系统等几何分析方法,研究了方程组中各部分的具体形式及计算方法,并通过数值算例验证了所提出方法的可行性。这套方法对于扩展柔性多体系统动力学分析的建模方式,改善前、后处理过程的效率以及提高动力学分析计算的精度有着重要的意义。
绝对节点坐标也是一种新型的有限元分析方法,这种方法的最大特点就是采用全局斜率作为节点变量。本文运用这种方法研究了柔性多体系统动力学,尤其是研究了大范围运动与变形相耦合的问题,通过算例验证了这种方法的可行性。并与等几何分析进行了比较,分析了两种方法在进行有限元分析时的异同,这对于在不同情况下选择适当的几何描述方法有着重要的意义。
在动力学分析的基础上,研究了与系统优化相关的柔性多体系统设计灵敏度分析。系统研究了有限差分法,直接微分法和伴随变量法等设计灵敏度分析方法,并分析了其各自优缺点。重点研究了柔性多体系统的设计灵敏度分析,提出了一种基于绝对节点坐标和连续介质力学的柔性系统灵敏度方程的组装方法。避免了使用符号微分方法推导系统灵敏度方程的繁琐过程,大幅提升了构建及求解系统灵敏度方程的效率。通过数值算例,对比了有限差分法以及运用所提出方法修改后的直接微分与伴随变量法。结果表明,直接微分法在系统方程构成、数值计算效率和精度等方面均优于其他两种方法,大大增强了直接微分法在基于绝对节点坐标的柔性多体系统灵敏度分析及优化过程中的应用价值。
此外,本文也对多体系统动力学方程组形式及其数值积分方法进行了研究。对常见的六种隐式积分方法从全局收敛性、能量耗散、违约稳定以及计算效率等方面进行了综合对比分析。研究结果对于在不同情况下选择适当的数值积分方法十分有益。
In this paper, the flexible multibody system (FMS) dynamics and its design sensitivity analysis are investigated based on the Isogeometric Analysis (IGA) and Absolute Nodal Coordinate Formulation (ANCF).
IGA is a newly proposed finite element method (FEM). Different from traditional FEMs, IGA employs the same discription framework for geometric modeling and finite element analysis (FEA). It can obtain the exact FEA model by directly meshing the NURBS geometry, which is hard to be done by traditional FEMs. To extend IGA into FMS, a Green-Lagrange strain tensor based method is proposed to solve the large rotation and deformation coupled problems. Furthermore, this thesis also proposes a continuum mechanics based IGA method to analyze FMS. All the components of the dynamic equations are deduced in detail and their numerical evaluation methods are reviewed. The feasibility of this formula-tion is verified by numerical example studies. The proposed approach has great importance in the extension of FMS modeling methods, improvements of the pre and post processing efficiency and the numerical calculation precision.
ANCF is another new FEM, whose most distinguished feature is the use of global slopes as nodal variables. In this thesis, ANCF is extended into FMS, especially in large rotation and deformation problems. The results are verified by numerical experiments and a comparison between ANCF and IGA is made. Differences between these two methods are featured out, which is valuable for the selection of appropriate geometric modeling method in different cases for FEA.
Design sensitivity analysis of FMS is investigated based on dynamic analysis of FMS. Finite difference method, direct differentiation method and adjoint variable method are systematically studied and their characteristics are analysed. An ANCF and continuum mechanics based method is proposed to assemble the system sensitivity equations, which avoids the sophisticated symbolic differentiation process and greatly improves the efficiency of construction and numerical integration of system sensitivity equations. Finite difference method and the revised direct differentiation and adjoint variable methods are compared through numerical examples. Results show that the revised direct differentiation method is better than the other two methods in the aspects of system equation construction, numerical integration and accuracy.All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based FMS.
In addition, the system dynamic equations and numerical integration methods are researched in detail. Six kinds of implicit integration methods are compared from the aspects of global convergence, energy preservation, kinematic constraint drift and numerical efficiency, which is valuable for the choice of integration methods in different circumstances.
引文
[1]Shabana A A. Flexible Multibody Dynamics: Review of Past and Recent Developments. Multi-body System Dynamics,1997,1(2):189-222.
[2]Wasfy T M, Noor A K. Computational strategies for flexible multibody systems. Applied Me-chanics Reviews,2003,56(6):553-613.
[3]Shabana A A, Wehage R A. A Coordinate Reduction Technique for Dynamic Analysis of Spatial Substructures with Large Angular Rotations. Journal of Structural Mechanics,1983,11(3):401-431.
[4]Shabana A A. Resonance Conditions and Deformable Body Co-ordinate Systems. Journal of Sound and Vibration,1996,192(1):389-398.
[5]Sunada W H, Dubowsky S. On the dynamic analysis and behavior of industrial robotic manip-ulators with elastic members. ASME Journal of Mechanisms Transmissions and Automations in Design,1983,105.
[6]Likins P. Hybrid-coordinate spacecraft dynamics using large deformation modal coordinates. As-tronautical Acta,1973,18(5):331-348.
[7]Song J O, Haug E J. Dynamic analysis of planar flexible mechanisms. Computer Methods in Applied Mechanics and Engineering,1980,24(3):359-381.
[8]Belytschko T, Hsieh B J. Non-linear transient finite element analysis with convected co-ordinates. International Journal for Numerical Methods in Engineering,1973,7(3):255-271.
[9]Hughes T J R, Winget J. Finite rotation effects in numerical integration of rate constitutive equa-tions arising in large-deformation analysis. International Journal for Numerical Methods in Engi-neering,1980,15(12):1862-1867.
[10]Flanagan D P, Taylor L M. An accurate numerical algorithm for stress integration with finite rotations. Computer Methods in Applied Mechanics and Engineering,1987,62(3):305-320.
[11]Rankin C C, Brogan F A. An Element Independent Corotational Procedure for the Treatment of Large Rotations. Journal of Pressure Vessel Technology,1986,108(2):165-174.
[12]Simo J C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering,1985,49(1):55-70.
[13]Simo J C, Vu-Quoc L. A three-dimensional finite-strain rod model, part Ⅱ:Computational aspects. Computer Methods in Applied Mechanics and Engineering,1986,58(1):79-116.
[14]Hughes T, Cottrell J, Bazilevs Y. Isogeometric analysis:CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering,2005, 194(39-41):4135-4195.
[15]Bazilevs Y, Hughes T. NURBS-based isogeometric analysis for the computation of flows about rotating components. Computational Mechanics,2008,43:143-150.
[16]Bazilevs Y, Michler C, Calo V, et al. Weak Dirichlet boundary conditions for wall-bounded turbu-lent flows. Computer Methods in Applied Mechanics and Engineering,2007,196(49-52):4853-4862.
[17]Bazilevs Y, Calo V, Cottrell J, et al. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering,2007,197(1-4):173-201.
[18]Akkerman I, Bazilevs Y, Calo V, et al. The role of continuity in residual-based variational multi-scale modeling of turbulence. Computational Mechanics,2008,41:371-378.
[19]Bazilevs Y, Akkerman I. Large eddy simulation of turbulent Taylor-Couette flow using isogeo-metric analysis and the residual-based variational multiscale method. Journal of Computational Physics,2010,229(9):3402-3414.
[20]Bazilevs Y, Calo V, Zhang Y, et al. Isogeometric Fluid-structure Interaction Analysis with Ap-plications to Arterial Blood Flow. Computational Mechanics,2006,38:310-322.
[21]Bazilevs Y, Calo V, Hughes T, et al. Isogeometric fluid-structure interaction:theory, algorithms, and computations. Computational Mechanics,2008,43:3-37.
[22]Bazilevs Y, Gohean J, Hughes T, et al. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Computer Methods in Applied Mechanics and Engineering,2009,198(45-46):3534-3550.
[23]Hughes T, Reali A, Sangalli G. Duality and unified analysis of discrete approximations in struc-tural dynamics and wave propagation:Comparison of p-method finite elements with k-method NURBS. Computer Methods in Applied Mechanics and Engineering,2008,197(49-50):4104-4124.
[24]Hughes T, Reali A, Sangalli G. Efficient quadrature for NURBS-bascd isogcometric analysis. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):301-313.
[25]Cottrell J, Hughes T, Reali A. Studies of refinement and continuity in isogeometric structural analysis. Computer Methods in Applied Mechanics and Engineering,2007,196(41-44):4160-4183.
