航天刚-弹-液耦合系统的弹-液耦合研究
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摘要
航天刚-弹-液耦合动力学中的弹-液耦合问题是关系到航天刚-弹-液耦合系统液固耦合机理研究和大规模液固耦合建模计算研究的重要课题。通过分析刚-弹-液耦合动力学拟变分原理的泛函,说明刚-弹-液耦合中的刚-弹耦合、刚-液耦合和弹-液耦合的特点。应用Lagrange乘子法,将无际边界条件纳入泛函中,通过识别Lagrange乘子,逐步说明弹-液耦合的机理。通过对泛函求驻值发现,无际边界条件由原来的先决条件转化为驻值条件,实现了从协调元到杂交元的过渡。通过分析泛函识别Lagrange乘子前后的驻值条件,明确了识别La-grange乘子可以有效地减少计算自由度。
This paper focuses on the elastic-liquid coupling problem in the rigid-elastic-liquid coupling dynamics.It is an important topic related to researches on mechanism and large-scale modeling and calculation of liquid-solid coupling in the aerospace rigid-elastic-liquid coupling system.Based on the analysis of the function of the quasi-variational principles for the rigid-elastic-liquid coupling dynamics,characteristics for rigidelastic coupling,rigid-liquid coupling and elastic-liquid coupling in the rigid-elastic-liquid coupling system were illustrated.Inter-element boundary conditions were plugged into the function by Lagrange multiplier method and the mechanization of the elastic-liquid coupling was illustrated step by step through the identification of Lagrange multipliers.Solving stationary values of function shows that inter-element boundary conditions convert from preconditions to stationary value conditions.It realizes the transition from compatible element model to the hybrid element model.Through analysis on stationary value conditions before and after identification of Lagrange multipliers,it is shown that the identified Lagrange multipliers can effectively reduce the degree of freedom for calculation.
This paper focuses on the elastic-liquid coupling problem in the rigid-elastic-liquid coupling dynamics.It is an important topic related to researches on mechanism and large-scale modeling and calculation of liquid-solid coupling in the aerospace rigid-elastic-liquid coupling system.Based on the analysis of the function of the quasi-variational principles for the rigid-elastic-liquid coupling dynamics,characteristics for rigidelastic coupling,rigid-liquid coupling and elastic-liquid coupling in the rigid-elastic-liquid coupling system were illustrated.Inter-element boundary conditions were plugged into the function by Lagrange multiplier method and the mechanization of the elastic-liquid coupling was illustrated step by step through the identification of Lagrange multipliers.Solving stationary values of function shows that inter-element boundary conditions convert from preconditions to stationary value conditions.It realizes the transition from compatible element model to the hybrid element model.Through analysis on stationary value conditions before and after identification of Lagrange multipliers,it is shown that the identified Lagrange multipliers can effectively reduce the degree of freedom for calculation.
引文
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[14]包光伟,王政伟.液体三维晃动特征问题的有限元数值计算方法[J].力学季刊,2003,24(2):185-190.BAO G W,WANG Z W.Finite element numerical method for three-dimensional sloshing characteristics of fluids[J].Chinese Quarterly of Mechanics,2003,24(2):185-190(in Chinese).
[15]陈建平,周儒荣,虞伟建.充液系统液体-多体耦合动力响应分析[J].力学学报,2004,36(6):724-731.CHEN J P,ZHOU R R,YU W J.Fluid multi-body coupling dynamic response analysis of fluid filled system[J].Chinese Journal of Theoretical and Applied Mechanics,2004,36(6):724-731(in Chinese).
[16]高索文,尹立中,王本利,等.矩形贮箱类液固耦合系统转动特性分析[J].振动与冲击,2000,19(3):17-19.GAO S W,YIN L Z,WANG B L,et al.Analysis of rotation characteristics of liquid solid coupling system for rectangular tanks[J].Journal of Vibration and Shock,2000,19(3):17-19(in Chinese).
[17]苟兴宇,李铁寿,马兴瑞,等.液固耦合系统中液体的有限幅晃动力及晃动力矩[J].应用数学和力学,2001,22(5):465-476.GOU X Y,LI T S,MA X R,et al.Finite amplitude sloshing power and sloshing torque in liquid solid coupling system[J].Applied Mathematics and Mechanics,2001,22(5):465-476(in Chinese).
[18]李青,王天舒,马兴瑞.充液航天器液体晃动和液固耦合动力学的研究与应用[J].力学进展,2012,42(4):471-480.LI Q,WANG T S,MA X R.Research and application of liquid sloshing and liquid-solid coupling dynamics in liquid filled spacecraft[J].Advances in Mechanics,2012,42(4):471-480(in Chinese).
