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连续介质分析动力学及其应用

梁立孚 郭庆勇 宋海燕

梁立孚, 郭庆勇, 宋海燕. 连续介质分析动力学及其应用[J]. 力学进展, 2019, 49(1): 201908. doi: 10.6052/1000-0992-17-019
引用本文: 梁立孚, 郭庆勇, 宋海燕. 连续介质分析动力学及其应用[J]. 力学进展, 2019, 49(1): 201908. doi: 10.6052/1000-0992-17-019
LIANG Lifu, GUO Qingyong, SONG Haiyan. Analytical dynamics of continuous medium and its application[J]. Advances in Mechanics, 2019, 49(1): 201908. doi: 10.6052/1000-0992-17-019
Citation: LIANG Lifu, GUO Qingyong, SONG Haiyan. Analytical dynamics of continuous medium and its application[J]. Advances in Mechanics, 2019, 49(1): 201908. doi: 10.6052/1000-0992-17-019

连续介质分析动力学及其应用

doi: 10.6052/1000-0992-17-019
基金项目: 国家自然科学基金项目资助课题 (一般力学的广义变分原理研究10272034);黑龙江省自然科学基金项目资助课题(电磁热弹性体耦合理论模型和计算方法研究A2015013).
详细信息
    作者简介:

    null

    作者简介:梁立孚, 1939年生, 哈尔滨工程大学教授, 博士生导师.主要研究方向:变分原理及其应用、连续介质分析动力学和耦合分析动力学.通过长期的研究, 提出变分的逆运算------变积的概念, 建立了变积方法,使得微积分学中的积分、微分和导数在变分学中都有了对应的概念------变积、变分和变导,从而初步地将变分学扩充为变积分学.变积的建立解决了建立变分原理(含广义变分原理)难的问题; 变导的应用,结合Lagrange-Hamilton体系,解决了将Lagrange方程应用于连续介质力学和其他学科的问题.研究耦合分析动力学(或者称为分析耦合动力学);解决了将Hamilton型变分原理和Lagrange方程应用于刚--弹、刚--液、刚--弹--液等耦合系统的问题;在航空、航天、航海等领域获得重要应用.应用可变函数选值域的理论和可变函数曲线接近度的理论研究非完整系统分析动力学,较好地解释了非完整力学中的一些长期存在的但难以说明的问题,进而研究了非完整系统分析动力学的理论框架.

  • 中图分类号: O31;

Analytical dynamics of continuous medium and its application

  • 摘要: 综述了国内和国外学者研究连续介质分析动力学问题的进展,阐明了本文主要论述将Lagrange方程应用于连续介质动力学的问题.论文采用Lagrange-Hamilton体系,分别论述了非保守非线性弹性动力学、不可压缩黏性流体动力学、黏弹性动力学、热弹性动力学、刚--弹耦合动力学和刚--液耦合动力学的Lagrange方程及其应用.论述了应用Lagrange方程建立有限元计算模型的问题. 最后,展望了将Lagrange方程应用于连续介质动力学问题的研究前景.

     

  • [1] 爱林根. 朱照宣 译. 1985. 连续统物理的基本原理. 南京: 江苏科学技术出版社

    (Eringen A C.1975. Basic~Principles~of~Continuum Physics. Academic Press).
    [2] 爱林根. 程昌钧, 俞焕然译. 1991. 连续统力学. 北京: 科学出版社

    (Eringen~A~C. 1967. Mechanics~of~Continua. New York: John Wiley and Sons, Inc).
    [3] 陈滨. 2010. 分析动力学 (第二版). 北京: 北京大学出版社

    (Chen ~B. 2010. Analytical~Dynamics (2nd edn). Beijing: Peking~University Press).
    [4] 陈滨, 梅凤翔. 1994. 中国非完整力学三十年. 开封: 河南大学出版社

    (Chen B, Mei F X.1994. Thirty Years for~Nonholonomic~Mechanics~in~China. Kaifeng: Henan~University~Press).
    [5] 程昌钧, 朱正佑. 2003. 关于粘弹性力学的一些进展. 自然杂志, 25: 1-11