[26]Cottrell J, Reali A, Bazilevs Y, et al. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering,2006,195(41-43):5257-5296.
[27]Benson D, Bazilevs Y, Hsu M, et al. Isogeometric shell analysis:The Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):276-289. Computa-tional Geometry and Analysis.
[28]Echter R, Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):374-382. Computa-tional Geometry and Analysis.
[29]Benson D, Bazilevs Y, Hsu M C, et al. A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering,2011,200(13-16):1367-1378.
[30]De Lorenzis L, Temizer, Wriggers P, et al. A large deformation frictional contact formulation using NURBS-based isogeometric analysis. International Journal for Numerical Methods in En-gineering,2011, pages n/a-n/a.
[31]Elguedj T, Buteri J R A. Isogeometric analysis for strain field measurements. Computer Methods in Applied Mechanics and Engineering,2011,200(1-4):40-56.
[32]Lu J. Isogeometric contact analysis: Geometric basis and formulation for frictionless contact. Computer Methods in Applied Mechanics and Engineering,2011,200(5-8):726-741.
[33]Lu J, Zhou X. Cylindrical element: Isogeometric model of continuum rod. Computer Methods in Applied Mechanics and Engineering,2011,200(1-4):233-241.
[34]Temizer I, Wriggers P, Hughes T. Contact treatment in isogeometric analysis with NURBS. Com-puter Methods in Applied Mechanics and Engineering,2011,200(9-12):1100-1112.
[35]张汉杰,王东东,轩军厂.薄梁板结构NURBS几何精确有限元分析.力学季刊,2010,4：469-477.
[36]Shabana A. An absolute nodal coordinate formulation for the large rotation and deformation anal-ysis of flexible bodies. Technical Report MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago,1996.
[37]Shabana A A. Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formu-lation. Multibody System Dynamics,1997, 1(3):339-348.
[38]Escalona J L, Hussien H A, Shabana A A. Application of the absolute nodal coordinate formulation to multibody system dynamics. Journal of Sound and Vibration,1998,214(5):833-851.
[39]Shabana A A. Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dynamics,1998,16(3):293-306.
[40]Shabana A A, Hussien H A, Escalona J L. Application of the absolute nodal coordinate formu-lation to large rotation and large deformation problems. Journal of Mechanical Design,1998, 120(2):188-195.
[41]Omar M A, Shabana A A. A two-dimensional shear deformable beam for large rotation and deformation problems. Journal of Sound and Vibration,2001,243(3):565-576.
[42]Dufva K E, Sopanen J T, Mikkola A M. A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. Journal of Sound and Vibration,2005,280(3-5):719-738.
[43]Kerkkanen K S, Sopanen J T, Mikkola A M. A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation. Journal of Mechanical Design,2005,127(4):621-630.
[44]Nachbagauer K, Gerstmayr J, Sinwel A S, et al. A linear and quadratic planar finite elementbased on the absolute nodal coordinate formulation, in: Proceedings of Proceedings of the 1 st Joint International Conferenceon Multibody system dynamics, Lappeenranta, Finland,2010.
[45]Dombrowski S V. Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody System Dynamics,2002,8(4):409-432.
[46]Yoo W S, Dmitrochenko 0, Park S J, et al. A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates:Application to a Rotating Strip. Mechanics Based Design of Structures and Machines: An International Journal,2005,33(3):399-422.
[47]Mikkola A, Dmitrochenko O, Matikainen M. Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2009,4(1):011004.
[48]Shabana A A, Yakoub R Y. Three dimensional absolute nodal coordinate formulation for beam elements: Theory. Journal of Mechanical Design,2001,123(4):606-613.
[49]Yakoub R Y, Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. Journal of Mechanical Design,2001,123(4):614-621.
[50]Garcia-Vallejo D, Mayo J, Escalona J L, et al. Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dynamics,2004,35(4):313-329.
[51]Gerstmayr J, Shabana A A. Efficient Integration Of The Elastic Forces And Thinthree-dimensional Beam Elements In The Absolute Nodal Coordinate Formulation, in:Proceedings of MULTIBODY DYNAMICS 2005, ECCOMAS Thematic Conference, Madrid, Spain,2005.
[52]Dmitrochenko O N, Pogorelov D Y. Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody System Dynamics,2003,10(1):17-43.
[53]Dmitrochenko O, Mikkola A. Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2008,3(4):041012-8.
[54]Dmitrochenko O, Mikkola A. Shear Correction for Thin Plate Finite Elements Based on the Ab-solute Nodal Coordinate Formulation. ASME Conference Proceedings,2009,2009(49019):909-917.
[55]K. D, A. S A. Use of the absolute nodal coordinate formulation in the analysis of thin plate structures. Technical Report MBS05-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago,2005.
[56]Mikkola A M, Shabana A A. A new plate element based on the absolute nodal coordinate formu-lation, in: Proceedings of Proceedings of the ASME 2001 DETC, Pittsburgh, America,2001.
[57]Mikkola A M, Shabana A A. A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody System Dynamics, 2003,9(3):283-309.
[58]Mikkola A M, Matikainen M K. Development of elastic forces for a large deformation plate ele-ment based on the absolute nodal coordinate formulation. Journal of Computational and Nonlinear Dynamics,2006,1(2):103-108.
[59]Matikainen M K, Schwab A, Mikkola A M. Comparison of Two Moderately Thick Plate Elements based on The Absolute Nodal Coordinate Formulation. in:Proceedings of Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2009, Warsaw, Poland,2009.
[60]Abbas L K, Rui X, Hammoudi Z S. Plate/shell element of variable thickness based on the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2010,224(2):127-141.
[61]Takahashi Y, Shinizu N. Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams, in:Proceedings of ASME Proceedings of Design Engineering Technical Conference, New York,1999, VIB-8203.
[62]Berzeri M, Campanelli M, Shabana A A. Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation. Multibody System Dynamics,2001,5(1):21-54.
[63]Sopanen J T, Mikkola A M. Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dynamics,2003,34(1-2):53-74.
[64]Yu L, Zhao Z, Tang J, et al. Integration of absolute nodal elements into multibody system. Non-linear Dynamics,2010,62(4):931-943.
[65]Dmitrochenko O, Mikkola A. Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate Formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2011,225(1):34-51.
[66]Yakoub R Y, Shabana A A. Use of cholesky coordinates and the absolute nodal coordinate for-mulation in the computer simulation of flexible multibody systems. Nonlinear Dynamics,1999, 20(3):267-282.
[67]Sugiyama H, Shabana A A. On the use of implicit integration methods and the absolute nodal co-ordinate formulation in the analysis of elasto-plastic deformation problems. Nonlinear Dynamics, 2004,37(3):245-270.
[68]Hussein B, Negrut D, Shabana A A. Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dynamics,2008,54(4):283-296.
[69]Tian Q, Chen L P, Zhang Y Q, et al. An Efficient Hybrid Method for Multibody Dynamics Simu-lation Based on Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2009,4(2):021009.
[70]Matikainen M K, Hertzen R, Mikkola A, et al. Elimination of high frequencies in the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2010,224(1):103-116.
[71]Gerslmayr J. Strain tensors in the absolute nodal coordinate and the floating frame of reference formulation. Nonlinear Dynamics,2003,34(1-2):133-145.
[72]Dibold M, Gerstmayr J, Irschik H. A Detailed Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems. Journal of Computational and Nonlinear Dynamics,2009,4(2):021006.
[73]Yoo W, Lee J, Park S, et al. Large Oscillations of a Thin Cantilever Beam:Physical Experiments and Simulation Using the Absolute Nodal Coordinate Formulation. Nonlinear Dynamics,2003, 34(1):3-29.
[74]Yoo W, Park S, Dmitrochenko O N, et al. Verification of Absolute Nodal Coordinate Formula-tion in Flexible Multibody Dynamics via Physical Experiments of Large Deformation Problems. Journal of Computational and Nonlinear Dynamics,2006, 1(1):81-93.
[75]Schwab A L, Gerstmayr J, Meijaard J P, et al. Comparison of three-dimensional flexible thin plate elements for multibody dynamic analysis:Finite element formulation and absolute nodal coordinate formulation. Las Vegas, NV:Amer Soc Mechanical Engineers,2007,1059-1070.
[76]Schwab A L, Meijaard J P. Comparison of Three-Dimensional Flexible Beam Elements for Dy-namic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formula-tion. Journal of Computational and Nonlinear Dynamics,2010,5(1):011010-10.
