柔性多体动力学计算方法与大型可展天线动力分析研究
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摘要
柔性多体动力学(Flexible multibody dynamics,FMD)发展已近40年,建模理论仍未尽善尽美,并面临进一步突破的难题;与建模理论相比,FMD计算技术和实验技术的研究更显得极为匮乏,尚有相当多的问题需要进一步深入探讨。
本文在建立柔性多体系统(Flexible multibody system,FMS)缩并模型的基础上,针对其求解分析问题进行了深入的研究,分别基于中心差分法和Newmark法提出了适用于FMD问题求解的子循环算法,该类算法的提出对FMD计算理论的发展将起到积极的推动作用,柔性多体动力学计算方法的研究工作包括以下几个方面:
1、应用有限元方法离散空间任意柔性体,通过浮动坐标系描述柔性体上任意点的坐标位置,并将其变形表达为广义模态坐标,建立了完备的FMS方程;将广义坐标变量分解为独立变量和非独立变量,得到了缩并型的FMS方程,在此基础上,深入分析了FMD问题求解中存在的特殊性,针对FMS方程固有的刚性问题,提出了应用子循环原理对常用的FMS方程计算方法进行修正,从而在提高FMD问题求解效率的同时,有效地处理FMS微分方程的刚性问题。
2、基于中心差分算法,通过将缩并型FMS方程中的待求变量分解为长、短周期变量域,采用不同的步长进行时域积分,推导出同步更新公式和子步更新公式,建立了适用于缩并型FMS方程求解的中心差分子循环算法,并应用直接积分逼近算子方法进行了该算法的稳定性分析,证明只要各积分域步长不超过其临界步长,该算法能保持良好的稳定性。在中心差分子循环算法中,子步循环是显式过程,因此,该算法仍存在一定程度的误差累积现象,然而算例表明,中心差分子循环算法可以在保持恰当计算精度的同时,大幅度提高了FMS方程的求解效率。
3、基于Newmark算法,采用类似的处理措施对子循环算法进行了修正,建立了适用于FMS方程求解的Newmark子循环计算公式,通过实时检查系统的能量平衡状态,并摄动修正积分步长,使子循环积分过程保持了良好的稳定性,得到了合理的数值计算结果。与中心差分子循环算法比较,Newmark子循环算法的同步更新过程和子步更新过程都进行了隐式迭代,消除了数值积分过程中的误差累积现象,算例表明,修正的Newmark子循环算法无论在计算精度方面还是在计算效率方面,都优于中心差分子循环算法。
FMD理论已普遍应用于星载可展天线展开过程的仿真分析中,但是在陆基车载可展天线设计中却尚未得到普遍应用,本文分别建立了车载可展天线的FMS模型、多刚体模型及有限元模型,分别将FMS模型计算结果与有限元模型计算结果、多刚体模型计算结果进行了对比分析,给出了相应的比较结论,这些结论对进一步拓展FMD理论的工程应用领域具有一定的参考意义。
1、建立了可展天线结构的有限元模型和FMS模型,分别对其进行了有限元分析和FMD分析,结果表明天线阵面在运动过程中,有限元分析结果与FMD分析结果之间存在一定的差异性;有限元分析计算仅仅得到了天线在大范围运动过程中由于自重及外载荷作用下的阵面变形状态,变形的时域曲线连续光滑且无波动现象,而FMD分析结果却明显反映出,由于天线的大范围运动惯性,造成了阵面的小幅度弹性变形,这种弹性变形的反过来影响了天线大范围运动的轨迹,体现了大范围运动和小幅度变形之间的耦合现象,这一分析结果更加符合天线阵面在运动过程中的实际状态。
2、分别采用可展天线多刚体模型和FMS模型,对其展开过程进行了多刚体分析和FMD动态分析,结果表明天线阵面FMD分析的结果与多刚体分析结果之间存在显著的差异,应用FMD逆动力学分析技术求得的内、外侧展开油缸驱动力大小悬殊,显示出天线不同位置的变形不一致性会给油缸造成不同的反作用力。通过FMD计算得到的天线转角和变形结果与实际现象保持了高度的一致性,而采用多刚体系统模型计算的展开油缸驱动力却导致展开转角和变形出现了不合实际的越界现象。这一结果表明对大型可展柔性天线的动力学分析而言,多刚体系统动力学有明显的不足之处。同时,为验证子循环算法对复杂FMS模型计算的有效性,应用子循环算法进行了天线展开过程的动态响应分析计算,比较结果显示了FMD子循环算法的普适性。
3、分别对天线系统倒竖过程和工作旋转过程进行了基于FMD的动态响应计算分析,分析结果显示:无论是否考虑风载荷作用,由于天线阵面运动的巨大惯性以及结构的柔性,阵面在运动初期均出现剧烈的变形波动现象,在稳态工作时,由于风载荷作用的周期变化特性,阵面变形也出现显著的周期性,这种周期性的变形状态,将导致天线系统电磁特性出现一定程度的精度下降,这一分析结果说明在进行大型阵面天线结构设计时,必须充分重视系统的惯性作用以及外界变化载荷的作用,对阵面结构进行适当的刚度加强,以满足天线系统足够的工作可靠性和精度要求。
Study of Flexible multi-body dynamics (FMD) has been developed nearly 40 years. Theory of the FMD modeling still doesn’t reach perfect condition and involves in difficult of farther breakthrough. Comparing with the modeling theory, studies of computational strategies and experiment technologies are more weakness. There are a lot of problems which wait for further more discussion.
Based on modeling a condensed formulation of FMD problem, this paper makes a deep study of its analysis problem and presents subcycling algorthms, which are suitable for the FMD problem, based on the central difference method and the Newmark algorithm respectively. This will actively promote development of the FMD computational theory. Research of the FMD computational methods includes several contents as following.
1、Applying the FEM method to discrete an arbitrary spatial flexible body, describing position of a point in the body by means of a float frame and measuring deformation of the body in a generalized mode coordinate style, a self-contained FMS formulation was established based on the second Lagrange equation. Separating the generalized variables to a group of independent variables and a group of dependent variables, a condensed FMS equation was established. Based on this result, Special problems, which exist in solution process of a FMS equation, are deeply analyzed. In order to deal with stiffness of the FMS differential equation, we proposed to modify the algorithms, which are frequently used in FMD problems, based on subcycling principles. Thereby, solution efficiency of the FMD problem can be enhanced and stiffness of the differential equation can be effectively managed at the same time.
2、Based on the central difference method, separating unknown variables of the condensed FMS equation in larger cycling domain and smaller cycling domain and using different step sizes to integrate these variables, common update formula and sub-step update formula are carried out and a central-difference-based sub-cycling algorithm, which is suitable for FMD problems, was established. An integral approximation operator method is used for analyzing stability of the sub-cycling algorithm. It is proved that the algorithm can hold stable property only if the step sizes in each domain do not exceed their critical limits. Due to sub-step cycles of the central-difference-based sub-cycling algorithm are explicit processes, there is still error accumulation phenomenon in the algorithm. However, numerical examples indicate that the central-difference-based sub-cycling algorithm can enhance the computational efficiency greatly without intensely dropping of the precision.
3、Also, based on the Newmark algorithm, modifying the sub-cycling by means of similar manner mentioned above, a Newmark-based sub-cycling, which is suitable for FMD problems, was presented. By means of checking energy balance status and changing the step sizes during the integral process, favourable stability of the sub-cycling can be preserved and reasonable numerical results can be obtained. Compared with the central-difference-based sub-cycling algorithm, the implicit iterative processes are performed whether in the common-update or in the sub-step-update. Accordingly, error accumulation phenomenon is eliminated during the numerical integrate process. Numerical examples indicate that the Newmark-based sub-cycling is more efficient and more precise than the central-difference-based sub-cycling algorithm.
FMD theory has been largely applied in simulation of deploying process of artificial satellite mounted antennas. However, this application has not been expanded to design of mobile-mounted deployable antenna. This paper established FEM model, multi rigid body model and FMS model of a mobile-mounted deployable antenna. Comparing computational results from the FMS model with that from the FEM model and that from the multi rigid body model, we got some relative conclusions. These conclusions have a little reference values for further developing engineering application domain of the FMD theory.