    (Cheng C J, Zhu Z Y.2003. Advance on theory of viscoelasticity. Nature Magazine, 25 : 1-11).
    [6] 蔡建乐, 梅凤翔. 2008. Lagrange系统lie点变换下的共形不变性与守恒量. 物理学报, 57: 5369-5373

    (Cai J L, Mei F X.2008. Conformal invariance and conserved quantity of Lagrange systems under lie point transformation. Acta Physica Sinica, 57: 5369-5373).
    [7] 董平, J N 罗赛托斯. 1979. 有限单元法---基本方法与实践. 北京: 国防工业出版社

    (Tong P, Rossettos J N.1979. Finite Element Method---Basic Technique and Implementation. Boston: MIT Press).
    [8] 戴世强, 邓学蓥, 段祝平, 黄永念, 黄筑平, 李家春, 连淇祥, 陆启韶, 沈青, 谈庆明, 陶祖莱, 王克仁, 王文标, 王自强, 解伯民, 姚振汉, 殷有泉, 余寿文, 张兆顺, 周显初, 朱如曾, 朱照宣. 2001. 20世纪理论和应用力学十大进展. 力学进展, 31: 322-326

    (Dai S Q, Deng X Y, Duan Z P, Huang Y N, Huang Z P, Li J C, Lian Q X, Lu Q S, Shen Q, Tan Q M, Tao Z L, Wang K R, Wang W B, Wang Z Q, Xie B M, Yao Z H, Yin Y Q, Yu S W, Zhang Z S, Zhou X C, Zhu R Z, Zhu Z X.2001. Top ten progresses of theoretical and applied mechanics in twenty century. Advances in Mechanics, 31: 322-326).
    [9] 范绪箕. 2009. 高速飞行器热结构分析与应用. 北京: 国防工业出版社

    (Fan X Q~. 2009. Thermal~Structures~Analysis~and~Applications~of High Speed~Vehicles. Beijing: National Defense Industry Press).
    [10] 冯晓九, 梁立孚. 2016. Lagrange方程应用于连续介质力学. 北京大学学报, 52: 597-607

    (Feng X J, Liang L F.2016. Lagrange equation applied to continuum mechanics. Acta Scientiarum Naturalium Universitatis Pekinensis, 52: 597-607).
    [11] 冯晓九, 梁立孚, 郭庆勇. 2016. 结构的刚--热弹耦合稳定性问题研究. 中国科学: 技术科学, 46: 1039-1047

    (Feng X J, Liang L F, Guo Q Y.2016. Investigation of structural stability of rigid-thermo-elastic coupling. Sci Sin Tech, 46: 1039-1047).
    [12] 冯晓九, 梁立孚, 宋海燕. 2016. 刚--弹--液耦合动力学的功能型拟变分原理. 中国科学: 技术科学, 46: 195-203

    (Feng X J, Liang L F, Song H Y.2016. Quasi variational principle of the rigid-elastic-liquid coupling dynamics. Sci Sin Tech, 46: 195-203).
    [13] 郭永新, 罗绍凯, 梅凤翔. 2004. 非完整约束系统几何动力学研究进展: Lagrange理论及其他. 力学进展, 34: 477-492

    (Guo Y X, Luo S K, Mei F X.2004. Progress of geometric dynamics of nonholonomic constrained mechanical systems: Lagrange theory and others. Advances in Mechanics, 34: 477-492).
    [14] 黄彬彬, 石志飞, 章梓茂. 2000. 压电材料变分原理逆问题的研究------动力学中的逆问题. 复合材料学报, 17: 103-106

    (Hang B B, Shi Z F, Zhang Z M.2000. On the inverse problem in calculus of variations for piezoelectric media---The inverse problem in dynamics. Acta Metallurgica Sinica (English letters), 17: 103-106).
    [15] 罗恩. 1990. 关于线粘弹性动力学中各种变分原理. 力学学报, 22: 484-489

    (Luo E.1990. On the variational principles for linear theory of dynamic viscoelasticity. Acta Mechanica Sinica, 22: 484-489).
    [16] 刘高联. 1989. 流体力学变分原理及其有限元法研究的进展. 上海力学, 10: 73-80