[77]Shabana A A, Mikkola A M. Use of the finite element absolute nodal coordinate formulation in modeling slope discontinuity. Journal of Mechanical Design,2003,125(2):342-350.
[78]Shabana A A, Maqueda L G. Slope discontinuities in the finite element absolute nodal coordinate formulation:gradient deficient elements. Multibody System Dynamics,2008,20(3):239-249.
[79]Sugiyama H, Escalona J L, Shabana A A. Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dynamics,2003,31(2):167-195.
[80]Lee S H, Park T W, Seo J H, et al. The development of a sliding joint for very flexible multi-body dynamics using absolute nodal coordinate formulation. Multibody System Dynamics,2008, 20(3):223-237.
[81]Hong D, Ren G. A modeling of sliding joint on one-dimensional flexible medium. Multibody System Dynamics,2011,26(1):91-106.
[82]Sanborn G, Shabana A. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody System Dynamics,2009,22(2):181-197.
[83]Lan P, Shabana A A. Integration of B-spline geometry and ANCF finite element analysis. Non-linear Dynamics,2010,61 (1-2):193-206.
[84]Lan P, Shabana A A. Rational Finite Elements and Flexible Body Dynamics. Journal of Vibration and Acoustics-transactions of The Asme,2010,132(4).
[85]Sugiyama H, Shabana A A. Application of plasticity theory and absolute nodal coordinate formu-lation to flexible multibody system dynamics. Journal of Mechanical Design,2004,126(3):478-487.
[86]Yu L, Zhao Z, Ren G. Multibody Dynamic Model of Web Guiding System With Moving Web. Journal Of Dynamic Systems Measurement And Control-transactions Of The Asme,2010,132(5).
[87]Sugiyama H, Suda Y. Non-linear elastic ring tyre model using the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K:Journal of Multi-body Dynamics,2009,223(3):211-219.
[88]Zhang Y, Tian Q, Chen L, et al. Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods. Multibody System Dynamics,2009, 21(3):281-303.
[89]Jung S, Park T, Chung W. Dynamic analysis of rubber-like material using absolute nodal coordi-nate formulation based on the non-linear constitutive law. Nonlinear Dynamics,2011,63:149-157.
[90]Sugiyama H, Gerstmayr J, Shabana A A. Deformation modes in the finite element absolute nodal coordinate formulation. Journal of Sound and Vibration,2006,298(4-5):1129-1149.
[91]Zhao J, Tian Q, Hu H. Modal Analysis of a Rotating Thin Plate via Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2011,6(4):041013.
[92]Tian Q, Zhang Y, Chen L, et al. Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Computers & Structures,2009,87(13-14):913-929.
[93]Tian Q, Zhang Y Q, Chen L P. Two-link Flexible Manipulator Modelling And Tip Trajectory Tracking Based On The Absolute Nodal Coordinate Method. International Journal Of Robotics & Automation,2009,24(2):103-114.
[94]田强,张云清,陈立平.含分数阻尼特性元件的多体系统动力学研究.力学学报,2009,(6)：920-928.
[95]田强,张云清,陈立平.基于增广拉格朗日方法的多柔体动力学研究.系统仿真学报,2009,(24)：7704-7710.
[96]田强,张云清,陈立平.柔性多体系统动力学绝对节点坐标方法研究进展.力学进展,2010,(2)：189-202.
[97]刘铖,田强,胡海岩.基于绝对节点坐标的多柔体系统动力学高效计算方法.力学学报,2010,(6)：1197-1205.
[98]虞磊,赵治华,任启鸿,等.基于绝对节点坐标的柔性体碰撞仿真.清华大学学报(自然科学版),2010,(7)：1135-1140.
[99]邹凡,刘锦阳.大变形薄板多体系统的动力学建模.应用力学学报,2010,(4)：740-745.
[100]沈凌杰,刘锦阳,余征跃.柔性梁斜碰撞问题的非线性动力学建模和实验研究.力学季刊,2006,(4)：568-577.
[101]Laulusa A, Bauchau O A. Review of Classical Approaches for Constraint Enforcement in Multi-body Systems. Journal of Computational and Nonlinear Dynamics,2008,3(1):011004.
[102]Bauchau O A, Laulusa A. Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems. Journal of Computational and Nonlinear Dynamics,2008,3(1):011005.
[103]Kurdila A, Papastavridis J G, Kamat M P. Role of Maggi's Equations in Computational Methods for Constrained Multibody Systems. J. Guid. Control Dyn.,1990,13(1):113-120.
[104]Papastavridis J G. Maggi's Equations of Motion and the Determina-tion of Constraint Reactions. J. Guid. Control Dyn.,1990,13(2):213-220.
[105]Hemami H, Weimer F C. Modeling of Nonholonomic Dynamic Systems With Applications. Jour-nal of Applied Mechanics,1981,48(1):177-182.
[106]Lotstedt P. Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints. SIAM Journal on Applied Mathematics,1982,42(2):pp.281-296.
[107]Gear C W, Leimkuhler B, Gupta G K. Automatic integration of Euler-Lagrange equations with constraints. Journal of Computational and Applied Mathematics,1985,12-13:77-90.
[108]Kane T R, Wang C F. On the Derivation of Equations of Motion. Journal of the Society for Industrial and Applied Mathematics,1965,13(2):pp.487-492.
[109]Jalon J. G, Unda J, Avello A, et al. Dynamic Analysis of Three-Dimensional Mechanisms in"Natural" Coordinates. ASME J. Mech., Transm., Autom. Des.,1987,109:460-465.
[110]Unda J, Jalon J. G, Losantos F, et al. A Comparative Study on Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems. ASME J. Mech., Transm., Autom. Des., 1987,109:466-474.
[111]Udwadia F E, Kalaba R E, Hee-Chang E. Equations of motion for constrained mechanical systems and the extended D'Alembert's principle. Q. Appl. Math.,1997, LV:321-331.
[112]Udwadia F E, Kalaba R E. A New Perspective on Constrained Motion, in: Proceedings of Proc. R. Soc., London: Royal Society of London, London, ROYAUME-UNI (1990-1995) (Revue),1992, 407-410.
[113]Udwadia F E. On constrained motion. Applied Mathematics and Computation,2005,164(2):313-320.12th International Workshop on Dynamics and Control.
[114]Kalaba R E, Udwadia F E. Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss's Principle. Journal of Applied Mechanics,1993,60(3):662-668.
[115]Kalaba R E, Udwadia F E. Lagrangian mechanics, Gauss's principle, quadratic programming, and generalized inverses: new equations for nonholonomically constrained discrete mechanical systems. Q. Appl. Math.,1994, LⅡ229-241.
[116]Udwadia F E, Kalaba R E. The Geometry of Constrained Motion. ZAMM-Journal of Ap-plied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik,1995, 75(8):637-640.
[117]Udwadia F E, Kalaba R E. The explicit Gibb-Appell equation and generalized inverse forms. Q. Appl. Math.,1998, LVI:277-288.
[118]Udwadia F E, Kalaba R E. What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems? Journal of Applied Mechanics,2002,69(3):335-339.
[119]Udwadia F E, Kalaba R E. On the foundations of analytical dynamics. International Journal of Non-Linear Mechanics,2002,37(6):1079-1090.
[120]Lilov L, Lorer M. Dynamic Analysis of Multirigid-Body System Based on the Gauss Principle. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathe-matik und Mechanik,1982,62(10):539-545.
[121]Blajer W. A Projection Method Approach to Constrained Dynamic Analysis. Journal of Applied Mechanics,1992,59(3):643-649.
[122]Blajer W. Projective formulation of Maggi's method for nonholonomic systems analysis. Journal of Guidance, Control, and Dynamics,1992,15(2):522-525.
[123]Blajer W, Schiehlen W, Schirm W. A projective criterion to the coordinate partitioning method for multibody dynamics. Archive of Applied Mechanics,1994,64(2):86-98.
[124]Blajer W. An orthonormal tangent space method for constrained multibody systems. Computer Methods in Applied Mechanics and Engineering,1995,121(1-4):45-57.
[125]Agrawal O P, Saigal S. Dynamic analysis of multi-body systems using tangent coordinates. Com-puters & Structures,1989,31(3):349-355.
