Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity
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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。Abstract: 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 thermopiezo-electricity 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.
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