Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity

DAI Tian-min

Volume 23 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(3): 229-238

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(3): 229-238.

Citation:

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(3): 229-238.

Citation:

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(3): 229-238.

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Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity

DAI Tian-min

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

Received Date: 2000-12-29
Rev Recd Date: 2001-09-11
Publish Date: 2002-03-15

Abstract

Abstract

The theories of thermopiezoelectricity and magnetoelasticty for microplar continua have been systemetically developed by W.Nowacki.In this paper the theories are restudied.The reason why they were restricted to linear cases is analyzed.The more general conservation principle of energy,energy balance equation and Hamilton principle of thermopiezoelectricity and magnetoelasticity for micropolar continua are established.The corresponding complete equations of motion and boundary conditions as well as balance equations of energy rate for local and nonlocal micropolar thermopiezo-electricity and magnetothermoelasticity are naturally derived.By means of two new functionals and total variation the boundary conditions of displacement,microrotation,electric potential and temperature are also given.
- nonlocal,
- micropolar,
- thermopiezoelectricity,
- magnetothermoelasticity,
- principle of energy conservation,
- Hamilton principle

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References(6)

References

[1]	戴天民. 微极连续统的耦合场理论的再研究(Ⅰ)——微极热弹性理论[J].应用数学和力学,2002,23(2):111-118.
[2]	Nowacki W. Theory of Asymmetric Elasticity[M]. Oxford:Pergamon Press,1986.
[3]	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.
[4]	Eringen A C. 非局部微极场论[M]. 戴天民译. 南京:江苏科学技术出版社,1982.
[5]	Stojanovic R. On the principle of virtual work in the theory of oriented elastic media[J]. ZAMM, 1973,53,779-782.
[6]	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.

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