[126]Betsch P. The discrete null space method for the energy consistent integration of constrained mechanical systems-Part I: Holonomic constraints. Computer Methods in Applied Mechanics and Engineering,2005,194(50-52):5159-5190.
[127]Betsch P, Leyendecker S. The discrete null space method for the energy consistent integration of constrained mechanical systems. Part Ⅱ:multibody dynamics. International Journal for Numerical Methods in Engineering,2006,67(4):499-552.
[128]Leyendecker S, Betsch P, Steinmann P. The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part Ⅲ:Flexible multibody dynamics. Multibody System Dynamics,2008,19(1):45-72.
[129]Baumgarte J. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics and Engineering,1972,1:1-16.
[130]Eich E, Hanke M. Regularization Methods for Constrained Mechanical Multibody Systems. Z. Angew. Math. Mech.,1995,75(10):761-773.
[131]Nikravesh P E, Wehage R A, Kwon O K. Euler Parameters in Computational Kinematics and Dynamics-Part 1 and Part 2. Journal of Mechanisms, Trasmissions, and Automation in Design, 1985,107(3):358-369.
[132]Park T W, Haug E J. A Hybrid Numerical Integration Method for Machine Dynamic Simulation. Journal of Mechanisms Transmissions and Automation in Design,1986,108(2):211-216.
[133]Chang C O, Nikravesh P E. An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems. Journal of Mechanisms Transmissions and Automation in De-sign,1985,107(4):488-492.
[134]Yoon S, Howe R M, Greenwood D T. Stability and Accuracy Analysis of Baumgarte's Constraint Violation Stabilization Method. Journal of Mechanical Design,1995,117(3):446-453.
[135]Lin S T, Hong M C. Stabilization Method for Numerical Integration of Multibody Mechanical Systems. Journal of Mechanical Design,1998,120(4):565-572.
[136]Park K C, Chiou J C. Stabilization of Computational Procedures for Constrained Dynamical Systems. J. Guid. Control Dyn.,1988,11(4):365-370.
[137]Bayo E, Jalon J G D, Serna M A. A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems. Computer Methods in Applied Mechanics and Engineering, 1988,71(2):183-195.
[138]Bayo E, Jalon J G, Avello A, et al. An efficient computational method for real time multibody dynamic simulation in fully cartesian coordinates. Computer Methods in Applied Mechanics and Engineering,1991,92(3):377-395.
[139]Newmark N M. A Method of Computation for Structural Dynamics. J. Engrg. Mech. Div.,1959, 112:67-94.
[140]Cardona A, Geradin M. Time integration of the equations of motion in mechanism analysis. Computers & Structures,1989,33(3):801-820.
[141]Gear C W. Numerical Initial Value Problems in Ordinary Differential Equations. PTR Upper Saddle River, NJ, USA:Prentice Hall,1971.
[142]Bottasso C L, Bauchau O A, Cardona A. Time-Step-Size-Independent Conditioning and Sensi-tivity to Perturbations in the Numerical Solution of Index Three Differential Algebraic Equations. Siam Journal on Scientific Computing,2007,29(1):397-414.
[143]Negrut D, Rampalli R, Ottarsson G, et al. On an Implementation of the Hilber-Hughes-Taylor Method in the Context of Index 3 Differential-Algebraic Equations of Multibody Dynamics (DETC2005-85096). Journal of Computational and Nonlinear Dynamics,2007,2(l):73-85.
[144]Hilber H M, Hughes T J R, Taylor R L. Improved numerical dissipation for time integration algo-rithms in structural dynamics. Earthquake Engineering & Structural Dynamics,1977,5(3):283-292.
[145]Chung J, Hulbert G M. A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-alpha Method. Journal of Applied Mechanics,1993, 60(2):371-375.
[146]Greene W H, Haftka R T. Computational aspects of sensitivity calculations in transient structural analysis. Computers & Structures,1989,32(2):433-443.
[147]Haftka R T, Gurdal Z. Elements of structural optimization,3 ed. Springer,1992.
[148]Chang C O, Nikravesh P E. Optimal design of mechanical systems with constraint violation stabilization method. Journal of mechanisms, transmissions, and automation in design,1985, 107(4):493-498.
[149]Dias J M P, Pereira M S. Sensitivity Analysis of Rigid-Flexible Multibody Systems. Multibody System Dynamics,1997,1 (3):303-322.
[150]Haug E J, Ehle P E. Second-order design sensitivity analysis of mechanical system dynamics. International Journal for Numerical Methods in Engineering,1982,18(11):1699-1717.
[151]Haug E J, Mani N K, Krishnaswami P. Design sensitivity analysis and optimization of dynamically driven systems, in:Haug E J, editor, Proceedings of Computer Aided Analysis and Optimization of Mechanical System Dynamics, Heidelberg, Berlin: Springer-Verlag,1984,555-636.
[152]Haug E J, Wehage R, Barman N C. Design sensitivity analysis of planar mechanism and machine dynamics. Journal of Mechanical Design,1981,103(3):560-570.
[153]Hsu Y, Anderson K S. Recursive sensitivity analysis for constrained multi-rigid-body dynamic systems design optimization. Structural and Multidisciplinary Optimization,2002,24(4):312-324.
[154]Maly T, Petzold L R. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Applied Numerical Mathematics,1996,20(1-2):57-79.
[155]Maria Augusta Ncto J A C A. Sensitivity analysis of flexible multibody systems using compos-ite materials components. International Journal for Numerical Methods in Engineering,2009, 77:386-413.
[156]Mukherjee R, Bhalerao K, Anderson K. A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis. Structural and Multidisciplinary Optimization,2008, 35(5):413-429.
[157]Serban R, Freeman J S. Identification and Identifiability of Unknown Parameters in Mullibody Dynamic Systems. Multibody System Dynamics,2001,5(4):335-350.
[158]Serban R, Haug E J. Kinematic and kinetic derivatives in multibody system analysis. Mechanics of structures and machines,1998,26(2):145-173.
[159]Wang X, Haug E J, Pan W. Implicit Numerical Integration for Design Sensitivity Analysis of Rigid Multibody Systems. Mechanics Based Design of Structures and Machines:An International Journal,2005,33(1):1-30.
[160]Bestle D, Eberhard P. Analyzing and Optimizing Multibody Systems. Mechanics of Structures and Machines,1992,20(1):67-92.
[161]Bestle D, Seybold J. Sensitivity analysis of constrained multibody systems. Archive of Applied Mechanics,1992,62(3):181-190.
[162]Cao Y, Li S, Petzold L. Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software. Journal of Computational and Applied Mathematics,2002,149(1):171-191.
[163]Li S, Petzold L, Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem. Applied Numerical Mathematics,2000,32(2):161-174.
[164]Liu X. Sensitivity analysis of constrained flexible multibody systems with stability considerations. Mechanism and machine theory,1996,31 (7):859-863.
[165]Bischof C, Carle A, Corliss G, et al. ADIFOR:Generating Derivative Codes from Fortran Pro-grams. Scientific Programming,1992, 1(1):11-29.
[166]Bischof C, Khademi P, Mauer A, et al. Adifor 2.0: automatic differentiation of Fortran 77 pro-grams. Computational Science & Engineering, IEEE,1996,3(3):18-32.
[167]Eberhard P. Analysis and optimization of complex multibody systems using advanced sensitiv-ity analysis methods, in:Proceedings of 3rd International Congress on Industrial and Applied Mathematics (ICIAM 95), Hamburg, Germany: Akademie Verlag Gmbh,1995,40-43.
[168]Griewank A, Reese S. On the calculation of Jacobian matrices by the Markowitz rule, in:Griewank A, Corliss G, editors, Proceedings of Automatic Differentiation of Algorithms:Theory, Implemen-tation, and Applications, Philadelphia,PA:SIAM,1991,126-135.
[169]Bhalerao K, Poursina M, Anderson K. An efficient direct differentiation approach for sensitivity analysis of flexible multibody systems. Multibody System Dynamics,2010,23(2):121-140.
[170]Jay O L, Negrut D. A Second Order Extension of the Generalized-a Method for Constrained Systems in Mechanics, in:Bottasso C L, editor, Proceedings of Multibody Dynamics. Springer Netherlands,2008,143-158.
[171]Lotstedt P, Petzold L. Numerical solution of nonlinear differential equations with algebraic con-straints I: Convergence results for backward differentiation formulas. Math. Comput.,1986, 46(174):491-516.