    (Liu G L.1989. Research development of variation principles finite element method in fluid mechanics. Chinese Quarterly Mechanics, 10: 73-80).
    [17] 刘锦阳, 洪嘉振. 2006. 温度场中的柔性梁系统动力学建模. 振动工程学报, 19: 469-474

    (Liu J Y, Hong J Z.2006. Geometric nonlinear formulation of flexible beam systems in temperature field. Journal of Vibration Engineering, 19: 469-474).
    [18] 梁立孚. 2011a. 论航天器动力学中的一个理论问题. 中国科学G, 41: 94-101

    (Liang L F.2011a. Investigation of a theoretical problem in spacecraft dynamics. Science in China (G), 41: 94-101).
    [19] 梁立孚. 2011b. 力学和电磁学中的变分原理及其应用. 哈尔滨: 哈尔滨工程大学出版社

    (Liang L F.2011b. Variational principles in mechanics and electromagnetics and their applications. Harbin: Harbin Engineering University Press).
    [20] 梁立孚, 刘宗民, 郭庆勇. 2013. 充液系统刚--液耦合动力学功能型拟变分原理. 哈尔滨工程大学学报, 34: 1514-1519

    (Liang L F, Liu Z M, Guo Q Y.2013. Quasi-variational principle of rigid-liquid coupling dynamics in liquid-filled system. Journal of Harbin Engineering University, 34: 1514-1519).
    [21] 梁立孚, 宋海燕, 樊涛, 刘宗民. 2015. 非保守系统的拟变分原理及其应用. 北京: 科学出版社

    (Liang L F, Song H Y, Fan T, Liu Z M.2015. Quasi-variational Principles of Non-conservative System and Their Applications. Beijing: Science~Press).
    [22] 梁立孚, 宋海燕, 郭庆勇. 2015. 应用 Lagrange方程研究刚弹耦合动力学. 哈尔滨工程大学学报, 36: 456-460

    (Liang L F, Song H Y, Guo Q Y.2015. Research on rigid-elastic coupling dynamics using Lagrange equation. Journal of Harbin Engineering University, 36: 456-460).
    [23] 梁立孚, 宋海燕, 李海波. 2016. 航天分析动力学. 北京: 科学出版社

    (Liang L F, Song H Y, Li H B.2016. Analytical~Dynamics~of Aerospace Systems. Beijing: Science~Press).
    [24] 梁立孚, 石志飞. 1993. 黏性流体力学的变分原理及其广义变分原理. 应用力学学报, 10: 119-123

    (Liang L F, Shi Z F.1993. Variational principles and generalized variational principles in hydrodynamics of viscous fluids. Chinese Journal of Applied~Mechanics, 10: 119-123).
    [25] 梁立孚, 周平. 2018. Lagrange方程应用于流体动力学. 哈尔滨工程大学学报, 39: 1-7

    (Liang L F, Zhou P.2018. Application of Lagrange equation in fluid mechanics. Journal of Harbin Engineering University, 39: 1-7).
    [26] 李青, 王天舒, 马兴瑞. 2012. 充液航天器液体晃动和液固耦合动力学的研究与应用. 力学进展, 42: 109-118

    (Li Q, Wang T S, Ma X R.Reviews on liquid sloshing dynamics and liquid-structure coupling dynamics in liquid-filled spacecrafts. Advances in Mechanics, 42: 109-118).
    [27] 梅凤翔. 2004. 约束力学系统的对称性与守恒量. 北京: 北京理工大学出版社

    (Mei~F X. 2004. Symmetries and Conserved Quantities of Constrained Mechanical Systems. Beijing: Beijing Institute of Technology Press).
    [28] 梅凤翔. 2013a. 分析力学 (上、下卷). 北京: 北京理工大学出版社

    (Mei F X.2013a. Analytical Mechanics (Volume 1, Volume 2). Beijing: Beijing Institute of Technology Press).
    [29] 梅凤翔. 2013b. 广义Birkhoff系统动力学. 北京: 科学出版社

    (Mei~F X. 2013b. Dynamics of Generalized Birkhoffan~System. Beijing: Science Press).
    [30] 梅凤翔, 罗绍凯, 赵跃宇. 1996. 中国分析力学40年. 北京理工大学学报, 16: 1-7

