重建极性连续统理论的基本定律和原理(Ⅷ)——全功能原理  

Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy

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》2005年第3期287-292,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472041;10072024);辽宁省教育委员会科研资助项目(990111001)

摘　　要：　进一步阐明了现有极性连续统力学的能量守恒定律在理论上的不完整性·　为能使之完整起见,提出了全功能原理及增率型全功能原理·　通过对它们的全变分。Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.

关 键 词：微极连续统 全功能 全虚功能 增率型 能量守恒定律 

分 类 号：O33[理学—一般力学与力学基础]