[172]Brenan K E, Engquist B E. Backward Differentiation Approximations of Nonlinear Differen-tial/Algebraic Systems. Mathematics of Computation,1988,51(184):pp.659-676.
[173]Arnold M, Bruls O. Convergence of the generalized-a scheme for constrained mechanical sys-tems. Multibody System Dynamics,2007,18(2):185-202.
[174]PieglL, Tiller W. The NURBS book. Heidelberg:Springer Verlag,1997.
[175]施法中.计算机辅助几何设计与非均匀有理B样条.中国,北京：高等教育出版社,2001.
[176]Cottrell J A, Hughes T J, Bazilevs Y. Isogeometric analysis:toward integration of CAD and FEA. The Atrium, Southern Gate, Chichester, West Sussex, PO198SQ, United Kingdom:John Wiley & Sons Inc,2009.
[177]Bonet J, Wood R D. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: Cambridge University Press,1997.
[178]Shabana A A. Computational continuum mechanics. New York, United States of America: Cam-bridge University Press,2008.
[179]Davis P, Rabinowitz P. Methods of Numerical Integration. San Diego, California: Academic Press Inc,1984.
[180]Berzeri M, Shabana A A. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration,2000,235(4):539-565.
[181]Gerstmayr J, Shabana A. Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation. Nonlinear Dynamics,2006,45:109-130.
[182]Bagley R L, Torvik P J. A Theoretical Basis for the Application of Fractional Calculus to Vis-coelasticity. Journal of Rheology,1983,27(3):201-210.
[183]Kilbas A, Srivastava H, Trujillo J. Theory and Applications of Fractional Differential Equations. Radarweg 29, P.O. Box 211,1000 AE Amsterdam, The Netherlands:Elsevier,2006.
[184]Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential/algebraic equations. Multibody System Dynamics,2007,18(4):599-617.
[185]丁洁玉.基于多体系统的灵敏度分析及动态优化设计：[博士学位论文].上海：上海大学,2008.
[2]Wasfy T M, Noor A K. Computational strategies for flexible multibody systems. Applied Me-chanics Reviews,2003,56(6):553-613.
[3]Shabana A A, Wehage R A. A Coordinate Reduction Technique for Dynamic Analysis of Spatial Substructures with Large Angular Rotations. Journal of Structural Mechanics,1983,11(3):401-431.
[4]Shabana A A. Resonance Conditions and Deformable Body Co-ordinate Systems. Journal of Sound and Vibration,1996,192(1):389-398.
[5]Sunada W H, Dubowsky S. On the dynamic analysis and behavior of industrial robotic manip-ulators with elastic members. ASME Journal of Mechanisms Transmissions and Automations in Design,1983,105.
[6]Likins P. Hybrid-coordinate spacecraft dynamics using large deformation modal coordinates. As-tronautical Acta,1973,18(5):331-348.
[7]Song J O, Haug E J. Dynamic analysis of planar flexible mechanisms. Computer Methods in Applied Mechanics and Engineering,1980,24(3):359-381.
[8]Belytschko T, Hsieh B J. Non-linear transient finite element analysis with convected co-ordinates. International Journal for Numerical Methods in Engineering,1973,7(3):255-271.
[9]Hughes T J R, Winget J. Finite rotation effects in numerical integration of rate constitutive equa-tions arising in large-deformation analysis. International Journal for Numerical Methods in Engi-neering,1980,15(12):1862-1867.
[10]Flanagan D P, Taylor L M. An accurate numerical algorithm for stress integration with finite rotations. Computer Methods in Applied Mechanics and Engineering,1987,62(3):305-320.
[11]Rankin C C, Brogan F A. An Element Independent Corotational Procedure for the Treatment of Large Rotations. Journal of Pressure Vessel Technology,1986,108(2):165-174.
[12]Simo J C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering,1985,49(1):55-70.
[13]Simo J C, Vu-Quoc L. A three-dimensional finite-strain rod model, part Ⅱ:Computational aspects. Computer Methods in Applied Mechanics and Engineering,1986,58(1):79-116.
[14]Hughes T, Cottrell J, Bazilevs Y. Isogeometric analysis:CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering,2005, 194(39-41):4135-4195.
[15]Bazilevs Y, Hughes T. NURBS-based isogeometric analysis for the computation of flows about rotating components. Computational Mechanics,2008,43:143-150.
[16]Bazilevs Y, Michler C, Calo V, et al. Weak Dirichlet boundary conditions for wall-bounded turbu-lent flows. Computer Methods in Applied Mechanics and Engineering,2007,196(49-52):4853-4862.
[17]Bazilevs Y, Calo V, Cottrell J, et al. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering,2007,197(1-4):173-201.
[18]Akkerman I, Bazilevs Y, Calo V, et al. The role of continuity in residual-based variational multi-scale modeling of turbulence. Computational Mechanics,2008,41:371-378.
[19]Bazilevs Y, Akkerman I. Large eddy simulation of turbulent Taylor-Couette flow using isogeo-metric analysis and the residual-based variational multiscale method. Journal of Computational Physics,2010,229(9):3402-3414.
[20]Bazilevs Y, Calo V, Zhang Y, et al. Isogeometric Fluid-structure Interaction Analysis with Ap-plications to Arterial Blood Flow. Computational Mechanics,2006,38:310-322.
[21]Bazilevs Y, Calo V, Hughes T, et al. Isogeometric fluid-structure interaction:theory, algorithms, and computations. Computational Mechanics,2008,43:3-37.
[22]Bazilevs Y, Gohean J, Hughes T, et al. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Computer Methods in Applied Mechanics and Engineering,2009,198(45-46):3534-3550.
[23]Hughes T, Reali A, Sangalli G. Duality and unified analysis of discrete approximations in struc-tural dynamics and wave propagation:Comparison of p-method finite elements with k-method NURBS. Computer Methods in Applied Mechanics and Engineering,2008,197(49-50):4104-4124.
[24]Hughes T, Reali A, Sangalli G. Efficient quadrature for NURBS-bascd isogcometric analysis. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):301-313.
[25]Cottrell J, Hughes T, Reali A. Studies of refinement and continuity in isogeometric structural analysis. Computer Methods in Applied Mechanics and Engineering,2007,196(41-44):4160-4183.
[26]Cottrell J, Reali A, Bazilevs Y, et al. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering,2006,195(41-43):5257-5296.
[27]Benson D, Bazilevs Y, Hsu M, et al. Isogeometric shell analysis:The Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):276-289. Computa-tional Geometry and Analysis.
[28]Echter R, Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements. Computer Methods in Applied Mechanics and Engineering,2010,199(5-8):374-382. Computa-tional Geometry and Analysis.
[29]Benson D, Bazilevs Y, Hsu M C, et al. A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering,2011,200(13-16):1367-1378.
[30]De Lorenzis L, Temizer, Wriggers P, et al. A large deformation frictional contact formulation using NURBS-based isogeometric analysis. International Journal for Numerical Methods in En-gineering,2011, pages n/a-n/a.
[31]Elguedj T, Buteri J R A. Isogeometric analysis for strain field measurements. Computer Methods in Applied Mechanics and Engineering,2011,200(1-4):40-56.
[32]Lu J. Isogeometric contact analysis: Geometric basis and formulation for frictionless contact. Computer Methods in Applied Mechanics and Engineering,2011,200(5-8):726-741.
[33]Lu J, Zhou X. Cylindrical element: Isogeometric model of continuum rod. Computer Methods in Applied Mechanics and Engineering,2011,200(1-4):233-241.
[34]Temizer I, Wriggers P, Hughes T. Contact treatment in isogeometric analysis with NURBS. Com-puter Methods in Applied Mechanics and Engineering,2011,200(9-12):1100-1112.
[35]张汉杰,王东东,轩军厂.薄梁板结构NURBS几何精确有限元分析.力学季刊,2010,4：469-477.
[36]Shabana A. An absolute nodal coordinate formulation for the large rotation and deformation anal-ysis of flexible bodies. Technical Report MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago,1996.
[37]Shabana A A. Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formu-lation. Multibody System Dynamics,1997, 1(3):339-348.
[38]Escalona J L, Hussien H A, Shabana A A. Application of the absolute nodal coordinate formulation to multibody system dynamics. Journal of Sound and Vibration,1998,214(5):833-851.
[39]Shabana A A. Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dynamics,1998,16(3):293-306.