1、FEM model and FMS model of a large mobile-mounted deployable antenna were respectively established. FEM analysis and FMD analysis are separately performed for the two models. Comparison of the results illustrate that some differences exist between the FEM analysis and the FMD analysis during motion process of the antenna frame. The FEM analysis only got hold of deformation condition of the frame resulting from its deadweight and external loads during a large range motion. Time-domain deformation curve is continued, slippy and without fluctuate phenomenon. On the contrary, the FMD analysis reflected evidently that a small range oscillating deformation was produced due to motion inertia of the frame. And this oscillation also affected motion trajectory of the frame by contraries. This interaction exhibited coupling between large range motion and small range deformation of the frame. And this result is more according with actual condition of the frame during motion process.
2、Deploying process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. A notable difference was displayed between the two results. Driving forces of frame deploying oil-cylinders, which were resulted from anti-dynamic analysis technique, revealed evident relativity between loads and locations. Rotation angle and deformation result from the FMS model are also according with actual phenomenon enough. On the contrary, Rotation angle and deformation result from the multi rigid-bodies model induced a bound exceeded phenomenon, which is unnatural. This result indicates that the multi rigid-bodies model is shortage for dynamic analysis of a large deployable flexible antenna. At the same time, to validate applicable property of the sub-cycling on a complicated FMS model, the Newmark integral and the Newmark-based sub-cycling were used to calculate dynamic response of the antenna, respectively. It shows that the subcycling algorithms can be used in a broad application area.
3、Inverse uprighting process and circumrotating process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. Results showed that whether wind loads are taken into account, a startup oscillation phenomenon usually existed during the motion process due to large inertia and flexibility of the frame. During circumrotating service status, deformation oscillation displayed distinctive periodicity due to periodic variety of the wind loads. This periodic deformation conditions will induce a dropping precision of electromagnetism of the antenna system. This result informed us that the inertia and the external variational loads need to be sufficiently regarded for design of a large frame antenna. To satisfy enough reliability and precision of an antenna, structure of the frame need to be strengthened appropriately.
本文在建立柔性多体系统(Flexible multibody system,FMS)缩并模型的基础上,针对其求解分析问题进行了深入的研究,分别基于中心差分法和Newmark法提出了适用于FMD问题求解的子循环算法,该类算法的提出对FMD计算理论的发展将起到积极的推动作用,柔性多体动力学计算方法的研究工作包括以下几个方面:
1、应用有限元方法离散空间任意柔性体,通过浮动坐标系描述柔性体上任意点的坐标位置,并将其变形表达为广义模态坐标,建立了完备的FMS方程;将广义坐标变量分解为独立变量和非独立变量,得到了缩并型的FMS方程,在此基础上,深入分析了FMD问题求解中存在的特殊性,针对FMS方程固有的刚性问题,提出了应用子循环原理对常用的FMS方程计算方法进行修正,从而在提高FMD问题求解效率的同时,有效地处理FMS微分方程的刚性问题。
2、基于中心差分算法,通过将缩并型FMS方程中的待求变量分解为长、短周期变量域,采用不同的步长进行时域积分,推导出同步更新公式和子步更新公式,建立了适用于缩并型FMS方程求解的中心差分子循环算法,并应用直接积分逼近算子方法进行了该算法的稳定性分析,证明只要各积分域步长不超过其临界步长,该算法能保持良好的稳定性。在中心差分子循环算法中,子步循环是显式过程,因此,该算法仍存在一定程度的误差累积现象,然而算例表明,中心差分子循环算法可以在保持恰当计算精度的同时,大幅度提高了FMS方程的求解效率。
3、基于Newmark算法,采用类似的处理措施对子循环算法进行了修正,建立了适用于FMS方程求解的Newmark子循环计算公式,通过实时检查系统的能量平衡状态,并摄动修正积分步长,使子循环积分过程保持了良好的稳定性,得到了合理的数值计算结果。与中心差分子循环算法比较,Newmark子循环算法的同步更新过程和子步更新过程都进行了隐式迭代,消除了数值积分过程中的误差累积现象,算例表明,修正的Newmark子循环算法无论在计算精度方面还是在计算效率方面,都优于中心差分子循环算法。
FMD理论已普遍应用于星载可展天线展开过程的仿真分析中,但是在陆基车载可展天线设计中却尚未得到普遍应用,本文分别建立了车载可展天线的FMS模型、多刚体模型及有限元模型,分别将FMS模型计算结果与有限元模型计算结果、多刚体模型计算结果进行了对比分析,给出了相应的比较结论,这些结论对进一步拓展FMD理论的工程应用领域具有一定的参考意义。
1、建立了可展天线结构的有限元模型和FMS模型,分别对其进行了有限元分析和FMD分析,结果表明天线阵面在运动过程中,有限元分析结果与FMD分析结果之间存在一定的差异性;有限元分析计算仅仅得到了天线在大范围运动过程中由于自重及外载荷作用下的阵面变形状态,变形的时域曲线连续光滑且无波动现象,而FMD分析结果却明显反映出,由于天线的大范围运动惯性,造成了阵面的小幅度弹性变形,这种弹性变形的反过来影响了天线大范围运动的轨迹,体现了大范围运动和小幅度变形之间的耦合现象,这一分析结果更加符合天线阵面在运动过程中的实际状态。
2、分别采用可展天线多刚体模型和FMS模型,对其展开过程进行了多刚体分析和FMD动态分析,结果表明天线阵面FMD分析的结果与多刚体分析结果之间存在显著的差异,应用FMD逆动力学分析技术求得的内、外侧展开油缸驱动力大小悬殊,显示出天线不同位置的变形不一致性会给油缸造成不同的反作用力。通过FMD计算得到的天线转角和变形结果与实际现象保持了高度的一致性,而采用多刚体系统模型计算的展开油缸驱动力却导致展开转角和变形出现了不合实际的越界现象。这一结果表明对大型可展柔性天线的动力学分析而言,多刚体系统动力学有明显的不足之处。同时,为验证子循环算法对复杂FMS模型计算的有效性,应用子循环算法进行了天线展开过程的动态响应分析计算,比较结果显示了FMD子循环算法的普适性。
3、分别对天线系统倒竖过程和工作旋转过程进行了基于FMD的动态响应计算分析,分析结果显示:无论是否考虑风载荷作用,由于天线阵面运动的巨大惯性以及结构的柔性,阵面在运动初期均出现剧烈的变形波动现象,在稳态工作时,由于风载荷作用的周期变化特性,阵面变形也出现显著的周期性,这种周期性的变形状态,将导致天线系统电磁特性出现一定程度的精度下降,这一分析结果说明在进行大型阵面天线结构设计时,必须充分重视系统的惯性作用以及外界变化载荷的作用,对阵面结构进行适当的刚度加强,以满足天线系统足够的工作可靠性和精度要求。
Study of Flexible multi-body dynamics (FMD) has been developed nearly 40 years. Theory of the FMD modeling still doesn’t reach perfect condition and involves in difficult of farther breakthrough. Comparing with the modeling theory, studies of computational strategies and experiment technologies are more weakness. There are a lot of problems which wait for further more discussion.
Based on modeling a condensed formulation of FMD problem, this paper makes a deep study of its analysis problem and presents subcycling algorthms, which are suitable for the FMD problem, based on the central difference method and the Newmark algorithm respectively. This will actively promote development of the FMD computational theory. Research of the FMD computational methods includes several contents as following.
1、Applying the FEM method to discrete an arbitrary spatial flexible body, describing position of a point in the body by means of a float frame and measuring deformation of the body in a generalized mode coordinate style, a self-contained FMS formulation was established based on the second Lagrange equation. Separating the generalized variables to a group of independent variables and a group of dependent variables, a condensed FMS equation was established. Based on this result, Special problems, which exist in solution process of a FMS equation, are deeply analyzed. In order to deal with stiffness of the FMS differential equation, we proposed to modify the algorithms, which are frequently used in FMD problems, based on subcycling principles. Thereby, solution efficiency of the FMD problem can be enhanced and stiffness of the differential equation can be effectively managed at the same time.
2、Based on the central difference method, separating unknown variables of the condensed FMS equation in larger cycling domain and smaller cycling domain and using different step sizes to integrate these variables, common update formula and sub-step update formula are carried out and a central-difference-based sub-cycling algorithm, which is suitable for FMD problems, was established. An integral approximation operator method is used for analyzing stability of the sub-cycling algorithm. It is proved that the algorithm can hold stable property only if the step sizes in each domain do not exceed their critical limits. Due to sub-step cycles of the central-difference-based sub-cycling algorithm are explicit processes, there is still error accumulation phenomenon in the algorithm. However, numerical examples indicate that the central-difference-based sub-cycling algorithm can enhance the computational efficiency greatly without intensely dropping of the precision.
