微极连续统的耦合场理论的再研究(Ⅱ)──微极热压电弹性理论和电磁热弹性理论  

Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity

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》2002年第3期229-238,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目 (10 0 72 0 2 4 ) ;国家自然科学基金委员会对外交流与合作资助(10 0 11130 2 35 );德意志研究联合会资助 (5 15 2 0 0 0 1)的国际合作研究项目 ;辽宁省教育委员会A类科研项目 (95 0 1110 0 1)

摘　　要：W .Nowacki曾建立起系统的微极热压电弹性理论和电磁热弹性理论·　戴天民对W .Nowacki建立的微极热压电弹性理论和电磁热弹性理论进行了再研究 ,对这些理论局限于线性情形的原因和它们的不完整处进行了分析·　针对这些理论中所存在的问题 ,建立起微极热压电弹性理论和电磁热弹性理论的更普遍的能量守恒原理和局部能量方程以及Hamilton原理·　从戴天民所建立的更普遍能量守恒原理和Hamilton原理很自然地推导出局部和非局部微极热压电和电磁热弹性理论的完整的运动方程和边界条件以及能率均衡方程·　通过引入两个新泛函和全变分还可另外得到位移、微转动、电势和温度边界条件·The theories of thermopiezoelectricity and magnetoelasticty for microplar continua have been systemetically developed by W.Nowacki. In this paper the theories are restudied. The reason why they were restricted to linear cases is analyzed. The more general conservation principle of energy, energy balance equation and Hamilton principle of thermopiezoelectricity and magnetoelasticity for micropolar continua are established. The corresponding complete equations of motion and boundary conditions as well as balance equations of energy rate for local and nonlocal micropolar thermopiezoelectricity and magnetothermoelasticity are naturally derived. By means of two new functionals and total variation the boundary conditions of displacement, microrotation, electric potential and temperature are also given.

关 键 词：热压电弹性 电磁热弹性理论 能量原理 HAMILTON原理 微极连续统 耦合场理论 

分 类 号：O33[理学—一般力学与力学基础]