[40]Shabana A A, Hussien H A, Escalona J L. Application of the absolute nodal coordinate formu-lation to large rotation and large deformation problems. Journal of Mechanical Design,1998, 120(2):188-195.
[41]Omar M A, Shabana A A. A two-dimensional shear deformable beam for large rotation and deformation problems. Journal of Sound and Vibration,2001,243(3):565-576.
[42]Dufva K E, Sopanen J T, Mikkola A M. A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. Journal of Sound and Vibration,2005,280(3-5):719-738.
[43]Kerkkanen K S, Sopanen J T, Mikkola A M. A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation. Journal of Mechanical Design,2005,127(4):621-630.
[44]Nachbagauer K, Gerstmayr J, Sinwel A S, et al. A linear and quadratic planar finite elementbased on the absolute nodal coordinate formulation, in: Proceedings of Proceedings of the 1 st Joint International Conferenceon Multibody system dynamics, Lappeenranta, Finland,2010.
[45]Dombrowski S V. Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody System Dynamics,2002,8(4):409-432.
[46]Yoo W S, Dmitrochenko 0, Park S J, et al. A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates:Application to a Rotating Strip. Mechanics Based Design of Structures and Machines: An International Journal,2005,33(3):399-422.
[47]Mikkola A, Dmitrochenko O, Matikainen M. Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2009,4(1):011004.
[48]Shabana A A, Yakoub R Y. Three dimensional absolute nodal coordinate formulation for beam elements: Theory. Journal of Mechanical Design,2001,123(4):606-613.
[49]Yakoub R Y, Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. Journal of Mechanical Design,2001,123(4):614-621.
[50]Garcia-Vallejo D, Mayo J, Escalona J L, et al. Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dynamics,2004,35(4):313-329.
[51]Gerstmayr J, Shabana A A. Efficient Integration Of The Elastic Forces And Thinthree-dimensional Beam Elements In The Absolute Nodal Coordinate Formulation, in:Proceedings of MULTIBODY DYNAMICS 2005, ECCOMAS Thematic Conference, Madrid, Spain,2005.
[52]Dmitrochenko O N, Pogorelov D Y. Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody System Dynamics,2003,10(1):17-43.
[53]Dmitrochenko O, Mikkola A. Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2008,3(4):041012-8.
[54]Dmitrochenko O, Mikkola A. Shear Correction for Thin Plate Finite Elements Based on the Ab-solute Nodal Coordinate Formulation. ASME Conference Proceedings,2009,2009(49019):909-917.
[55]K. D, A. S A. Use of the absolute nodal coordinate formulation in the analysis of thin plate structures. Technical Report MBS05-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago,2005.
[56]Mikkola A M, Shabana A A. A new plate element based on the absolute nodal coordinate formu-lation, in: Proceedings of Proceedings of the ASME 2001 DETC, Pittsburgh, America,2001.
[57]Mikkola A M, Shabana A A. A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multibody System Dynamics, 2003,9(3):283-309.
[58]Mikkola A M, Matikainen M K. Development of elastic forces for a large deformation plate ele-ment based on the absolute nodal coordinate formulation. Journal of Computational and Nonlinear Dynamics,2006,1(2):103-108.
[59]Matikainen M K, Schwab A, Mikkola A M. Comparison of Two Moderately Thick Plate Elements based on The Absolute Nodal Coordinate Formulation. in:Proceedings of Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2009, Warsaw, Poland,2009.
[60]Abbas L K, Rui X, Hammoudi Z S. Plate/shell element of variable thickness based on the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2010,224(2):127-141.
[61]Takahashi Y, Shinizu N. Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams, in:Proceedings of ASME Proceedings of Design Engineering Technical Conference, New York,1999, VIB-8203.
[62]Berzeri M, Campanelli M, Shabana A A. Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation. Multibody System Dynamics,2001,5(1):21-54.
[63]Sopanen J T, Mikkola A M. Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dynamics,2003,34(1-2):53-74.
[64]Yu L, Zhao Z, Tang J, et al. Integration of absolute nodal elements into multibody system. Non-linear Dynamics,2010,62(4):931-943.
[65]Dmitrochenko O, Mikkola A. Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate Formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2011,225(1):34-51.
[66]Yakoub R Y, Shabana A A. Use of cholesky coordinates and the absolute nodal coordinate for-mulation in the computer simulation of flexible multibody systems. Nonlinear Dynamics,1999, 20(3):267-282.
[67]Sugiyama H, Shabana A A. On the use of implicit integration methods and the absolute nodal co-ordinate formulation in the analysis of elasto-plastic deformation problems. Nonlinear Dynamics, 2004,37(3):245-270.
[68]Hussein B, Negrut D, Shabana A A. Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dynamics,2008,54(4):283-296.
[69]Tian Q, Chen L P, Zhang Y Q, et al. An Efficient Hybrid Method for Multibody Dynamics Simu-lation Based on Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2009,4(2):021009.
[70]Matikainen M K, Hertzen R, Mikkola A, et al. Elimination of high frequencies in the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,2010,224(1):103-116.
[71]Gerslmayr J. Strain tensors in the absolute nodal coordinate and the floating frame of reference formulation. Nonlinear Dynamics,2003,34(1-2):133-145.
[72]Dibold M, Gerstmayr J, Irschik H. A Detailed Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems. Journal of Computational and Nonlinear Dynamics,2009,4(2):021006.
[73]Yoo W, Lee J, Park S, et al. Large Oscillations of a Thin Cantilever Beam:Physical Experiments and Simulation Using the Absolute Nodal Coordinate Formulation. Nonlinear Dynamics,2003, 34(1):3-29.
[74]Yoo W, Park S, Dmitrochenko O N, et al. Verification of Absolute Nodal Coordinate Formula-tion in Flexible Multibody Dynamics via Physical Experiments of Large Deformation Problems. Journal of Computational and Nonlinear Dynamics,2006, 1(1):81-93.
[75]Schwab A L, Gerstmayr J, Meijaard J P, et al. Comparison of three-dimensional flexible thin plate elements for multibody dynamic analysis:Finite element formulation and absolute nodal coordinate formulation. Las Vegas, NV:Amer Soc Mechanical Engineers,2007,1059-1070.
[76]Schwab A L, Meijaard J P. Comparison of Three-Dimensional Flexible Beam Elements for Dy-namic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formula-tion. Journal of Computational and Nonlinear Dynamics,2010,5(1):011010-10.
[77]Shabana A A, Mikkola A M. Use of the finite element absolute nodal coordinate formulation in modeling slope discontinuity. Journal of Mechanical Design,2003,125(2):342-350.
[78]Shabana A A, Maqueda L G. Slope discontinuities in the finite element absolute nodal coordinate formulation:gradient deficient elements. Multibody System Dynamics,2008,20(3):239-249.
[79]Sugiyama H, Escalona J L, Shabana A A. Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dynamics,2003,31(2):167-195.
[80]Lee S H, Park T W, Seo J H, et al. The development of a sliding joint for very flexible multi-body dynamics using absolute nodal coordinate formulation. Multibody System Dynamics,2008, 20(3):223-237.
[81]Hong D, Ren G. A modeling of sliding joint on one-dimensional flexible medium. Multibody System Dynamics,2011,26(1):91-106.
[82]Sanborn G, Shabana A. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody System Dynamics,2009,22(2):181-197.
[83]Lan P, Shabana A A. Integration of B-spline geometry and ANCF finite element analysis. Non-linear Dynamics,2010,61 (1-2):193-206.
[84]Lan P, Shabana A A. Rational Finite Elements and Flexible Body Dynamics. Journal of Vibration and Acoustics-transactions of The Asme,2010,132(4).
[85]Sugiyama H, Shabana A A. Application of plasticity theory and absolute nodal coordinate formu-lation to flexible multibody system dynamics. Journal of Mechanical Design,2004,126(3):478-487.
[86]Yu L, Zhao Z, Ren G. Multibody Dynamic Model of Web Guiding System With Moving Web. Journal Of Dynamic Systems Measurement And Control-transactions Of The Asme,2010,132(5).
[87]Sugiyama H, Suda Y. Non-linear elastic ring tyre model using the absolute nodal coordinate formulation. Proceedings of the Institution of Mechanical Engineers, Part K:Journal of Multi-body Dynamics,2009,223(3):211-219.