    (Mei F X, Luo S K, Zhao Y Y.1996. Forty years for analytical mechanics in China. Journal of Beijing Institute of Technology, 16: 1-7).
    [31] 梅凤翔, 尚玫. 2000. 一阶lagrange系统的lie对称性与守恒量. 物理学报, 49: 1901-1903

    (Mei F X, Shang M.2000. Lie symmetries and conserved quantities of first order lagrange systems. Acta Phys Sin, 49: 1901-1903).
    [32] 闵桂荣, 郭舜. 1998. 航天器热控制. 北京: 科学出版社

    (Min~G R, Guo S. 1998. Spacecraft~Thermal~Control. Beijing: Science Press).
    [33] 马兴瑞, 王本利, 苟兴宇. 2001. 航天器动力学------若干问题进展及应用. 北京: 科学出版社

    (Ma~X R, Wang~B L, Gou~X Y. 2001. Spacecraft~Dynamics: The~Advances~of~Several~Problems and Its Application. Beijing: Science Press).
    [34] 沈惠川. 1998. 弹性力学的Lagrange形式: 用Routh方法建立弹性有限变形问题的基本方程. 数学物理学报, 18: 78-88

    (Shen H C.1998. Lagrange formalism of elasticity: Building the basic equations on finite-deformation problems by Routh's method. Acta Mathematieaentia, 18: 78-88).
    [35] 汪家訸. 1958. 分析动力学. 北京: 高等教育出版社

    (Wang J H.1958. Analytical Dynamics. Beijing: Higher Education Press).
    [36] 王琪, 陆启韶. 2001. 多体系统Lagrange方程数值算法的研究进展. 力学进展, 31: 9-17

    (Wang Q, Lu Q S. 2001. Advances in the numerical methods for Lagrange's equations of multibody systems. Advances in Mechanics, 31: 9-17).
    [37] 王作君, 郑德忠, 郑成博, 郑世科. 2011. 电磁弹性动力学初边值问题12类变量广义变分原理. 计算力学学报, 28: 63-65

    (Wang Z J, Zheng D Z, Zheng C B, Zheng S K.2011. Twelve-field generalized variational principles for initial-boundary-value problem of magneto-electroelasto dynamics. Chinese Journal of Computational Mechanics, 28: 63-65).
    [38] 王照林, 刘延柱. 2002. 充液系统动力学. 北京: 科学出版社

    (Wang~Z L, Liu Y Z. 2002. Dynamics of Liquid-filled~System. Beijing: Science Press).
    [39] 杨炳渊, 史晓鸣, 梁强. 2008. 高超声速有翼导弹多场耦合动力学的研究和进展 (下). 强度与环境, 35: 55-62

    (Yang B Y, Shi X M, Liang Q.2008. Investigation and development of the multi-physics coupling dynamics on the hypersonic winged missiles. Structure & Environment Engineering, 35: 55-62).
    [40] 杨挺青. 1990. 粘弹性力学. 武汉: 华中科技大学出版社

    (Yang~T Q. 1990. Viscoelasticity. Wuhan: Huazhong University of Technology Press).
    [41] 周平, 梁立孚. 2017. 非保守系统的Lagrange方程. 哈尔滨工程大学学报, 38: 452-459

    (Zhou P, Liang L F.2017. Lagrange equation of non-conservative systems. Journal of Harbin Engineering University, 38: 452-459).
    [42] 周平, 赵淑红, 梁立孚. 2009. 含阻尼非保守分析力学的拟变分原理. 北京理工大学学报, 29: 565-569

    (Zhou P, Zhao S H, Liang L F.2009. Quasi-variational principles on non-conservative analytical mechanics with damping. Journal of Beijing Institute of Technology (Natural Science Edition), 29: 565-569).
    [43] 钟万勰. 2002. 应用力学对偶体系. 北京: 科学出版社

    (Zhong W X.2002. Duality Method in Applied Mechanics. Beijing: Science Press).
    [44] 张毅, 范存新, 梅凤翔. 2006. Lagrange系统对称性的摄动与hojman型绝热不变量. 物理学报, 55: 3237-3240