3、Also, based on the Newmark algorithm, modifying the sub-cycling by means of similar manner mentioned above, a Newmark-based sub-cycling, which is suitable for FMD problems, was presented. By means of checking energy balance status and changing the step sizes during the integral process, favourable stability of the sub-cycling can be preserved and reasonable numerical results can be obtained. Compared with the central-difference-based sub-cycling algorithm, the implicit iterative processes are performed whether in the common-update or in the sub-step-update. Accordingly, error accumulation phenomenon is eliminated during the numerical integrate process. Numerical examples indicate that the Newmark-based sub-cycling is more efficient and more precise than the central-difference-based sub-cycling algorithm.
FMD theory has been largely applied in simulation of deploying process of artificial satellite mounted antennas. However, this application has not been expanded to design of mobile-mounted deployable antenna. This paper established FEM model, multi rigid body model and FMS model of a mobile-mounted deployable antenna. Comparing computational results from the FMS model with that from the FEM model and that from the multi rigid body model, we got some relative conclusions. These conclusions have a little reference values for further developing engineering application domain of the FMD theory.
1、FEM model and FMS model of a large mobile-mounted deployable antenna were respectively established. FEM analysis and FMD analysis are separately performed for the two models. Comparison of the results illustrate that some differences exist between the FEM analysis and the FMD analysis during motion process of the antenna frame. The FEM analysis only got hold of deformation condition of the frame resulting from its deadweight and external loads during a large range motion. Time-domain deformation curve is continued, slippy and without fluctuate phenomenon. On the contrary, the FMD analysis reflected evidently that a small range oscillating deformation was produced due to motion inertia of the frame. And this oscillation also affected motion trajectory of the frame by contraries. This interaction exhibited coupling between large range motion and small range deformation of the frame. And this result is more according with actual condition of the frame during motion process.
2、Deploying process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. A notable difference was displayed between the two results. Driving forces of frame deploying oil-cylinders, which were resulted from anti-dynamic analysis technique, revealed evident relativity between loads and locations. Rotation angle and deformation result from the FMS model are also according with actual phenomenon enough. On the contrary, Rotation angle and deformation result from the multi rigid-bodies model induced a bound exceeded phenomenon, which is unnatural. This result indicates that the multi rigid-bodies model is shortage for dynamic analysis of a large deployable flexible antenna. At the same time, to validate applicable property of the sub-cycling on a complicated FMS model, the Newmark integral and the Newmark-based sub-cycling were used to calculate dynamic response of the antenna, respectively. It shows that the subcycling algorithms can be used in a broad application area.
3、Inverse uprighting process and circumrotating process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. Results showed that whether wind loads are taken into account, a startup oscillation phenomenon usually existed during the motion process due to large inertia and flexibility of the frame. During circumrotating service status, deformation oscillation displayed distinctive periodicity due to periodic variety of the wind loads. This periodic deformation conditions will induce a dropping precision of electromagnetism of the antenna system. This result informed us that the inertia and the external variational loads need to be sufficiently regarded for design of a large frame antenna. To satisfy enough reliability and precision of an antenna, structure of the frame need to be strengthened appropriately.
引文
[1] Fischer, O., Theoretical Foundation for the mechanics of Living Mechanisms (in German), Teubner Leipzig, 1906.
[2] Wittenburg J.,多体系统的动力学,第15届国际力学会议,中文译稿,力学进展,1982, 12.
[3] Roberson, R. E., Wittenburg, J., A Dynamical Formalism for an Arbitrary Number of Inter-connected Rigid Bodies. With reference to the Problem of Satellite Attitude Control. 3rd IFAC Congr.. 1966, proc. London(1968), 460.2-460.9.
[4] Hooker, W. W., Margoulis, G., The Dynaical Attitude Equations for an n-Body Satellite, J. of Astronaut. Sci., 1965, 12: 123-128.
[5] Hooker W. W., Leliakov I. P., Lyons M. G., Margulies G., Reaction-boom attitute control systems, Journal of spacecraft and rockets, 1987,11:1337-1343.
[6] Kane T. R., Dynamics of nonholonomic system. Journal of applied mechanics,1961,3(10): 121-123.
[7] Wittenburg J.(谢传锋译),多刚体系统动力学,北京:北京航空航天出版社,1986。
[8] Maguns K. ed., Dynamics of Multi-body System, Springer, Berlin, 1978.
[9] Huang, E. J. ed., Computer Aided Analysis and Optimization of Mechanical System Dynamics, Springer, Berlin, 1984.
[10] Bianchi G., Scheihlen W. O. ed., Dynamics of Multibody System, Springer, Berlin,1986.
[11]陈滨,含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟-第一部分:动力学建模,导弹与航天运载技术,1997年第1期,27-37。
[12]陈滨,含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟-第二部分:系统动态特性的计算模拟结果,导弹与航天运载技术,1997年第3期,33-40。
[13]于清,柔性多体系统单向递推组集建模方法与通用仿真软件的实现,上海交通大学博士学位论文,(1998)
[14]舒兴高,基于多体动力学的轮轨关系与摆式客车控制的仿真研究,上海交通大学博士学位论文,(1997)
[15]张大钧,柔性多体系统动力学理论方法与实验研究,天津大学博士论文,(1991)。
[16]员超,柔性机械臂的主动控制研究,天津大学博士论文,(1993)。
[17]王建明,计及动力刚化的柔性多体系统动力学理论、方法及实验研究,天津大学博士论文,(1997)。
[18]陆佑方,汽车柔性多体系统动力学建模综述,汽车技术,1997年第5期,1-7。
[19]贾书惠,人造地球卫星的姿态确定,力学与实践,1990年第5期,72-76.
[20]费从宇,柔性机械臂动力学、逆动力学和主动控制中的若干问题的研究,哈尔滨工业大学博士论文,(1992).
[21]王琪,多体系统动力学的Lagrange算法研究,北京航空航天大学博士论文,(1996)。
[22]范子杰,机器人柔性手臂的动力学分析及其粘弹性大阻尼控制的研究,西安交通大学博士论文,(1989)
[23]覃正;叶尚辉;刘明治;柔性多体系统动力学研究及存在的问题;力学进展;1994第2期。
[24]洪嘉振主编,全国多体系统动力学与控制学术会议论文集,北京:北京理工大学出版社,1996。
[25]洪嘉振主编,多体系统动力学:理论、计算方法和应用[M]上海:上海交通大学出版社,1992。
[26] Hoston R. L., Multibody Dynamics-Model and Analysis Methods, Applied Mechanics Review, 1991, Vol. 44, No. 3:109-117.
[27] Argyris J. H., Helsey S. and Kaneel H., Matrix methods for structural analysis: A précis of recent developments, Macmillan, New York, 1964
[28] Belytschko T. and Hsieh B. J., Non-linear transient finite element analysis with convected coordinates, International Journal for Numerical Methods in Engineering, 1973,7:255–271.
[29] Housner J. M., Convected transient analysis for large space structure maneuver and deploy- ment, Proc of 25th Struct, Struct Dyn and Materials Conf, 1984, AIAA Paper No. 84-1023, 616-629.
[30] Housner J. M., Wu S. C., Chang C. W., A finite element method for time varying geometry in multibody structures, Proc of 29th Struct, Struct Dyn and Materials Conf, 1988, AIAA Paper No. 88: 22-34.
[31] Banerjee, A. K., Kane T. R., Dynamics of a plate in large overall motion, Journal of Applied Mechanics, Transactions ASME, Dec, 1989, 56(4): 887-892.
[32] Banerjee A .K ., Dickens J. M, Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation, Journal of Guidance, Control and Dynamics, 1990, 19: 221-227.
[33] Banerjee A. K., Lemak M. E., Multi-Flexible Body Dynamics Capturing Motion-Induced Stifness, ASME Journal of Applied Mechanics, 1991, 58:766-775.
[34] Banerjee A .K ., Block-Diagonal Equations for M ultibody Elastodynamics with Geometric Stiffness and Constraints, Journal of Guidance, Control and Dynamics, 1993, 16(6): 1092- 1100.
[35]洪嘉振,计算多体系统动力学,上海交通大学出版社,1999年.
[36] Petzold L and Lotstedt P, Numerical solution of nonlinear differential equations with algebraic constraints, II: Practical implementation, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 1986,7: 720–733.
