重建极性连续统理论的基本定律和原理(Ⅴ)——极性热力连续统  

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅴ)-Polar Thermomechanical Continua

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11期1108-1113,共6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项目(990111001)

摘　　要：　在对传统的微极热弹性理论和热压电弹性理论已进行过再研究的基础上重建极性热力连续统的较为完整的基本均衡方程和边界条件·　从较为完整的虚功率原理推导出微极热弹性理论的运动方程和局部能率均衡方程·　从较为完整的Hamilton原理通过全变分自然地推导出运动方程,熵均衡方程以及所有边界条件·　给出的新的动量均衡方程和局部能率均衡方程与现有理论的结果存在本质的差异·　通过过渡和归结可从微极热弹性理论分别得到微态热弹性理论的和偶应力热弹性动力学的结果·　最后。The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity . The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle . The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case , respectively . Finally , the results of micropolar thermopiezoelectricity are directly given .

关 键 词：极性 热弹性理论 热压电弹性理论 基本方程 边界条件 

分 类 号：O33[理学—一般力学与力学基础]