[19]LIANG L F,SONG H Y.Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics[J].Science China Physics,Mechanics and Astronomy,2013,56(11):2192-2199.
[20]梁立孚,刘宗民,郭庆勇.充液系统刚-液耦合动力学功能型拟变分原理[J].哈尔滨工程大学学报,2013,34(12):1514-1519.LIANG L F,LIU Z M,GUO Q Y.The rigid liquid coupled dynamic functional quasi variational principle of the fluid system[J].Journal of Harbin Engineering University,2013,34(12):1514-1519(in Chinese).
[21]冯晓九,梁立孚,宋海燕.刚-弹-液耦合动力学功能型拟变分原理[J].中国科学E辑,2017,46(2):195-203.FENG X J,LIANG L F,SONG H Y.Rigid,elastic fluid coupling dynamics,functional quasi variational principles[J].Chinese Science E Series,2017,46(2):195-203(in Chinese).
[22]梁立孚,郭庆勇.刚体动力学的拟变分原理及其应用[J].力学学报,2010,42(2):300-305.LIANG L F,GUO Q Y.Quasi variational principles for rigid body dynamics and their applications[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):300-305(in Chinese).
[23]钱伟长.广义变分原理[M].北京:知识出版社,1985.QIAN W C.Generalized variational principle[M].Beijing:Knowledge Press,1985(in Chinese).
[24]WASHIZU K.Variational method in elasticity and plasticity[M].New York:Pergamon Press,1982.
[25]钱伟长.弹性理论中广义变分原理的研究及其在有限元计算中的应用[J].力学与实践,1979,1(1):16-24.QIAN W C.The study of the principle of generalized variational principles in elastic theory and its application in finite element calculation[J].Mechanics in Engineering,1979,1(1):16-24(in Chinese).
[26]XING J T.Developments of numerical method for linear and nonlinear fluid-solid interaction dynamics with applications[J].Advances in Mechanics,2016,46(2):95-139.
[2]梁立孚,宋海燕,李海波.航天分析动力学[M].北京:科学出版社,2016.LIANG L F,SONG H Y,LI H B.Aerospace analytical dynamics[M].Beijing:Science Press,2016(in Chinese).
[3]杜建镔,王勖成.旋转周期性含液容器的流固耦合动力学特性分析[J].清华大学学报(自然科学版),1999,39(8):108-116.DU J B,WANG X C.Fluid solid coupling dynamic characteristics of rotating periodic liquid containing containers[J].Journal of Tsinghua University(Natural Science Edition),1999,39(8):108-116(in Chinese).
[4]刘习军,张素侠,刘国英,等.矩形弹性壳液耦合系统中的重力波分析[J].力学学报,2006,38(1):106-112.LIU X J,ZHANG S X,LIU G Y,et al.Gravity wave analysis in rectangular elastic shell and fluid coupling system[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):106-112(in Chinese).
[5]马兴瑞,王本利,苟兴宇.航天器动力学---若干问题进展及应用[M].北京:科学出版社,2001.MA X R,WANG B L,GOU X Y.Some problems of spacecraft dynamics:Development and applications[M].Beijing:Science Press,2001(in Chinese).
[6]邢景棠,周盛,崔尔杰.流固耦合力学概述[J].力学进展,1997,27(1):19-38.XING J T,ZHOU S,CUI E J.Fluid solid coupling mechanics[J].Advances in Mechanics,1997,27(1):19-38(in Chinese).
[7]王勖成.有限单元法[M].北京:清华大学出版社,2003.WANG X C.The finite element method[M].Beijing:Tsinghua University Press,2003(in Chinese).
[8]李磊,任业军,蔡斌,等.进动圆筒内液体流动不稳定的非线性特征[J].力学学报,2005,37(1):64-72.LI L,REN Y J,CAI B,et al.Nonlinear characteristics of liquid flow instability in precession cylinders[J].Chinese Journal of Theoretical and Applied Mechanics,2005,37(1):64-72(in Chinese).
[9]席如青,曲广吉.在低微重力下卫星液体晃动力学应用研究[J].航天器工程,1997,6(1-2):18-26.XI R Q,QU G J.Application of liquid sloshing dynamics in satellite under low gravity[J].Spacecraft Engineering,1997,6(1-2):18-26(in Chinese).
[10]李英波,冯正进.充液航天器液体晃动等效力学模型的建立[J].上海航天,2003(4):1-5.LI Y B,FENG Z J.Establishment of equivalent mechanical model for liquid sloshing in liquid filled spacecraft[J].Aerospace Shanghai,2003(4):1-5(in Chinese).
[11]王佳栋,周叮,刘伟庆.带环形隔板圆柱形储液罐中液体晃动的解析研究[J].振动与冲击,2010,29(2):54-59.WANG J D,ZHOU D,LIU W Q.Analytical study of liquid sloshing in cylindrical tank with annular baffles[J].Journal of Vibration and Shock,2010,29(2):54-59(in Chinese).
