RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (8): 867-874.

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RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

戴天民

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

收稿日期:2001-03-13 修回日期:2002-04-01 出版日期:2002-08-18 发布日期:2002-08-18
基金资助:
the National Natural Science Foundation of China(10072024);the Interna tional Cooperation Project of the NSFC(1001130235)and the DFG(51520001);the Research Foundation of Liaoning Education Committee(990111001)

RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

DAI Tian-min

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

Received:2001-03-13 Revised:2002-04-01 Online:2002-08-18 Published:2002-08-18
Supported by:
the National Natural Science Foundation of China(10072024);the Interna tional Cooperation Project of the NSFC(1001130235)and the DFG(51520001);the Research Foundation of Liaoning Education Committee(990111001)

摘要/Abstract

摘要： The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola’s theorem. These basic equations and the boundary conditions together with the initial conditions may be used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.

Abstract: The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola’s theorem. These basic equations and the boundary conditions together with the initial conditions may be used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.

中图分类号:

戴天民. RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(8): 867-874.

DAI Tian-min . RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(8): 867-874.

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RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

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