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  

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

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》2003年第10期998-1004,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10072024);辽宁省教育委员会基础研究基金资助项目(990111001)

摘　　要：　重建微态连续统理论和偶应力理论的动量和动量矩均衡定律以及能量守恒定律,并由这些定律自然地推导出相应的局部和非局部均衡方程·　这些结果可由耦合型微极连续统理论过渡和归结而得到·　把推导出的结果和传统的质量和微惯性守恒定律以及熵不等式结合在一起就构成微态连续统理论和偶应力理论的基本均衡定律和方程体系·　还弄清了以前的各种连续统理论的不完整性层次·　最后。The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for microplar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally,some special cases are conveniently derived.

关 键 词：微极连续统 偶应力理论 耦合型的 基本均衡定律 均衡方程 

分 类 号：O33[理学—一般力学与力学基础]