[37] Haug, E., J., Computer-Aided Kinematics and Dynamics of Mechanical Systems. Boston,London, Sydney, Toronto: Allyn and Bacon, 1989
[38] Shabana AA, Dynamics of flexible bodies using generalized Newton-Euler equations, ASME J. Dyn. Syst., Meas., Control. 1990(112): 496-503.
[39] Hsiao KM and Jang J, Dynamic analysis of planar flexible mechanisms by corotational formulation, Comput. Methods Appl. Mech. Eng. 1991(87): 1-14.
[40] Elkaranshawy HA and Dokainish MA. Corotational finite elementanalysis of planar flexible multibody systems, Comput. Struct. 1995,54(5): 881-890.
[41] Ibrahimbegovic A and Al Mikdad M.. On dynamics of finite rotations of 3D beams, Comput Methods in Appl Sci 96, Third ECCOMAS Comput Fluid Dyn Conf and the 2nd ECCOMAS Conf on Numer Methods in Eng. 1996: 447-453.
[42] Housner JM, Wu SC, and Chang CW. A finite element method for time varying geometry in multibody structures, Proc of 29th Struct, Struct Dyn and Materials Conf, 1988,AIAA Paper No 88–2234.
[43] Dan Negrut,Jose L. Ortiz;On an approach for the linearization of the differentialalgebraic equations of multibody dynamics;Proceedings of IDETC/MESA 2005,2005 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications,September 24-28, 2005, Long Beach, USA,DETC2005-85109
[44] B. Gavrea,D. Negrut,F.A. Potra;The newmark integration method for simulation of multibody systems: analytical considerations;Proceedings of IMECE 2005 ,ASME International Mechanical Engineering Congress and Exposition 2005, November 5-11, 2005, Orlando, USA,IMECE2005-81770
[45] Belytschko T and Hsieh B J, Non-linear transient finite element analysis with convected co-ordinates, Int. J. Numer. Methods Eng.. 1973(7): 255-271.
[46] Belytschko T, Chiapetta RL, and Bartel HD.. Efficient large scale non-linear transient analysis by finite elements, Int. J. Numer. Methods Eng.. 1976(10): 579-596.
[47] Hughes TJR and Winget J.. Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis, Int. J. Numer. Methods Eng.. 1980, 15(12): 1862-1867.
[48] Flanagan DP and Taylor LM, An accurate numerical algorithm for stress integration with finite rotations, Comput. Methods Appl. Mech. Eng.. 1987,62: 305-320.
[49] Rice DL and Ting EC.. Large displacement transient analysis of flexible structures, Int. J. Numer. Methods Eng.. 1993, 36: 1541-1562.
[50] Wasfy TM. Modeling continuum multibody systems using the finite element method and element convected frames, Proc of 23rd ASME Mechanisms Conf, Minneapolis MN, 1994, 327-336.
[51] Iura M and Atluri SN. Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames, Comput. Struct. 1995,55(3): 453-462.
[52] Lim H and Taylor RL. An explicit-implicit method for flexible-rigid multibody systems, Finite Elem. Anal. Design , 2001,37: 881-900.
[53] Gear CW.. Simultaneous numerical solution of differential algebraic equations, IEEE Trans. Circuit Theory, 1971,18: 89-95.
[54] Chace M A, Analysis of the time dependence of multi-freedom mechanical systems in relative coordinates, ASME J. Eng. Ind.. 1967, 89(1):119-125.
[55] Wittenburg J. Dynamics of Systems of Rigid Bodies, BF Teubner, Stuttgart. 1977.
[56] Roberson R E. The path matrix of graph, its construction and its use in evaluating certain products, Comput. Methods Appl. Mech. Eng.. 1984, 24: 47-56.
[57] Book W J, Recursive Lagrangian dynamics of flexible manipulator arms, Int. J. Robot. Res.. 1984, 3(3): 87-101.
[58] Changizi K and Shabana A A.. A recursive formulation for the dynamics analysis of open loop deformable multibody systems, J of Appl Acoust.. 1988, 55: 687-693.
[59] Bae D S, Hwang R S, and Haug E J. A recursive formulation for real-time dynamic simulation, Adv in Des Automation ASME, New York, 1988, 499-508.
[60] Shabana A A Dynamics of flexible bodies using generalized Newton-Euler equations, ASME J. Dyn. Syst., Meas., Control. 1990, 112: 496-503.
[61] Shabana A A. Constrained motion of deformable bodies, Int. J. Numer. Methods Eng.. 1991, 32: 1813-1831.
[62] Shabana A A, Hwang YL and Wehage RA. Projection methods in flexible multibody dynamics, Part I: Kinematics, Part II: Dynamics and recursive projection methods, Int. J. Numer. Methods Eng.. 1992,35: 1927-1966.
[63] Amirouche FML and Xie M. Explicit matrix formulation of the dynamical equations for flexible multibody systems: A recursive approach, Comput. Struct.. 1993, 46(2): 311-321.
[64] Hwang Y L. Projection and recursive methods in flexible multibody dynamics, PhD Thesis, Dept of Mechanical Engineering, University of Illinois at Chicago. (1992).
[65] Hwang Y L and Shabana A A.. Decoupled joint-elastic coordinate formulation for the analysisof closed-chain flexible multibody systems, ASME J. Mech. Des. 1994,116(3): 961-963.
[66] Bae D S, Hwang R S, and Haug E J, A recursive formulation for real-time dynamic simulation, Adv in Des Automation ASME, New York, 1988, 499-508.
[67] Hwang R S, Bae D S, Haug EJ, and Kuhl J G. Parallel processing for real-time dynamic system simulation, Adv in De Automation, ASME, New York, 1988, 509-518.
[68] Jain A and Rodriguez G, Recursive flexible multibody system dynamics using spatial operators, J. Guid. Control Dyn.. 1992,15(6): 1453-1466.
[69] Cetinkunt S and Book W J. Symbolic modeling of flexible manipulators, Proc of 1987 IEEE Int Conf on Robotics and Automation, 1987, 2074-2080.
[70] Fisette P, Samin JC, Willems PW. Contribution to symbolic analysis of deformable multibody systems, Int. J. Numer. Methods Eng.. 1991,32: 1621-1635.
[71] Melzer E.. Symbolic computations in flexible multibody systems, Nonlinear Dyn. 1996,9(1-2): 147-163.
[72] Shi P, McPhee J, and Heppler GR.. A deformation field for Euler-Bernoulli beams with applications to flexible multibody dynamics, Multibody Syst. Dyn.. 2001, 5: 79-104.
[73] Metaxas D and Koh E. Flexible multibody dynamics and adaptive finite element techniques for model synthesis estimation, Comput. Methods Appl. Mech. Eng.. 1996,136: 1-25.
[74] Ma Z. D. and Perkins N. C.. Modeling of track-wheel-terrain interaction for dynamic simulation of tracked vehicles: Numerical implementation and further results, Paper No DETC2001/VIB-21310, Proc of ASME 2001 DETC, Pittsburgh PA. 2001.
[75]黄永安,多体系统动力学的辛几何积分方法研究摘要, http://www.yahuang.org
[76] Belytschko, Ted; Mullen, Robert.Stability of explicit-implicit mesh partitions in time integration. International Journal for Numerical Methods in Engineering, 1978, 12(10): 1575-1586
[77] Neal M. O., Belytschko, Ted. Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems.Computers and Structures, 1989, 31(6): 871-880
[78]高晖,李光耀,钟志华,张维刚.汽车碰撞计算机仿真中的子循环法分析,机械工程学报, 2005年11期, 98-101
[79]郑阳明,褚庆昕.多时间步长时域有限差分法.电子学报,2004,9:1504-1506
[80]郑阳明,褚庆昕.多时间步长时域有限差分法分析微波电路.微波学报,2005,4: 11-14
[81] Tamer M Wasfy, Ahmed K Noor. Computational strategies for flexible multibody systems, Applied Mechanics Reviews, November, 2003, 56(6): 553-613
[82] Alexander R M and Lawrence K L.. An experimental investigation ofthedynamic response of an elastics mechanism. ASME journal of engineering for industry, 1974, 96(1):268-274
[83] Turcic D A,Midha A.Dynamic analysis of elastic mechanism systems.Part I:Applications.ASME journal of Dynamic systems, Measurement and Control.. 1984, 106:249-254
[84] Nagarajan S,Turcic D A. Experimental verification of critical speed ranges for elastic closed loop linkage systems.ASME journal of Mechanical Design, 1992, 114:126-130
[85] Hastings G G,Book W JA linear dynamic model for flexible robotic manipulators. IEEE Control systems magazine.. 1987, 1: 61-64
[86]王建明,洪嘉振,王示,周学军,柔性多体系统动力学实验研究。宇航学报,1999,20(1): 107-111
[87] Juang Jer-Nan, Horta L G,Robertshaw H.. A slewing control experiment for flexible structures. Journal of Guidance Control and Dynamics, 1986, 9(5): 599-607
[88] Thornton WA,Willmert KD,and Khan MR.. Mechanism optimization via optimality criteriontechniques, ASME J. Mech. Des. 1979,101: 392-397.