[88]Zhang Y, Tian Q, Chen L, et al. Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods. Multibody System Dynamics,2009, 21(3):281-303.
[89]Jung S, Park T, Chung W. Dynamic analysis of rubber-like material using absolute nodal coordi-nate formulation based on the non-linear constitutive law. Nonlinear Dynamics,2011,63:149-157.
[90]Sugiyama H, Gerstmayr J, Shabana A A. Deformation modes in the finite element absolute nodal coordinate formulation. Journal of Sound and Vibration,2006,298(4-5):1129-1149.
[91]Zhao J, Tian Q, Hu H. Modal Analysis of a Rotating Thin Plate via Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics,2011,6(4):041013.
[92]Tian Q, Zhang Y, Chen L, et al. Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Computers & Structures,2009,87(13-14):913-929.
[93]Tian Q, Zhang Y Q, Chen L P. Two-link Flexible Manipulator Modelling And Tip Trajectory Tracking Based On The Absolute Nodal Coordinate Method. International Journal Of Robotics & Automation,2009,24(2):103-114.
[94]田强,张云清,陈立平.含分数阻尼特性元件的多体系统动力学研究.力学学报,2009,(6)：920-928.
[95]田强,张云清,陈立平.基于增广拉格朗日方法的多柔体动力学研究.系统仿真学报,2009,(24)：7704-7710.
[96]田强,张云清,陈立平.柔性多体系统动力学绝对节点坐标方法研究进展.力学进展,2010,(2)：189-202.
[97]刘铖,田强,胡海岩.基于绝对节点坐标的多柔体系统动力学高效计算方法.力学学报,2010,(6)：1197-1205.
[98]虞磊,赵治华,任启鸿,等.基于绝对节点坐标的柔性体碰撞仿真.清华大学学报(自然科学版),2010,(7)：1135-1140.
[99]邹凡,刘锦阳.大变形薄板多体系统的动力学建模.应用力学学报,2010,(4)：740-745.
[100]沈凌杰,刘锦阳,余征跃.柔性梁斜碰撞问题的非线性动力学建模和实验研究.力学季刊,2006,(4)：568-577.
[101]Laulusa A, Bauchau O A. Review of Classical Approaches for Constraint Enforcement in Multi-body Systems. Journal of Computational and Nonlinear Dynamics,2008,3(1):011004.
[102]Bauchau O A, Laulusa A. Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems. Journal of Computational and Nonlinear Dynamics,2008,3(1):011005.
[103]Kurdila A, Papastavridis J G, Kamat M P. Role of Maggi's Equations in Computational Methods for Constrained Multibody Systems. J. Guid. Control Dyn.,1990,13(1):113-120.
[104]Papastavridis J G. Maggi's Equations of Motion and the Determina-tion of Constraint Reactions. J. Guid. Control Dyn.,1990,13(2):213-220.
[105]Hemami H, Weimer F C. Modeling of Nonholonomic Dynamic Systems With Applications. Jour-nal of Applied Mechanics,1981,48(1):177-182.
[106]Lotstedt P. Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints. SIAM Journal on Applied Mathematics,1982,42(2):pp.281-296.
[107]Gear C W, Leimkuhler B, Gupta G K. Automatic integration of Euler-Lagrange equations with constraints. Journal of Computational and Applied Mathematics,1985,12-13:77-90.
[108]Kane T R, Wang C F. On the Derivation of Equations of Motion. Journal of the Society for Industrial and Applied Mathematics,1965,13(2):pp.487-492.
[109]Jalon J. G, Unda J, Avello A, et al. Dynamic Analysis of Three-Dimensional Mechanisms in"Natural" Coordinates. ASME J. Mech., Transm., Autom. Des.,1987,109:460-465.
[110]Unda J, Jalon J. G, Losantos F, et al. A Comparative Study on Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems. ASME J. Mech., Transm., Autom. Des., 1987,109:466-474.
[111]Udwadia F E, Kalaba R E, Hee-Chang E. Equations of motion for constrained mechanical systems and the extended D'Alembert's principle. Q. Appl. Math.,1997, LV:321-331.
[112]Udwadia F E, Kalaba R E. A New Perspective on Constrained Motion, in: Proceedings of Proc. R. Soc., London: Royal Society of London, London, ROYAUME-UNI (1990-1995) (Revue),1992, 407-410.
[113]Udwadia F E. On constrained motion. Applied Mathematics and Computation,2005,164(2):313-320.12th International Workshop on Dynamics and Control.
[114]Kalaba R E, Udwadia F E. Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss's Principle. Journal of Applied Mechanics,1993,60(3):662-668.
[115]Kalaba R E, Udwadia F E. Lagrangian mechanics, Gauss's principle, quadratic programming, and generalized inverses: new equations for nonholonomically constrained discrete mechanical systems. Q. Appl. Math.,1994, LⅡ229-241.
[116]Udwadia F E, Kalaba R E. The Geometry of Constrained Motion. ZAMM-Journal of Ap-plied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik,1995, 75(8):637-640.
[117]Udwadia F E, Kalaba R E. The explicit Gibb-Appell equation and generalized inverse forms. Q. Appl. Math.,1998, LVI:277-288.
[118]Udwadia F E, Kalaba R E. What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems? Journal of Applied Mechanics,2002,69(3):335-339.
[119]Udwadia F E, Kalaba R E. On the foundations of analytical dynamics. International Journal of Non-Linear Mechanics,2002,37(6):1079-1090.
[120]Lilov L, Lorer M. Dynamic Analysis of Multirigid-Body System Based on the Gauss Principle. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathe-matik und Mechanik,1982,62(10):539-545.
[121]Blajer W. A Projection Method Approach to Constrained Dynamic Analysis. Journal of Applied Mechanics,1992,59(3):643-649.
[122]Blajer W. Projective formulation of Maggi's method for nonholonomic systems analysis. Journal of Guidance, Control, and Dynamics,1992,15(2):522-525.
[123]Blajer W, Schiehlen W, Schirm W. A projective criterion to the coordinate partitioning method for multibody dynamics. Archive of Applied Mechanics,1994,64(2):86-98.
[124]Blajer W. An orthonormal tangent space method for constrained multibody systems. Computer Methods in Applied Mechanics and Engineering,1995,121(1-4):45-57.
[125]Agrawal O P, Saigal S. Dynamic analysis of multi-body systems using tangent coordinates. Com-puters & Structures,1989,31(3):349-355.
[126]Betsch P. The discrete null space method for the energy consistent integration of constrained mechanical systems-Part I: Holonomic constraints. Computer Methods in Applied Mechanics and Engineering,2005,194(50-52):5159-5190.
[127]Betsch P, Leyendecker S. The discrete null space method for the energy consistent integration of constrained mechanical systems. Part Ⅱ:multibody dynamics. International Journal for Numerical Methods in Engineering,2006,67(4):499-552.
[128]Leyendecker S, Betsch P, Steinmann P. The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part Ⅲ:Flexible multibody dynamics. Multibody System Dynamics,2008,19(1):45-72.
[129]Baumgarte J. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics and Engineering,1972,1:1-16.
[130]Eich E, Hanke M. Regularization Methods for Constrained Mechanical Multibody Systems. Z. Angew. Math. Mech.,1995,75(10):761-773.
[131]Nikravesh P E, Wehage R A, Kwon O K. Euler Parameters in Computational Kinematics and Dynamics-Part 1 and Part 2. Journal of Mechanisms, Trasmissions, and Automation in Design, 1985,107(3):358-369.
[132]Park T W, Haug E J. A Hybrid Numerical Integration Method for Machine Dynamic Simulation. Journal of Mechanisms Transmissions and Automation in Design,1986,108(2):211-216.
[133]Chang C O, Nikravesh P E. An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems. Journal of Mechanisms Transmissions and Automation in De-sign,1985,107(4):488-492.
[134]Yoon S, Howe R M, Greenwood D T. Stability and Accuracy Analysis of Baumgarte's Constraint Violation Stabilization Method. Journal of Mechanical Design,1995,117(3):446-453.
[135]Lin S T, Hong M C. Stabilization Method for Numerical Integration of Multibody Mechanical Systems. Journal of Mechanical Design,1998,120(4):565-572.
[136]Park K C, Chiou J C. Stabilization of Computational Procedures for Constrained Dynamical Systems. J. Guid. Control Dyn.,1988,11(4):365-370.