    (Zhang Y, Fan C X, Feng X M.2006. Perturbation of symmetries and hojman adiabatic invariants for Lagrangian systems. Acta Physica Sinica, 55: 3237-3240).
    [45] 张毅, 梅凤翔. 2004. 非保守力与非完整约束对lagrange系统noether对称性的影响. 物理学报, 53: 661-665

    (Zhang Y, Mei F X.2004. Effects of non-conservative forces and nonholonomic constraints on noether symmetries of a Lagrange system. Acta Physica Sinica, 53: 661-665).
    [46] Altay G, Dokmeci M C.2005. Variational principles for the equations of porous piezoelectric ceramics. IEEE Transactions on Ultrasonics Ferroelectrics & Frequency Control, 52: 2112-2119.
    [47] Auffray N, Dell'Isola F, Eremeyev V, Madeo A, Rosi G.2015. Analytical continuum mechanics la Hamilton-Piola least action principle for second gradient continua and capillary fluids. Mathematics & Mechanics of Solids, 20: 375-417.
    [48] Chien W Z.1984. Variational principles and generalized variational principles in hydrodynamics of viscous fluids. Applied Mathematics and Mechanics (English Edition), 5: 305-322.
    [49] Chen X W, Liu C, Mei F X.2008. Conformal invariance and Hojman conserved quantities of first order Lagrange systems. Chinese Physics B, 17: 3180-3184.
    [50] Eringen A C.1962. Nonlinear theory of continuous media. Journal of Applied Mechanics, 31: 368-377.
    [51] Fahrenthold E P, Koo J C.1999. Discrete hamilton's equations for viscous compressible fluid dynamics. Computer Methods in Applied Mechanics & Engineering, ~178: 1-22.
    [52] Granados A L M.1998. Variational principles in~continuum~mechanics. Boletin Tecnico/Technical Bulletin, 36: 19-42.
    [53] Gouin H.2008. Variational theory of mixtures in continuum mechanics. European Journal of Mechanics-B/Fluids, ~9: 469-491.
    [54] Hanyga A, Seredynska M.2008. Hamiltonian and Lagrangian theory of viscoelasticity. Continuum Mechanics & Thermodynamics, 19: 475-492.
    [55] Hean C R, Fahrenthold E P.2017. Discrete Lagrange equations for reacting thermofluid dynamics in arbitrary Lagrangian-Eulerian frames. Computer Methods in Applied Mechanics & Engineering, 313: 303-320.
    [56] Goldstein H, Poole C P, Safko J L.2001. Classical Mechanics (3rd Edition). Addison-Wesley.
    [57] Hamilton WR. Part I 1834, Part II 1835. On a general method in dynamics. Philosophical Transaction of the Royal Society, Part I 1834: 247-308, Part II 1835: 95-144.
    [58] Irschik H, Holl H J.2002. The equations of Lagrange written for a non-material volume. Acta Mechanica, 153: 231-248.
    [59] Irschik H, Holl H J.2015. Lagrange's equations for open systems, derived via the method of fictitious particles, and written in the Lagrange description of continuum mechanics. Acta Mechanica, 226: 63-79.
    [60] Kim G, Senda Y.2007. A methodology for coupling an atomic model with a continuum model using an extended Lagrange function. Journal of Physics Condensed Matter An Institute of Physics Journal, 19: 246203.
    [61] Kim Jinkyu, Dargush G F, Ju Y K.2013. Extended framework of Hamilton's principle for continuum dynamics. International Journal of Solids and Structures, 50: 3418-3429.
    [62] Kuang Z B.2014. Theory of Electroelasticity. Springer.
    [63] Lyakhov A. F.1992. Variational formulation of the problem of mooring (anchor) line dynamics. International Journal of Fluid Mechanics Research, 21: 116-120.
    [64] Longatte E, Bendjeddou Z, Souli M.2003. Application of arbitrary Lagrange Euler formulations to flow-induced vibration problems. Journal of Pressure Vessel Technology, 125: 225-233.
    [65] Luo E, Kuang J S.1999. Some basic principles for linear coupled dynamic thermopiezoelectricity. Sci. China Ser. A-Math, 42: 1292-1300.
