DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether’s Theorem[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1005-1011.
 Citation: DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether’s Theorem[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1005-1011.

# Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether’s Theorem

• Received Date: 2002-05-19
• Rev Recd Date: 2003-05-09
• Publish Date: 2003-10-15
• The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether.s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics.The new concrete forms of various conservation laws of couple stress elasticity are derived.The precise nature of these conservation laws which result from the given invariance requirements are established.Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper.
•  [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] Mindlin R D, Tiersten H F. Effects of couple stress in linear elasticity [J]. Arch Rat Mech Anal,1962,11:415-448. [4] Toupin R A. Theories of elasticity with couple-stress [J]. Arch Rat Mech Anal, 1964,17: 85-112. [5] Eringen A C. Linear theory of micropolar elasticity[J]. J Math Mech, 1966,15: 909-923. [6] Eringen A C. Theoryofmicropolarfluids[J].J Math Mech,1966,16:1-18. [7] Atkinson C, Leppington F G. Some calculations of the energy-release rate G for cracks in micropolar and couple-stress elastic media[J]. Int J Fracture, 1974,10: 599-602. [8] Atkinson C, Leppington F G. The effect of couple-stresses on the tip of a crack[J]. Int J Solids Struct, 1977,13:1103-1122. [9] Eshelby J D. The energy-momentum tensor of complex continua[A]. In: Kroener E, Anthony K H Eds. Continuum Models of Discrete Systems[C]. Waterloo: University of Waterloo Press, 1980:651-665. [10] Jaric J. Conservation laws of the J-integral type in micropolar elastostatics[J]. Int J Engng Sci,1978,16: 967-984. [11] Knowles J K, Sternberg E. On a class of conservation laws in linearizeci and finite elastostatics[J].Arch Rat Mech Anal, 1972,44:187-211. [12] 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(5):271-279. [13] Fletzer D C. Conservation laws in linear elastodynamics [J]. Arch Rat Me ch Anal, 1976,60: 329-353. [14] 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(3):184-189. [15] DAI Tian-min. Some path in dependent integrals for micropolar media [J]. Int J Solids Struct, 1986,22(7) :729-735. [16] Vukobrat M. Conservation laws in micropolar elastodynamics and path-independent integrals[J]. Int J Engng Sci, 1989,27(9): 1093-1106. [17] Lubarda V A, Markenscoff X. Conservation laws in couple stress elasticity[J]. J Mech Phys Solids,2000,48: 553-564. [18] Budiansky B, Rice J R. Conservation laws and energy-release rates [J].J Appl Mech,1973,40:201-203. [19] DAI Tian-min. On basic laws and principles for continuum field theories[A]. In: CHIEN Wei-zang Ed. Proceedings of the 4 th International Conference on Nonlinear Mechanics [C]. Shanghai: Shanghai University Press,2002,29-41.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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