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

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

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: 2281
- HTML全文浏览量: 129
- PDF下载量: 959
- 被引次数: 0
出版历程
- 收稿日期: 2002-04-11
- 修回日期: 2003-05-09
- 刊出日期: 2003-10-15

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

DAI Tian-min

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

摘要

摘要: 重建微态连续统理论和偶应力理论的动量和动量矩均衡定律以及能量守恒定律,并由这些定律自然地推导出相应的局部和非局部均衡方程。这些结果可由耦合型微极连续统理论过渡和归结而得到。把推导出的结果和传统的质量和微惯性守恒定律以及熵不等式结合在一起就构成微态连续统理论和偶应力理论的基本均衡定律和方程体系。还弄清了以前的各种连续统理论的不完整性层次。最后,给出了几种特殊情形。
- 微极连续统 /
- 偶应力理论 /
- 耦合型的 /
- 基本均衡定律 /
- 均衡方程
Abstract: The purpose is to reestablish the balance laws of momentum,angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory.The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for microplar continuum theory,respectively.The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality.The incomplete degrees of the former related continuum theories are clarified.Finally,some special cases are conveniently derived.
- micromorphic continuum /
- couple stress theory /
- coupled /
- basic balance law /
- balance equatio

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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]	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.
[3]	Eringen A C, Suhubi E R. Nonlinear theory of sinple microelastic solids-Ⅰ [J].Int J Engng Sci, 1964,2:189-203.
[4]	Eringen A C, Sububi E R. Nonlinear theory of simple microelastic solids-Ⅱ [J]. Int J Engng Sci,1964,2:389-404.
[5]	Eringen A C. Mechanicsofmicromorphicmaterials[A].In:Gortler H Ed. Proc 11th Int Congr Appl Mech[C]. Berlin: Springer-Verlag, 1966,131-138.
[6]	Eringen A C.Microcontinuum Field Theories[M]. New York:Springer-Verlag,1999.
[7]	Soos E. Uniqueness theorems for homogeneous, isotropic, simple elastic and thermoelastic materials having a microstructure [J]. Int JEngng Sci,1969,7:257-268.
[8]	Eringen A C. Balance laws of micromorphic continua revisited [J]. Int J Engng Sci, 1992,30 (6):805-810.
[9]	Mindlin R D, Tiersten H E. Effects of couple stresses in linear elasticity [J]. Arch Rat Mech Anal,1962,11:415-448.
[10]	Toupin R A. Theories of elasticity with couple stresses [J]. Arch Rat Mech Anal, 1964,17:85-112.
[11]	Eringen A C. Linear theory of micropolar elasticity [J]. Journal of Mathematics and Mechanics,1996,15(6) :909-923.
[12]	Eringen A C. Theory of micropolar fluids [J].Journal of Mathematics and Mechanics, 1966,15(1):1-18.
[13]	DAI Tian-min. New laws and principles for continuum mechanics-Part Ⅰ: Balance laws and equations[A].In: CHIEN Wei-zang Ed. Proceedings of the 4th International Conference on Nonlinear Mechanics [C]. Shanghai: Shanghai University Press, 2002,206-209.
[14]	Stojanovic R. On the principle of virtual work in the theory of oriented elastic media[J]. Z Angew Math Mech, 1973,53: T79-T82.
[15]	戴天民.带有微结构的连续统中新的能量守恒定律和C-D不等式[J].应用数学和力学,2001,22(2):119-126.
[16]	戴天民.广义连续统场论中新的功能及功率能率原理[J].应用数学和力学,2001,22(11):1111-1118.
[17]	A C爱林根,C B卡法达.微极场论[M].戴天民译.南京:江苏科学技术出版社,1982,17-23.
[18]	戴天民.不带微结构的连续统中新的能量守恒定律和C-D不等式[J].应用数学和力学,2001,22(2):111-118.

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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

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60余篇(E-mail:tianmin-dai@yahoo.com.cn).

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Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

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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

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 (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

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60余篇(E-mail:tianmin-dai@yahoo.com.cn).