Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy

DAI Tian-min

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DAI Tian-min. Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy[J]. Applied Mathematics and Mechanics, 2005, 26(3): 287-292.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy[J]. Applied Mathematics and Mechanics, 2005, 26(3): 287-292.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy[J]. Applied Mathematics and Mechanics, 2005, 26(3): 287-292.

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Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy

DAI Tian-min

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

Received Date: 2003-08-29
Rev Recd Date: 2004-11-26
Publish Date: 2005-03-15

Abstract

Abstract

Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Viatotal variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.
- micropolar continua,
- total work and energy,
- total virtual work and energy,
- incremental rate type,
- conservation law of energy

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References(11)

References

[1]	戴天民.广义连续统场论中新的功能及功率能原理[J].应用数学和力学，2001,22(11):1111—1118.
[2]	戴天民.广义连续统场论中新的增率型功率和能率原理[J].应用数学和力学，2001,22(12):1243—1248.
[3]	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.
[4]	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.
[5]	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.
[6]	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[J].应用数学和力学，2003，24(11)：1101—1107
[7]	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.
[8]	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.
[9]	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—1222.
[10]	Eringen A C.Continuum Physics[M].Vol.Ⅳ. New York, London: Academic Press, 1976，1—38.
[11]	匡震邦. 非线性连续统介质力学基础[M]. 西安：西安交通大学出版社，1989,118—126.