[89] Cleghorn WL,Fenton RG,and Tabarrok B.. Optimum design of high-speed flexible mechanisms, Mech. Mach. Theory.. 1981, 16(4): 399-406.
[90] Liou FW and Lou CJ.. An efficient design approach for flexible mechanisms, Comput. Struct. 1992,44(5): 965-971.
[91] Liou FW and Liu JD.. A parametric study on the design of multibody systems with elastic members, Mech. Mach. Theory. 1994,29(8): 1219-1232.
[92] Liu X.. Sensitivity analysis of constrained flexible multibody systems with stability considerations, Mech. Mach. Theory. 1996,31(7): 859-864.
[93] Ider SK and Oral S.. Optimum design of flexible multibody systems with dynamic behavior constraints, Eur. J. Mech. A/Solids.. 1996,15(2): 351-359.
[94] Oral S and Ider SK.. Optimum design of high-speed flexible robotic arms with dynamic behavior constraints, Comput. Struct.. 1997, 65(2): 255-259.
[95]罗鹰.大型星载可展开天线的动力优化设计与工程结构的系统优化设计.西安电子科技大学博士学位论文. 2004
[96]李刚.空间可展天线结构的设计分析与索膜结构分析.浙江大学博士学位论文, 2004
[97] Das. A., Obal M. W, Revolutionary Satelite Structural Systems Technology: A Vision for the future, Aerospace Conference, 1998 IEEE, Volume 2, 1998.
[98] Takano.T., Large Deployable Antennas Concepts and Realization, Antennas and Propagation Society,1999,IEEE International Symposium 1999,Volume 3.
[99] Freeland. R. E., Survey of Deployment Antenna Concepts: Large Space Antenna Systems Technology, NASA-2269, Part I, 1983.
[100] Chew. M., Kumar. P. Conceptual Design of Deployable Space Structures from the viewpoint of symmetry, Int. J. Space Structures,1993.
[101] John. M. Primary Requirements for Large Space Structure, AIAA-81-0443, 2nd AIAA Conf. on Large Space Platforms, 1981.
[102] Ribble T. W., Woods A. A. On the Design of Large Space Deployable Modular Antenna Reflector, 15th Aerospace Mechanisms Symposium, NASA-2181-CP.
[103]韦娟芳,星载天线结构的发展趋势。航天科技集团五院有效载荷研讨会论文集,2001年9月.
[104] Gunnar Tibert, Depolyment Tensegrity Structure for Space Applications, Royal institute of Technology Department of Mechanics.2002.
[105] Guest S. D., Pelegrino S. A new Concept for solid surface deployable antennas. Acta Astronautica 38,2(1996). [106 ] Miura K., Pelegrino S. Structural concepts.1999.
[107] Crone G., Large deployable reflector antenna for advanced mobile communications. ESA/Industry Briefing Meeting. 9 May, 2000
[108] Freeland. R. E., Bilyeu.G.D., VeaL G R. Development of flight hardware for a large inflatable antenna experiment. In 46th International Astronautical Congress(Oslo,Norway,2-6 October 1995).
[109]关富玲,李刚,夏劲松,余永辉.充气可展空间结构,卫星结构与机构技术进展研讨会会议论文集,总装备部卫星技术专业组,2003年9月.
[110]陈务军,空间展开桁架结构设计原理与展开动力学分析理论研究,浙江大学博士学位论文(1998).
[111]陈向阳,可展桁架结构展开过程和动力响应分析与结构设计,浙江大学博士学位论文(2000) .
[112]张京街,弹簧驱动空间可展精架结构设计与分析理论研究,浙江大学博士学位论文(200 1) .
[113]胡其彪,空间可伸展结构的设计与动力学分析研究,浙江人学博士学位论文(2001).
[114]岳建如,空间可动机构结构设计与控制分析,浙江大学博士学位论文(2002).
[115] TRW. Inc. TRW-built AstroMesh reflector deployed aboard Thuraya spacecraft. http://www. trw.com (5 December 2000).
[116] Tbomson. M. W. The AstroMesh deployable reflector. In IUTAM-LASS Symposium on Deployable Structures: Theory and Application, Cambridge.U K,1998.
[117]陆佑方.柔性多体系统动力学,北京:高等教育出版社,1996。
[118]陈向阳.可展桁架展开过程模拟的违约校正.计算力学学报, 2002, 1: 74-77
[119]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, 3: 300-306
[120] Anthony Gravouil, Alain Combescure; Multi-time-step explicit-implicit method for non-linear structural dynamics; International journal for numerical methods in engineering; 2001, 50:199-225
[121] Hughes TJR, Liu WK. Implicit-explicit finite elements in transient analysis: stability theory. Journal of Applied Mechanics. 1978,45: 371-374
[122] Hughes TJR, Liu WK. Implicit-explicit finite elements in transient analysis: implementation and numerical examples. Journal of Applied Mechanics. 1978, 45: 375-378
[123] Belytschko T, Lu Y Y. An explicit multi-time step integration for parabolic and hyperbolic systems. In: New Methods Trans. Anal., PVP-Vol. 246/AMD-Vol,143,ASME, New York, 1992, 25-39
[124] W. J. T. Daniel. A study of the stability of subcycling algorithms in structural dynamis. Computer Methods in Applied Mechanics and Engineering, 1998, 156: 1-13
[125] W. J. T. DanielAnalysis and implementation of a new constant acceleration subcycling algorithm. International journal for numerical methods in engineering; 1997, 40: 2841-2855
[126] W. J. T. Daniel. A partial velocity approach to subcycling structural dynamics. Computer Methods in Applied Mechanics and Engineering, 2003, 192: 375-394
[127] W. J. T. Daniel. The subcycled Newmark algorithm; Computational Mechanics. 1997, 20: 272-281
[128] K. J. Bathe, E. L. Wilson.(林公豫等译).有限元分析中的数值方法.北京:科学出版社, 1985.
[129] Belytschko T, Lu YY. Stability analysis of elemental explicit-implicit partitions by Fourier methods. Computer Methods in Applied Mechanics and Engineering. 1992, 95: 87-96
[130] Liu WK, Lin J. Stability of mixed time integration schemes for transient thermal analysis. Numerical Heat Transfer. 1982, 5: 211-222
[131] Belytschko T, Smolinski P, Liu WK Stability of multi-time step partitioned integrators for first-order finite element systems. Computer Methods in Applied Mechanics and Engineering. 1985, 49: 281-297
[132] Smolinski P, Sleith S. Belytschko T Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations. Computational Mechanics. 1996, 18: 236-244
[133] Farhat C, Crivelli L, Geradin M.. On the spectral stability of time integration algorithms for a class of constrained dynamics problems. AIAA 34th Structural Dynamics Meeting. 1993
[134] Nickell R. E.. On the stability of approximation operators in problems of structural dynamics. Int J Solids Struct, 1971,7(3): 301-19
[135] G. L. Goudreau and R. L. Taylor. Evaluation of numerical integration methods in elastodynamics. International journal of solids and structures, 1971, 7: 301-319
[136] K. J. Bathe and E. L. Wilson. Stability and accuracu analysis of direct integration methods. International journal of earthquake engineering and structutal dynamics. 1973, 1: 283-291
[137]黄秋艳,多柔体系统动力学建模及符号演算的研究,西安电子科技大学硕士学位论文,2004
[138]蔡国平,洪嘉振.旋转运动柔性梁的假设模态方法研究.力学学报,2005,1:48-56.
[139] Hughs PC.. Model identities for elastic bodies with application to vehicle dynamics and control. J. Applied Mechanics. 1980, 47(1): 177-184
[140] Skelton RE, Hughs PC.. Modal Cost Analysis for linear Matrix-second-order System. J. Dynamic System, Measurement and Control. 1980, 102: 151-158
[141] N. M. Newmark. A method of computation for structural dynamics. ASCE, Journal of Engineering mechanics division, 1959, 85:67-94
[142] Kedar G. K. and Adrian J. L.. Parallel asynchronous variational integrators. International Journal for Numerical Methods in Engineering. Published online in www. interscience.wiley.com. DOI: 10.1002/nme. 1880.2006.
