Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law

DAI Tian-min

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(2): 151-158

DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law[J]. Applied Mathematics and Mechanics, 2006, 27(2): 151-158.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law[J]. Applied Mathematics and Mechanics, 2006, 27(2): 151-158.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law[J]. Applied Mathematics and Mechanics, 2006, 27(2): 151-158.

PDF( 329 KB)

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law

DAI Tian-min

Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P. R. China

Received Date: 2004-04-09
Rev Recd Date: 2005-11-12
Publish Date: 2006-02-15

Abstract

Abstract

Through a comparison between the expressions of master balance laws and the conservation laws derived by the use of Noether. s thorem a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energy-momentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly perceived through the intuition. Finally, some existing results are reduced immediately as special cases.
- unified master balance law,
- physical field quantity,
- conservation law,
- energy-momentum,
- energy-angular momentum,
- energy-energy

FullText(HTML)

References(27)

References

[1]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅰ)——微极连续统[J].应用数学和力学，2003,24(10):991—997.
[2]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅱ)——微态连续统理论和偶应力理论[J].应用数学和力学，2003,24(10):998—1004.
[3]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅲ)——Noether定理[J].应用数学和力学，2003,24(10):1005—1011.
[4]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅳ)——表面守恒积分[J]. 应用数学和力学，2003,24(11):1101—1107.
[5]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅴ)——极性热力连续统[J].应用数学和力学，2003,24(11):1108—1113.
[6]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅵ)——质量和惯性守恒定律[J]. 应用数学和力学，2003,24(12):1211—1216.
[7]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅶ)——增率型[J].应用数学和力学，2003,24(12):1217—1221.
[8]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅷ)——全功能原理[J].应用数学和力学，2005,26(3):287—292.
[9]	戴天民.重建极性连续统理论的基本定律和原理 (Ⅸ)——热力学[J]. 应用数学和力学，2005,26(6):653—658.
[10]	Truesdell C.A First Course in Rational Continuum Mechanics[M].VolⅠ.New York:San Francisco,London: Academic Press, 1977.
[11]	黄筑平. 连续介质力学基础[M].北京：高等教育出版社，2003.
[12]	Eringen A C.Continuum Physics[M].Vol Ⅱ.New York:Springer-Verlag, 1976.
[13]	Mueller I.Thermodynamics[M].Boston,London,Melbourne: Pitman Advanced Publishing Program, 1985.
[14]	Eringen A C.Continuum Physics[M].Vol Ⅳ.New York:Springer-Verlag, 1976.
[15]	Eringen A C. Nonlocal elasticity and waves[A].In:Thoft-Christensen P Ed.Continuum Mechanics Aspect of Geodynamics and Rock Fracture Mechanics[C].Dordrecht: D Reidel Publ Co,1974,81—105.
[16]	戴天民.三组非局部热性热力连续统的均衡方程和跳变条件[J].中国科学,A辑，1997,27(12):1106—1110.
[17]	Jaric J. Conservation laws of the J-integral type in micropolar elastostatics[J].Internat J Engng Sci,1978,16:967—984. doi: 10.1016/0020-7225(78)90055-1
[18]	Knowles J K,Sternberg E. On a class of conservation laws in linearized and finite elasticity[J].Arch Rat Mech Anal,1972,44:187—211.
[19]	Fletzer D C. Conservation laws in linear elastodynamics[J].Arch Rat Mech Anal,1976,60:329—353.
[20]	金伏生.非保守场守恒定律及某类连续介质力学的守恒定律[J].力学学报，1983,15(2):184—189.
[21]	DAI Tian-min. Some path-independent integrals for micropolar media[J].Internat J Solids Struct,1986,22(7):729—735. doi: 10.1016/0020-7683(86)90117-4
[22]	Vukobrat M. Conservation laws in micropolar elastodynamics and path-independent integrals[J].Internat J Engng Sci,1989,27(9):1093—1106. doi: 10.1016/0020-7225(89)90087-6
[23]	JIANG Qing.Conservation laws in linear viscoelastodynamics[J].Journal of Elasticity,1986,16:213—219. doi: 10.1007/BF00043587
[24]	DAI Tian-min. On basic laws and principles for continuum field theories[A].In: CHIEN Wei-zang Ed.Proceedings of the 4th International Conference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press, 2002:29—41.
[25]	Eshelby J D.The continuum theory of lattice defects[A].In: Seitz F,Turnbull D Eds.Solid State Physics[C].Vol 3.New York: Academic Press,1956:79—144.
[26]	Eshelby J D. Energy relations and the nrgy-momentum tensor in continuum mechanics[A].In:Kanninen M F, Adler W F, Rosenfeld A,Jaffee R Eds.Inelastic Behavior of Solids[C].New York: Mc Graw-Hill,1970:77—114.
[27]	戴天民.微极线性弹性动力学的守恒定律和跳变条件[J].力学学报，1981,13(3):271—279.