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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (3): 249-258.

• 论文 • 上一篇    下一篇

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY

戴天民   

  1. Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P. R. China
  • 收稿日期:2000-12-29 修回日期:2001-09-11 出版日期:2002-03-18 发布日期:2002-03-18
  • 基金资助:
    the National Natural Science Foundation of China(10072024);the International Cooperation Project of the NSFC(10011130235)and the DFG(51520001);the Research Foundation of the Liaoning Education Committee(990111001)

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY

DAI Tian-min   

  1. Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P. R. China
  • Received:2000-12-29 Revised:2001-09-11 Online:2002-03-18 Published:2002-03-18
  • Supported by:
    the National Natural Science Foundation of China(10072024);the International Cooperation Project of the NSFC(10011130235)and the DFG(51520001);the Research Foundation of the Liaoning Education Committee(990111001)

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摘要： The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically 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 thermopiezoelectricity 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.

Abstract: The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically 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 thermopiezoelectricity 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.

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