重建极性连续统理论的基本定律和原理(Ⅺ)——兼容性问题  

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅺ)——Consistency Problems

作　　者：戴天民[1] 

机构地区：[1]辽宁大学数学系和数学应用中心,沈阳110036

出　　处：《应用数学和力学》2007年第2期147-155,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472041)

摘　　要：对现有连续统场论中存在若干有关兼容性问题进行了简略的评论.根据重建的极性的连续统基本定律阐述三类兼容性问题.第一类是讨论各基本定律间的兼容性问题.第二类是讨论微极连续统基本定律兼容一般连续统基本定律的问题.第三类是讨论微极连续统基本定律兼容刚体动力学基本方程的问题.推导出的结果有助于深刻理解各种连续统理论的基本定律体系的结构和它们之间的联系.明确地指出,在传统的连续统场论的基本均衡定律的框架下,相容性问题是不可能自然地得到解决.Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discussed the consistency problems between the basic laws for polar continua. The second art discussed the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discussed the consistency problems between the basic laws for mieropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us get a deeper understanding of the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained also show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.

关 键 词：微极连续统 非极性连续统 刚体 基本定律 兼容性问题 

分 类 号：O33[理学—一般力学与力学基础]