    [66] Luo E, Zhu H J, Yuan L.2006. Unconventional Hamilton-type variational principles for electromagnetic elastodynamics. Sci. China Ser. G-Phys. Mech. Astron, 49: 119-128.
    [67] Lagrange J L. (Joseph Louis). 1811 (Originally published in l788). Méanique analytique, Paris: Ve Courcier.
    [68] Liang L F, Liu D K, Song H Y.2005. The generalized quasi-variational principles of non-conservative systems with two kinds of variables. Science in China (Series G), 48: 600-613.
    [69] Liang L F, Liu S Q, Zhou J S.2009. Quasi-variational principles of single flexible body dynamics and their applications. Science in China (G), 52: 775-78.
    [70] Liang L F, Song H Y.2013. Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics. Science China Physics, Mechanics & Astronomy, 56: 2192-2199.
    [71] Liu Y H, Zhang H M.2007. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation. Appl Math Mech (English Edition), 28: 193-200.
    [72] Mei F X.2000. Form invariance of Lagrange system. Journal of Beijing Institute of Technology (English Edition), 87:175-182.
    [73] Mei F X, Xu X J.2005. Form invariances and lutzky conserved quantities for Lagrange systems. Chinese Physics B, 14: 449-451.
    [74] Maximov G A.2010. A generalized variational principle for dissipative hydrodynamics and its application to Biot's theory for the description of a fluid shear relaxation. Acta Acustica United with Acustica, 96: 199-207.
    [75] Mahmoudkhani S.2017. Dynamics of a mass-spring-beam with 0: 1: 1 internal resonance using the analytical and continuation method. International Journal of Non-Linear Mechanics, 97: 48-67.
    [76] Orlov D, Apker T, He C, Othman H, Corke T.2006. Modeling and experiment of leading edge separation control using SDBD plasma actuators. Wildlife Research, 37: 447-455.
    [77] Pian H H, Tong P.1972. Finite Element Method in Contimuum Mechanics. New York: Academic Press.
    [78] Patel M P, Ng T T, Vasudevan S, Corke T C, He C.2007. Plasma actuators for hingeless aerodynamic control of an unmanned air vehicle. Journal of Aircraft, 44: 1264-1274.
    [79] Seiranyan A P.1984. On a problem of Lagrange. Mechanics of Solids, 19: 100-111.
    [80] Song H Y, Hou G L, Sun H, Liang L F.2015. Rigid--elastic-thermal coupling dynamics and its application. Advances in Mechanical Engineering, 7: 1-8.
    [81] Song H Y, Liu Z M, Huang Y H.2013. Dual form of generalized variational principles for piezoelectricity. International Journal of Nonlinear Sciences and Numerical Simulation, 14: 205-209.
    [82] Song H Y, Zhou Z G, Liang L F, Liu Z M.2009. Generalized variational principles of electro-magneto-thermo-elasto-dynamics. Proceedings of ASME International Mechanical Engineering Congress and Exposition, 11: 243-248.
    [83] Souchet R.2014. Continuum mechanics and Lagrange equations with generalised coordinates. International Journal of Engineering Science, 76: 27-33.
    [84] Tran-Cong T.1996. A variational principle for fluid mechanics. Archive of Applied Mechanics, 67: 96-104.
    [85] Yang Q, Lv Q C, Liu Y R.2017. Hamilton's principle as inequality for inelastic bodies. Continuum Mechanics & Thermodynamics, 29: 747-756.
    [86] Zenkour A.1989. Hamilton's mixed variational formula for dynamical problems of anisotropic elastic bodies. Sm Archives, 14: 103-114.
    [87] Zheng C B, Liu B, Wang Z J, Zheng S K.2010. Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics. Appl. Math. Mech, 31: 471-480.
    [88] Zhavoronok S I.2015. On the variational formulation of the extended thick anisotropic shells theory of I. N. vekua type. Procedia Engineering, 111: 888-895.
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  • 收稿日期:  2017-09-27
  • 刊出日期:  2019-02-08

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