重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

戴天民

重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

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,已发表专著译著12部和论文60余篇(E-mail:tianmin_dai@yahoo.com.cn).

中图分类号: O33
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- 文章访问数: 2706
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- 被引次数: 0
出版历程
- 收稿日期: 2002-07-03
- 修回日期: 2003-06-06
- 刊出日期: 2003-11-15

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅳ)-Surface Couservation Laws

DAI Tian-min

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

摘要

摘要: 从普遍均衡定律的平移和转动的不变性出发来重新建立较为完整的微极热力连续统的表面守恒定律,提出了广义的能量动量和能量动量矩张量.给出了Piola型、Cauchy型和Kirchhoff型微极热力连续统的表面守恒定律的具体形式.现有的结果都可以当做是特殊情形从该结果自然地推导出来,并可从归结过程中清楚地看出现有理论的不完整性程度.非局部微极热力连续统的表面守恒定律可通过局部化得到.
- 表面守恒定律 /
- 微极热力连续统 /
- 广义能量动量张量 /
- 广义能量动量矩张量
Abstract: The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.
- surface conservation law /
- micropolar thermomechanical continuum /
- generalized energy-momentum tensor /
- generalized energy-moment of momentum tensor

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参考文献(18)

[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]	Gross D.Beitrag zu den Dynamischen Problemen der Bruchmechanik[M].Habilitationsschrift der Universitaet Stuttgart:Verlay der Universiteat Stuttgrat,1974.
[5]	Jaric J.Conservation laws of the J-integral type in micropolar elastostatics[J].Int J Engng Sci,1978,16:967-984.
[6]	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.
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[8]	金伏生.非保守场守恒定律及某类连续介质力学的守恒律[J].力学学报,1983,15(3):184-189.
[9]	DAI Tlan-min.Some path independent integrals for micropolar media[J].Int J Solids Struct,1986,22(7):729-735.
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[11]	Jaric J.The energy release rate and the J-integral in nonlocal micropolar field theory[J].Int J Engng Sci,1990,28(12):1303-1313.
[12]	DAI Tian-min.Generalized surface conservation laws for nonlocal polar thermomechanical continua[A].In:CHIEN Wei-zang Ed.Proceedings of the 3rd International Conference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press,1998,181,184.
[13]	Buggisch H,Gross D,Krueger K H.Einige Erhaltungssaetze der Kontinuumsmechanik yom J-Integral Typ[J].Ing Archiv,1981,50:103-111.
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[18]	Kraemer D.On the applicability of the Iintegral in fracture mechanics[J].Arch Appl Mech,1993,63:551-555.

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重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

作者简介:
戴天民(1931- ),男,满族,辽宁开原人,教授,博士,已发表专著译著12部和论文60余篇(E-mail:tianmin_dai@yahoo.com.cn).

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Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅳ)-Surface Couservation Laws

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留言板

重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

作者简介: 戴天民(1931- ),男,满族,辽宁开原人,教授,博士,已发表专著译著12部和论文60余篇(E-mail:tianmin_dai@yahoo.com.cn).

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出版历程

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅳ)-Surface Couservation Laws

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,已发表专著译著12部和论文60余篇(E-mail:tianmin_dai@yahoo.com.cn).