[143] Agrawal O P, Shabana A A, Dynamic analysis of multibody systems using component modes, Comput. Struct. 1985, 21(6):1303–1312.
[144] Canavin J R, Likins P W, Floating reference frames for flexible spacecraft, J. Spacecr. Rockets, 1977, 14(12): 724–732.
[145] Cavin R K, Dusto A R, Hamilton’s principle: Finite element methods and flexible body dynamics, AIAA J. 1977, 15:1684-1690.
[146]刘钦鹏,段宝岩,杨东武.柔性空间展开机构动力学建模研究.机械设计,2006, 23(3):1-4
[147]娄平,曾庆元。2节点6自由度直梁单元。湖南科技大学学报(自然版),2004年04期,19(4):29-32.
[148] Pan W, Haug E J. Dynamic simulation of general flexible multibody systems. [J]. Mech. Struct. Mach, 1999, 27(2): 217-251.
[149]张汝清,殷学纲。计算结构动力学。重庆:重庆大学出版社,1987
[150] Shabana A A. Transient analysis of flexible multibody systems Part I: dynamics of flexible bodies [J].Comput.Methods Appl. Mech. Eng,1986, 54:75-91.
[151]朱大炜。基于模态综合法的雷达天线机构柔体动力学仿真研究,上海交通大学硕士学位论文, 2007.
[2] Wittenburg J.,多体系统的动力学,第15届国际力学会议,中文译稿,力学进展,1982, 12.
[3] Roberson, R. E., Wittenburg, J., A Dynamical Formalism for an Arbitrary Number of Inter-connected Rigid Bodies. With reference to the Problem of Satellite Attitude Control. 3rd IFAC Congr.. 1966, proc. London(1968), 460.2-460.9.
[4] Hooker, W. W., Margoulis, G., The Dynaical Attitude Equations for an n-Body Satellite, J. of Astronaut. Sci., 1965, 12: 123-128.
[5] Hooker W. W., Leliakov I. P., Lyons M. G., Margulies G., Reaction-boom attitute control systems, Journal of spacecraft and rockets, 1987,11:1337-1343.
[6] Kane T. R., Dynamics of nonholonomic system. Journal of applied mechanics,1961,3(10): 121-123.
[7] Wittenburg J.(谢传锋译),多刚体系统动力学,北京:北京航空航天出版社,1986。
[8] Maguns K. ed., Dynamics of Multi-body System, Springer, Berlin, 1978.
[9] Huang, E. J. ed., Computer Aided Analysis and Optimization of Mechanical System Dynamics, Springer, Berlin, 1984.
[10] Bianchi G., Scheihlen W. O. ed., Dynamics of Multibody System, Springer, Berlin,1986.
[11]陈滨,含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟-第一部分:动力学建模,导弹与航天运载技术,1997年第1期,27-37。
[12]陈滨,含铰接间隙与杆件柔性的空间伸展机构单元的动力学建模与计算模拟-第二部分:系统动态特性的计算模拟结果,导弹与航天运载技术,1997年第3期,33-40。
[13]于清,柔性多体系统单向递推组集建模方法与通用仿真软件的实现,上海交通大学博士学位论文,(1998)
[14]舒兴高,基于多体动力学的轮轨关系与摆式客车控制的仿真研究,上海交通大学博士学位论文,(1997)
[15]张大钧,柔性多体系统动力学理论方法与实验研究,天津大学博士论文,(1991)。
[16]员超,柔性机械臂的主动控制研究,天津大学博士论文,(1993)。
[17]王建明,计及动力刚化的柔性多体系统动力学理论、方法及实验研究,天津大学博士论文,(1997)。
[18]陆佑方,汽车柔性多体系统动力学建模综述,汽车技术,1997年第5期,1-7。
[19]贾书惠,人造地球卫星的姿态确定,力学与实践,1990年第5期,72-76.
[20]费从宇,柔性机械臂动力学、逆动力学和主动控制中的若干问题的研究,哈尔滨工业大学博士论文,(1992).
[21]王琪,多体系统动力学的Lagrange算法研究,北京航空航天大学博士论文,(1996)。
[22]范子杰,机器人柔性手臂的动力学分析及其粘弹性大阻尼控制的研究,西安交通大学博士论文,(1989)
[23]覃正;叶尚辉;刘明治;柔性多体系统动力学研究及存在的问题;力学进展;1994第2期。
[24]洪嘉振主编,全国多体系统动力学与控制学术会议论文集,北京:北京理工大学出版社,1996。
[25]洪嘉振主编,多体系统动力学:理论、计算方法和应用[M]上海:上海交通大学出版社,1992。
[26] Hoston R. L., Multibody Dynamics-Model and Analysis Methods, Applied Mechanics Review, 1991, Vol. 44, No. 3:109-117.
[27] Argyris J. H., Helsey S. and Kaneel H., Matrix methods for structural analysis: A précis of recent developments, Macmillan, New York, 1964
[28] Belytschko T. and Hsieh B. J., Non-linear transient finite element analysis with convected coordinates, International Journal for Numerical Methods in Engineering, 1973,7:255–271.
[29] Housner J. M., Convected transient analysis for large space structure maneuver and deploy- ment, Proc of 25th Struct, Struct Dyn and Materials Conf, 1984, AIAA Paper No. 84-1023, 616-629.
[30] Housner J. M., Wu S. C., Chang C. W., A finite element method for time varying geometry in multibody structures, Proc of 29th Struct, Struct Dyn and Materials Conf, 1988, AIAA Paper No. 88: 22-34.
[31] Banerjee, A. K., Kane T. R., Dynamics of a plate in large overall motion, Journal of Applied Mechanics, Transactions ASME, Dec, 1989, 56(4): 887-892.
[32] Banerjee A .K ., Dickens J. M, Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation, Journal of Guidance, Control and Dynamics, 1990, 19: 221-227.
[33] Banerjee A. K., Lemak M. E., Multi-Flexible Body Dynamics Capturing Motion-Induced Stifness, ASME Journal of Applied Mechanics, 1991, 58:766-775.
[34] Banerjee A .K ., Block-Diagonal Equations for M ultibody Elastodynamics with Geometric Stiffness and Constraints, Journal of Guidance, Control and Dynamics, 1993, 16(6): 1092- 1100.
[35]洪嘉振,计算多体系统动力学,上海交通大学出版社,1999年.
[36] Petzold L and Lotstedt P, Numerical solution of nonlinear differential equations with algebraic constraints, II: Practical implementation, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 1986,7: 720–733.
[37] Haug, E., J., Computer-Aided Kinematics and Dynamics of Mechanical Systems. Boston,London, Sydney, Toronto: Allyn and Bacon, 1989
[38] Shabana AA, Dynamics of flexible bodies using generalized Newton-Euler equations, ASME J. Dyn. Syst., Meas., Control. 1990(112): 496-503.
[39] Hsiao KM and Jang J, Dynamic analysis of planar flexible mechanisms by corotational formulation, Comput. Methods Appl. Mech. Eng. 1991(87): 1-14.
[40] Elkaranshawy HA and Dokainish MA. Corotational finite elementanalysis of planar flexible multibody systems, Comput. Struct. 1995,54(5): 881-890.
[41] Ibrahimbegovic A and Al Mikdad M.. On dynamics of finite rotations of 3D beams, Comput Methods in Appl Sci 96, Third ECCOMAS Comput Fluid Dyn Conf and the 2nd ECCOMAS Conf on Numer Methods in Eng. 1996: 447-453.
[42] Housner JM, Wu SC, and Chang CW. A finite element method for time varying geometry in multibody structures, Proc of 29th Struct, Struct Dyn and Materials Conf, 1988,AIAA Paper No 88–2234.
[43] Dan Negrut,Jose L. Ortiz;On an approach for the linearization of the differentialalgebraic equations of multibody dynamics;Proceedings of IDETC/MESA 2005,2005 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications,September 24-28, 2005, Long Beach, USA,DETC2005-85109
[44] B. Gavrea,D. Negrut,F.A. Potra;The newmark integration method for simulation of multibody systems: analytical considerations;Proceedings of IMECE 2005 ,ASME International Mechanical Engineering Congress and Exposition 2005, November 5-11, 2005, Orlando, USA,IMECE2005-81770
[45] Belytschko T and Hsieh B J, Non-linear transient finite element analysis with convected co-ordinates, Int. J. Numer. Methods Eng.. 1973(7): 255-271.
