重建极性连续统理论的基本定律和原理(Ⅲ)——Noether定理

戴天民

重建极性连续统理论的基本定律和原理(Ⅲ)——Noether定理

戴天民

辽宁大学, 数学系和数学应用中心, 沈阳, 110036

基金项目: 国家自然科学基金资助项目(10072024);辽宁省教育委员会基础研究基金资助项目(990111001)

详细信息

作者简介:
戴天民(1931- ),男,满族,辽宁开原人,教授,博士,博士生导师,已发表专著译著12部和论文620余篇(E-mail:tianmin-dai@yahoo.com.cn).

中图分类号: O33
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- 文章访问数: 2203
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出版历程
- 收稿日期: 2002-05-19
- 修回日期: 2003-05-09
- 刊出日期: 2003-10-15

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

DAI Tian-min

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

摘要

摘要: 对现有的各种偶应力理论进行了认真的再研究,目的是要提出一个耦合型的Noether定理并由此重新建立偶应力弹性动力学的较为完整的守恒定律和相应的均衡方程。这里给出了新的各种守恒定律和均衡方程的具体形式,并建立起从给定的不变性要求所得到的这类守恒定律的确切属性。最后,由这里的结果自然地推导出各种特殊情形;并可自然地过渡到微极连续统的结果。
- Noether定理 /
- 偶应力弹性动力学 /
- 偶应力弹性静力学 /
- 守恒定律
Abstract: 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.
- Noether’s theorem /
- couple stress elastodynamics /
- couple stress elastostatics /
- conservation law

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参考文献(19)

[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.
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[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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重建极性连续统理论的基本定律和原理(Ⅲ)——Noether定理

作者简介:
戴天民(1931- ),男,满族,辽宁开原人,教授,博士,博士生导师,已发表专著译著12部和论文620余篇(E-mail:tianmin-dai@yahoo.com.cn).

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

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留言板

重建极性连续统理论的基本定律和原理(Ⅲ)——Noether定理

作者简介: 戴天民(1931- ),男,满族,辽宁开原人,教授,博士,博士生导师,已发表专著译著12部和论文620余篇(E-mail:tianmin-dai@yahoo.com.cn).

计量

出版历程

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

计量

出版历程

目录

作者简介:
戴天民(1931- ),男,满族,辽宁开原人,教授,博士,博士生导师,已发表专著译著12部和论文620余篇(E-mail:tianmin-dai@yahoo.com.cn).