[12]黄华,杨雷,张熇,等.航天器贮箱大幅液体晃动三维质心面等效模型研究[J].宇航学报,2010,31(1):55-59.HUANG H,YANG L,ZHANG H,et al.The equivalent model of three dimensional centroid surface for large liquid sloshing in spacecraft tanks[J].Journal of Astronautics,2010,31(1):55-59(in Chinese).
[13]贺元军,马兴瑞,王本利.微重环境下平移圆柱贮箱液固耦合系统的动力响应研究[J].西安交通大学学报,2006,40(9):1083-1087.HE Y J,MA X R,WANG B L.Research on dynamic response of liquid-solid coupling system of translational cylindrical tanks under microgravity environment[J].Journal of Xi’an Jiao Tong University,2006,40(9):1083-1087(in Chinese).
[14]包光伟,王政伟.液体三维晃动特征问题的有限元数值计算方法[J].力学季刊,2003,24(2):185-190.BAO G W,WANG Z W.Finite element numerical method for three-dimensional sloshing characteristics of fluids[J].Chinese Quarterly of Mechanics,2003,24(2):185-190(in Chinese).
[15]陈建平,周儒荣,虞伟建.充液系统液体-多体耦合动力响应分析[J].力学学报,2004,36(6):724-731.CHEN J P,ZHOU R R,YU W J.Fluid multi-body coupling dynamic response analysis of fluid filled system[J].Chinese Journal of Theoretical and Applied Mechanics,2004,36(6):724-731(in Chinese).
[16]高索文,尹立中,王本利,等.矩形贮箱类液固耦合系统转动特性分析[J].振动与冲击,2000,19(3):17-19.GAO S W,YIN L Z,WANG B L,et al.Analysis of rotation characteristics of liquid solid coupling system for rectangular tanks[J].Journal of Vibration and Shock,2000,19(3):17-19(in Chinese).
[17]苟兴宇,李铁寿,马兴瑞,等.液固耦合系统中液体的有限幅晃动力及晃动力矩[J].应用数学和力学,2001,22(5):465-476.GOU X Y,LI T S,MA X R,et al.Finite amplitude sloshing power and sloshing torque in liquid solid coupling system[J].Applied Mathematics and Mechanics,2001,22(5):465-476(in Chinese).
[18]李青,王天舒,马兴瑞.充液航天器液体晃动和液固耦合动力学的研究与应用[J].力学进展,2012,42(4):471-480.LI Q,WANG T S,MA X R.Research and application of liquid sloshing and liquid-solid coupling dynamics in liquid filled spacecraft[J].Advances in Mechanics,2012,42(4):471-480(in Chinese).
[19]LIANG L F,SONG H Y.Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics[J].Science China Physics,Mechanics and Astronomy,2013,56(11):2192-2199.
[20]梁立孚,刘宗民,郭庆勇.充液系统刚-液耦合动力学功能型拟变分原理[J].哈尔滨工程大学学报,2013,34(12):1514-1519.LIANG L F,LIU Z M,GUO Q Y.The rigid liquid coupled dynamic functional quasi variational principle of the fluid system[J].Journal of Harbin Engineering University,2013,34(12):1514-1519(in Chinese).
[21]冯晓九,梁立孚,宋海燕.刚-弹-液耦合动力学功能型拟变分原理[J].中国科学E辑,2017,46(2):195-203.FENG X J,LIANG L F,SONG H Y.Rigid,elastic fluid coupling dynamics,functional quasi variational principles[J].Chinese Science E Series,2017,46(2):195-203(in Chinese).
[22]梁立孚,郭庆勇.刚体动力学的拟变分原理及其应用[J].力学学报,2010,42(2):300-305.LIANG L F,GUO Q Y.Quasi variational principles for rigid body dynamics and their applications[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):300-305(in Chinese).
[23]钱伟长.广义变分原理[M].北京:知识出版社,1985.QIAN W C.Generalized variational principle[M].Beijing:Knowledge Press,1985(in Chinese).
[24]WASHIZU K.Variational method in elasticity and plasticity[M].New York:Pergamon Press,1982.
[25]钱伟长.弹性理论中广义变分原理的研究及其在有限元计算中的应用[J].力学与实践,1979,1(1):16-24.QIAN W C.The study of the principle of generalized variational principles in elastic theory and its application in finite element calculation[J].Mechanics in Engineering,1979,1(1):16-24(in Chinese).
[26]XING J T.Developments of numerical method for linear and nonlinear fluid-solid interaction dynamics with applications[J].Advances in Mechanics,2016,46(2):95-139.
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