[46] Belytschko T, Chiapetta RL, and Bartel HD.. Efficient large scale non-linear transient analysis by finite elements, Int. J. Numer. Methods Eng.. 1976(10): 579-596.
[47] Hughes TJR and Winget J.. Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis, Int. J. Numer. Methods Eng.. 1980, 15(12): 1862-1867.
[48] Flanagan DP and Taylor LM, An accurate numerical algorithm for stress integration with finite rotations, Comput. Methods Appl. Mech. Eng.. 1987,62: 305-320.
[49] Rice DL and Ting EC.. Large displacement transient analysis of flexible structures, Int. J. Numer. Methods Eng.. 1993, 36: 1541-1562.
[50] Wasfy TM. Modeling continuum multibody systems using the finite element method and element convected frames, Proc of 23rd ASME Mechanisms Conf, Minneapolis MN, 1994, 327-336.
[51] Iura M and Atluri SN. Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames, Comput. Struct. 1995,55(3): 453-462.
[52] Lim H and Taylor RL. An explicit-implicit method for flexible-rigid multibody systems, Finite Elem. Anal. Design , 2001,37: 881-900.
[53] Gear CW.. Simultaneous numerical solution of differential algebraic equations, IEEE Trans. Circuit Theory, 1971,18: 89-95.
[54] Chace M A, Analysis of the time dependence of multi-freedom mechanical systems in relative coordinates, ASME J. Eng. Ind.. 1967, 89(1):119-125.
[55] Wittenburg J. Dynamics of Systems of Rigid Bodies, BF Teubner, Stuttgart. 1977.
[56] Roberson R E. The path matrix of graph, its construction and its use in evaluating certain products, Comput. Methods Appl. Mech. Eng.. 1984, 24: 47-56.
[57] Book W J, Recursive Lagrangian dynamics of flexible manipulator arms, Int. J. Robot. Res.. 1984, 3(3): 87-101.
[58] Changizi K and Shabana A A.. A recursive formulation for the dynamics analysis of open loop deformable multibody systems, J of Appl Acoust.. 1988, 55: 687-693.
[59] Bae D S, Hwang R S, and Haug E J. A recursive formulation for real-time dynamic simulation, Adv in Des Automation ASME, New York, 1988, 499-508.
[60] Shabana A A Dynamics of flexible bodies using generalized Newton-Euler equations, ASME J. Dyn. Syst., Meas., Control. 1990, 112: 496-503.
[61] Shabana A A. Constrained motion of deformable bodies, Int. J. Numer. Methods Eng.. 1991, 32: 1813-1831.
[62] Shabana A A, Hwang YL and Wehage RA. Projection methods in flexible multibody dynamics, Part I: Kinematics, Part II: Dynamics and recursive projection methods, Int. J. Numer. Methods Eng.. 1992,35: 1927-1966.
[63] Amirouche FML and Xie M. Explicit matrix formulation of the dynamical equations for flexible multibody systems: A recursive approach, Comput. Struct.. 1993, 46(2): 311-321.
[64] Hwang Y L. Projection and recursive methods in flexible multibody dynamics, PhD Thesis, Dept of Mechanical Engineering, University of Illinois at Chicago. (1992).
[65] Hwang Y L and Shabana A A.. Decoupled joint-elastic coordinate formulation for the analysisof closed-chain flexible multibody systems, ASME J. Mech. Des. 1994,116(3): 961-963.
[66] Bae D S, Hwang R S, and Haug E J, A recursive formulation for real-time dynamic simulation, Adv in Des Automation ASME, New York, 1988, 499-508.
[67] Hwang R S, Bae D S, Haug EJ, and Kuhl J G. Parallel processing for real-time dynamic system simulation, Adv in De Automation, ASME, New York, 1988, 509-518.
[68] Jain A and Rodriguez G, Recursive flexible multibody system dynamics using spatial operators, J. Guid. Control Dyn.. 1992,15(6): 1453-1466.
[69] Cetinkunt S and Book W J. Symbolic modeling of flexible manipulators, Proc of 1987 IEEE Int Conf on Robotics and Automation, 1987, 2074-2080.
[70] Fisette P, Samin JC, Willems PW. Contribution to symbolic analysis of deformable multibody systems, Int. J. Numer. Methods Eng.. 1991,32: 1621-1635.
[71] Melzer E.. Symbolic computations in flexible multibody systems, Nonlinear Dyn. 1996,9(1-2): 147-163.
[72] Shi P, McPhee J, and Heppler GR.. A deformation field for Euler-Bernoulli beams with applications to flexible multibody dynamics, Multibody Syst. Dyn.. 2001, 5: 79-104.
[73] Metaxas D and Koh E. Flexible multibody dynamics and adaptive finite element techniques for model synthesis estimation, Comput. Methods Appl. Mech. Eng.. 1996,136: 1-25.
[74] Ma Z. D. and Perkins N. C.. Modeling of track-wheel-terrain interaction for dynamic simulation of tracked vehicles: Numerical implementation and further results, Paper No DETC2001/VIB-21310, Proc of ASME 2001 DETC, Pittsburgh PA. 2001.
[75]黄永安,多体系统动力学的辛几何积分方法研究摘要, http://www.yahuang.org
[76] Belytschko, Ted; Mullen, Robert.Stability of explicit-implicit mesh partitions in time integration. International Journal for Numerical Methods in Engineering, 1978, 12(10): 1575-1586
[77] Neal M. O., Belytschko, Ted. Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems.Computers and Structures, 1989, 31(6): 871-880
[78]高晖,李光耀,钟志华,张维刚.汽车碰撞计算机仿真中的子循环法分析,机械工程学报, 2005年11期, 98-101
[79]郑阳明,褚庆昕.多时间步长时域有限差分法.电子学报,2004,9:1504-1506
[80]郑阳明,褚庆昕.多时间步长时域有限差分法分析微波电路.微波学报,2005,4: 11-14
[81] Tamer M Wasfy, Ahmed K Noor. Computational strategies for flexible multibody systems, Applied Mechanics Reviews, November, 2003, 56(6): 553-613
[82] Alexander R M and Lawrence K L.. An experimental investigation ofthedynamic response of an elastics mechanism. ASME journal of engineering for industry, 1974, 96(1):268-274
[83] Turcic D A,Midha A.Dynamic analysis of elastic mechanism systems.Part I:Applications.ASME journal of Dynamic systems, Measurement and Control.. 1984, 106:249-254
[84] Nagarajan S,Turcic D A. Experimental verification of critical speed ranges for elastic closed loop linkage systems.ASME journal of Mechanical Design, 1992, 114:126-130
[85] Hastings G G,Book W JA linear dynamic model for flexible robotic manipulators. IEEE Control systems magazine.. 1987, 1: 61-64
[86]王建明,洪嘉振,王示,周学军,柔性多体系统动力学实验研究。宇航学报,1999,20(1): 107-111
[87] Juang Jer-Nan, Horta L G,Robertshaw H.. A slewing control experiment for flexible structures. Journal of Guidance Control and Dynamics, 1986, 9(5): 599-607
[88] Thornton WA,Willmert KD,and Khan MR.. Mechanism optimization via optimality criteriontechniques, ASME J. Mech. Des. 1979,101: 392-397.
[89] Cleghorn WL,Fenton RG,and Tabarrok B.. Optimum design of high-speed flexible mechanisms, Mech. Mach. Theory.. 1981, 16(4): 399-406.
[90] Liou FW and Lou CJ.. An efficient design approach for flexible mechanisms, Comput. Struct. 1992,44(5): 965-971.
[91] Liou FW and Liu JD.. A parametric study on the design of multibody systems with elastic members, Mech. Mach. Theory. 1994,29(8): 1219-1232.
[92] Liu X.. Sensitivity analysis of constrained flexible multibody systems with stability considerations, Mech. Mach. Theory. 1996,31(7): 859-864.
[93] Ider SK and Oral S.. Optimum design of flexible multibody systems with dynamic behavior constraints, Eur. J. Mech. A/Solids.. 1996,15(2): 351-359.
[94] Oral S and Ider SK.. Optimum design of high-speed flexible robotic arms with dynamic behavior constraints, Comput. Struct.. 1997, 65(2): 255-259.