[137]Bayo E, Jalon J G D, Serna M A. A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems. Computer Methods in Applied Mechanics and Engineering, 1988,71(2):183-195.
[138]Bayo E, Jalon J G, Avello A, et al. An efficient computational method for real time multibody dynamic simulation in fully cartesian coordinates. Computer Methods in Applied Mechanics and Engineering,1991,92(3):377-395.
[139]Newmark N M. A Method of Computation for Structural Dynamics. J. Engrg. Mech. Div.,1959, 112:67-94.
[140]Cardona A, Geradin M. Time integration of the equations of motion in mechanism analysis. Computers & Structures,1989,33(3):801-820.
[141]Gear C W. Numerical Initial Value Problems in Ordinary Differential Equations. PTR Upper Saddle River, NJ, USA:Prentice Hall,1971.
[142]Bottasso C L, Bauchau O A, Cardona A. Time-Step-Size-Independent Conditioning and Sensi-tivity to Perturbations in the Numerical Solution of Index Three Differential Algebraic Equations. Siam Journal on Scientific Computing,2007,29(1):397-414.
[143]Negrut D, Rampalli R, Ottarsson G, et al. On an Implementation of the Hilber-Hughes-Taylor Method in the Context of Index 3 Differential-Algebraic Equations of Multibody Dynamics (DETC2005-85096). Journal of Computational and Nonlinear Dynamics,2007,2(l):73-85.
[144]Hilber H M, Hughes T J R, Taylor R L. Improved numerical dissipation for time integration algo-rithms in structural dynamics. Earthquake Engineering & Structural Dynamics,1977,5(3):283-292.
[145]Chung J, Hulbert G M. A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-alpha Method. Journal of Applied Mechanics,1993, 60(2):371-375.
[146]Greene W H, Haftka R T. Computational aspects of sensitivity calculations in transient structural analysis. Computers & Structures,1989,32(2):433-443.
[147]Haftka R T, Gurdal Z. Elements of structural optimization,3 ed. Springer,1992.
[148]Chang C O, Nikravesh P E. Optimal design of mechanical systems with constraint violation stabilization method. Journal of mechanisms, transmissions, and automation in design,1985, 107(4):493-498.
[149]Dias J M P, Pereira M S. Sensitivity Analysis of Rigid-Flexible Multibody Systems. Multibody System Dynamics,1997,1 (3):303-322.
[150]Haug E J, Ehle P E. Second-order design sensitivity analysis of mechanical system dynamics. International Journal for Numerical Methods in Engineering,1982,18(11):1699-1717.
[151]Haug E J, Mani N K, Krishnaswami P. Design sensitivity analysis and optimization of dynamically driven systems, in:Haug E J, editor, Proceedings of Computer Aided Analysis and Optimization of Mechanical System Dynamics, Heidelberg, Berlin: Springer-Verlag,1984,555-636.
[152]Haug E J, Wehage R, Barman N C. Design sensitivity analysis of planar mechanism and machine dynamics. Journal of Mechanical Design,1981,103(3):560-570.
[153]Hsu Y, Anderson K S. Recursive sensitivity analysis for constrained multi-rigid-body dynamic systems design optimization. Structural and Multidisciplinary Optimization,2002,24(4):312-324.
[154]Maly T, Petzold L R. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Applied Numerical Mathematics,1996,20(1-2):57-79.
[155]Maria Augusta Ncto J A C A. Sensitivity analysis of flexible multibody systems using compos-ite materials components. International Journal for Numerical Methods in Engineering,2009, 77:386-413.
[156]Mukherjee R, Bhalerao K, Anderson K. A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis. Structural and Multidisciplinary Optimization,2008, 35(5):413-429.
[157]Serban R, Freeman J S. Identification and Identifiability of Unknown Parameters in Mullibody Dynamic Systems. Multibody System Dynamics,2001,5(4):335-350.
[158]Serban R, Haug E J. Kinematic and kinetic derivatives in multibody system analysis. Mechanics of structures and machines,1998,26(2):145-173.
[159]Wang X, Haug E J, Pan W. Implicit Numerical Integration for Design Sensitivity Analysis of Rigid Multibody Systems. Mechanics Based Design of Structures and Machines:An International Journal,2005,33(1):1-30.
[160]Bestle D, Eberhard P. Analyzing and Optimizing Multibody Systems. Mechanics of Structures and Machines,1992,20(1):67-92.
[161]Bestle D, Seybold J. Sensitivity analysis of constrained multibody systems. Archive of Applied Mechanics,1992,62(3):181-190.
[162]Cao Y, Li S, Petzold L. Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software. Journal of Computational and Applied Mathematics,2002,149(1):171-191.
[163]Li S, Petzold L, Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem. Applied Numerical Mathematics,2000,32(2):161-174.
[164]Liu X. Sensitivity analysis of constrained flexible multibody systems with stability considerations. Mechanism and machine theory,1996,31 (7):859-863.
[165]Bischof C, Carle A, Corliss G, et al. ADIFOR:Generating Derivative Codes from Fortran Pro-grams. Scientific Programming,1992, 1(1):11-29.
[166]Bischof C, Khademi P, Mauer A, et al. Adifor 2.0: automatic differentiation of Fortran 77 pro-grams. Computational Science & Engineering, IEEE,1996,3(3):18-32.
[167]Eberhard P. Analysis and optimization of complex multibody systems using advanced sensitiv-ity analysis methods, in:Proceedings of 3rd International Congress on Industrial and Applied Mathematics (ICIAM 95), Hamburg, Germany: Akademie Verlag Gmbh,1995,40-43.
[168]Griewank A, Reese S. On the calculation of Jacobian matrices by the Markowitz rule, in:Griewank A, Corliss G, editors, Proceedings of Automatic Differentiation of Algorithms:Theory, Implemen-tation, and Applications, Philadelphia,PA:SIAM,1991,126-135.
[169]Bhalerao K, Poursina M, Anderson K. An efficient direct differentiation approach for sensitivity analysis of flexible multibody systems. Multibody System Dynamics,2010,23(2):121-140.
[170]Jay O L, Negrut D. A Second Order Extension of the Generalized-a Method for Constrained Systems in Mechanics, in:Bottasso C L, editor, Proceedings of Multibody Dynamics. Springer Netherlands,2008,143-158.
[171]Lotstedt P, Petzold L. Numerical solution of nonlinear differential equations with algebraic con-straints I: Convergence results for backward differentiation formulas. Math. Comput.,1986, 46(174):491-516.
[172]Brenan K E, Engquist B E. Backward Differentiation Approximations of Nonlinear Differen-tial/Algebraic Systems. Mathematics of Computation,1988,51(184):pp.659-676.
[173]Arnold M, Bruls O. Convergence of the generalized-a scheme for constrained mechanical sys-tems. Multibody System Dynamics,2007,18(2):185-202.
[174]PieglL, Tiller W. The NURBS book. Heidelberg:Springer Verlag,1997.
[175]施法中.计算机辅助几何设计与非均匀有理B样条.中国,北京：高等教育出版社,2001.
[176]Cottrell J A, Hughes T J, Bazilevs Y. Isogeometric analysis:toward integration of CAD and FEA. The Atrium, Southern Gate, Chichester, West Sussex, PO198SQ, United Kingdom:John Wiley & Sons Inc,2009.
[177]Bonet J, Wood R D. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: Cambridge University Press,1997.
[178]Shabana A A. Computational continuum mechanics. New York, United States of America: Cam-bridge University Press,2008.
[179]Davis P, Rabinowitz P. Methods of Numerical Integration. San Diego, California: Academic Press Inc,1984.
[180]Berzeri M, Shabana A A. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration,2000,235(4):539-565.
[181]Gerstmayr J, Shabana A. Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation. Nonlinear Dynamics,2006,45:109-130.
[182]Bagley R L, Torvik P J. A Theoretical Basis for the Application of Fractional Calculus to Vis-coelasticity. Journal of Rheology,1983,27(3):201-210.
[183]Kilbas A, Srivastava H, Trujillo J. Theory and Applications of Fractional Differential Equations. Radarweg 29, P.O. Box 211,1000 AE Amsterdam, The Netherlands:Elsevier,2006.
[184]Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential/algebraic equations. Multibody System Dynamics,2007,18(4):599-617.
[185]丁洁玉.基于多体系统的灵敏度分析及动态优化设计：[博士学位论文].上海：上海大学,2008.