Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia

DAI Tian-min

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DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1211-1216.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1211-1216.

Citation:

DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1211-1216.

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Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia

DAI Tian-min

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

Received Date: 2002-09-06
Rev Recd Date: 2003-06-27
Publish Date: 2003-12-15

Abstract

Abstract

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds. transport theorem was presented. Combining these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization.
- polar continua,
- coupled,
- transport theorem,
- conservation law of mass and inertia

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References(11)

References

[1]	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.
[2]	DAI Tian-min.New laws and principles for continuum mechanics-Part Ⅱ:Energy rate and power[A].In:Ibid[C].Shanghai:Shanghai University Press,2002,210-212.
[3]	DAI Tian-min.On basic laws and principles for continuum field theories[A].In:Ibid[C].Shanghai:Shanghai University Press,2002,29-41.
[4]	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.
[5]	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):998-1014.
[6]	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):1015-1021.
[7]	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.
[8]	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.
[9]	戴天民.极性连续统的增率型运动方程和边界条件[J].应用数学和力学,2000,21(3):221-225.
[10]	Eringen A C.连续统物理的基本原理[M].朱照宣译.南京:江苏科学技术出版社,1985.
[11]	Eringen A C,Kafadar C B.微极场论[M].戴天民译.南京:江苏科学技术出版社,1982.