[95]罗鹰.大型星载可展开天线的动力优化设计与工程结构的系统优化设计.西安电子科技大学博士学位论文. 2004
[96]李刚.空间可展天线结构的设计分析与索膜结构分析.浙江大学博士学位论文, 2004
[97] Das. A., Obal M. W, Revolutionary Satelite Structural Systems Technology: A Vision for the future, Aerospace Conference, 1998 IEEE, Volume 2, 1998.
[98] Takano.T., Large Deployable Antennas Concepts and Realization, Antennas and Propagation Society,1999,IEEE International Symposium 1999,Volume 3.
[99] Freeland. R. E., Survey of Deployment Antenna Concepts: Large Space Antenna Systems Technology, NASA-2269, Part I, 1983.
[100] Chew. M., Kumar. P. Conceptual Design of Deployable Space Structures from the viewpoint of symmetry, Int. J. Space Structures,1993.
[101] John. M. Primary Requirements for Large Space Structure, AIAA-81-0443, 2nd AIAA Conf. on Large Space Platforms, 1981.
[102] Ribble T. W., Woods A. A. On the Design of Large Space Deployable Modular Antenna Reflector, 15th Aerospace Mechanisms Symposium, NASA-2181-CP.
[103]韦娟芳,星载天线结构的发展趋势。航天科技集团五院有效载荷研讨会论文集,2001年9月.
[104] Gunnar Tibert, Depolyment Tensegrity Structure for Space Applications, Royal institute of Technology Department of Mechanics.2002.
[105] Guest S. D., Pelegrino S. A new Concept for solid surface deployable antennas. Acta Astronautica 38,2(1996). [106 ] Miura K., Pelegrino S. Structural concepts.1999.
[107] Crone G., Large deployable reflector antenna for advanced mobile communications. ESA/Industry Briefing Meeting. 9 May, 2000
[108] Freeland. R. E., Bilyeu.G.D., VeaL G R. Development of flight hardware for a large inflatable antenna experiment. In 46th International Astronautical Congress(Oslo,Norway,2-6 October 1995).
[109]关富玲,李刚,夏劲松,余永辉.充气可展空间结构,卫星结构与机构技术进展研讨会会议论文集,总装备部卫星技术专业组,2003年9月.
[110]陈务军,空间展开桁架结构设计原理与展开动力学分析理论研究,浙江大学博士学位论文(1998).
[111]陈向阳,可展桁架结构展开过程和动力响应分析与结构设计,浙江大学博士学位论文(2000) .
[112]张京街,弹簧驱动空间可展精架结构设计与分析理论研究,浙江大学博士学位论文(200 1) .
[113]胡其彪,空间可伸展结构的设计与动力学分析研究,浙江人学博士学位论文(2001).
[114]岳建如,空间可动机构结构设计与控制分析,浙江大学博士学位论文(2002).
[115] TRW. Inc. TRW-built AstroMesh reflector deployed aboard Thuraya spacecraft. http://www. trw.com (5 December 2000).
[116] Tbomson. M. W. The AstroMesh deployable reflector. In IUTAM-LASS Symposium on Deployable Structures: Theory and Application, Cambridge.U K,1998.
[117]陆佑方.柔性多体系统动力学,北京:高等教育出版社,1996。
[118]陈向阳.可展桁架展开过程模拟的违约校正.计算力学学报, 2002, 1: 74-77
[119]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, 3: 300-306
[120] Anthony Gravouil, Alain Combescure; Multi-time-step explicit-implicit method for non-linear structural dynamics; International journal for numerical methods in engineering; 2001, 50:199-225
[121] Hughes TJR, Liu WK. Implicit-explicit finite elements in transient analysis: stability theory. Journal of Applied Mechanics. 1978,45: 371-374
[122] Hughes TJR, Liu WK. Implicit-explicit finite elements in transient analysis: implementation and numerical examples. Journal of Applied Mechanics. 1978, 45: 375-378
[123] Belytschko T, Lu Y Y. An explicit multi-time step integration for parabolic and hyperbolic systems. In: New Methods Trans. Anal., PVP-Vol. 246/AMD-Vol,143,ASME, New York, 1992, 25-39
[124] W. J. T. Daniel. A study of the stability of subcycling algorithms in structural dynamis. Computer Methods in Applied Mechanics and Engineering, 1998, 156: 1-13
[125] W. J. T. DanielAnalysis and implementation of a new constant acceleration subcycling algorithm. International journal for numerical methods in engineering; 1997, 40: 2841-2855
[126] W. J. T. Daniel. A partial velocity approach to subcycling structural dynamics. Computer Methods in Applied Mechanics and Engineering, 2003, 192: 375-394
[127] W. J. T. Daniel. The subcycled Newmark algorithm; Computational Mechanics. 1997, 20: 272-281
[128] K. J. Bathe, E. L. Wilson.(林公豫等译).有限元分析中的数值方法.北京:科学出版社, 1985.
[129] Belytschko T, Lu YY. Stability analysis of elemental explicit-implicit partitions by Fourier methods. Computer Methods in Applied Mechanics and Engineering. 1992, 95: 87-96
[130] Liu WK, Lin J. Stability of mixed time integration schemes for transient thermal analysis. Numerical Heat Transfer. 1982, 5: 211-222
[131] Belytschko T, Smolinski P, Liu WK Stability of multi-time step partitioned integrators for first-order finite element systems. Computer Methods in Applied Mechanics and Engineering. 1985, 49: 281-297
[132] Smolinski P, Sleith S. Belytschko T Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations. Computational Mechanics. 1996, 18: 236-244
[133] Farhat C, Crivelli L, Geradin M.. On the spectral stability of time integration algorithms for a class of constrained dynamics problems. AIAA 34th Structural Dynamics Meeting. 1993
[134] Nickell R. E.. On the stability of approximation operators in problems of structural dynamics. Int J Solids Struct, 1971,7(3): 301-19
[135] G. L. Goudreau and R. L. Taylor. Evaluation of numerical integration methods in elastodynamics. International journal of solids and structures, 1971, 7: 301-319
[136] K. J. Bathe and E. L. Wilson. Stability and accuracu analysis of direct integration methods. International journal of earthquake engineering and structutal dynamics. 1973, 1: 283-291
[137]黄秋艳,多柔体系统动力学建模及符号演算的研究,西安电子科技大学硕士学位论文,2004
[138]蔡国平,洪嘉振.旋转运动柔性梁的假设模态方法研究.力学学报,2005,1:48-56.
[139] Hughs PC.. Model identities for elastic bodies with application to vehicle dynamics and control. J. Applied Mechanics. 1980, 47(1): 177-184
[140] Skelton RE, Hughs PC.. Modal Cost Analysis for linear Matrix-second-order System. J. Dynamic System, Measurement and Control. 1980, 102: 151-158
[141] N. M. Newmark. A method of computation for structural dynamics. ASCE, Journal of Engineering mechanics division, 1959, 85:67-94
[142] Kedar G. K. and Adrian J. L.. Parallel asynchronous variational integrators. International Journal for Numerical Methods in Engineering. Published online in www. interscience.wiley.com. DOI: 10.1002/nme. 1880.2006.
[143] Agrawal O P, Shabana A A, Dynamic analysis of multibody systems using component modes, Comput. Struct. 1985, 21(6):1303–1312.
[144] Canavin J R, Likins P W, Floating reference frames for flexible spacecraft, J. Spacecr. Rockets, 1977, 14(12): 724–732.
[145] Cavin R K, Dusto A R, Hamilton’s principle: Finite element methods and flexible body dynamics, AIAA J. 1977, 15:1684-1690.
[146]刘钦鹏,段宝岩,杨东武.柔性空间展开机构动力学建模研究.机械设计,2006, 23(3):1-4
[147]娄平,曾庆元。2节点6自由度直梁单元。湖南科技大学学报(自然版),2004年04期,19(4):29-32.
[148] Pan W, Haug E J. Dynamic simulation of general flexible multibody systems. [J]. Mech. Struct. Mach, 1999, 27(2): 217-251.
[149]张汝清,殷学纲。计算结构动力学。重庆:重庆大学出版社,1987
[150] Shabana A A. Transient analysis of flexible multibody systems Part I: dynamics of flexible bodies [J].Comput.Methods Appl. Mech. Eng,1986, 54:75-91.
[151]朱大炜。基于模态综合法的雷达天线机构柔体动力学仿真研究,上海交通大学硕士学位论文, 2007.