微极连续统的耦合场理论的再研究(I)——微极热弹性理论

基金项目: 国家自然科学基金资助项目(10072024);国家自然科学基金委员会(10011130235);德意志研究联合会(51520001)资助的国际合作研究项目;辽宁省教育委员会A类科研项目(990111001)

Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity

Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P R China

摘要: 在传统的微极连续统理论框架下微极热弹性理论问题已被某些学者提出并做过讨论。这篇文章对现有的微极热弹性理论进行了再研究,找出了该理论局限于线性情形的原因。建立了微极热弹性理论的更为普遍的虚功原理和新的内力虚功表达式以及Hamilton原理。从这个新的Hamilton原理不仅可以得到运动方程、熵均衡方程、应力和偶应力以及热量边界条件,而且还可同时推导出位移和微转动以及温度边界条件。
- 微极介质 /
- 热弹性理论 /
- 虚功原理 /
- Hamilton原理
Abstract: Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the thoery of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed.The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.
- micropolar continua /
- thermoelasticity /
- principle of virtual work /
- Hamilton principle

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