重建极性连续统理论的基本定律和原理(Ⅶ)——增率型

基金项目: 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资助项目(990111001)

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅶ)——Incremental Rate Type

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

摘要: 目的是建立微极连续统增率型的较为完整的运动方程,边界条件和能率方程.为此,先给出较为完整的变形梯度及其逆的定义.接着推导出各种应力率和偶应力率间的新关系式.最后,作为一种特殊情形得到连续统力学的耦合的增率型运动方程、边界条件和能率方程.
- 耦合的 /
- 运动方程 /
- 边界条件 /
- 能率 /
- 增率型 /
- 微极连续统
Abstract: The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.
- coupled /
- equation of motion /
- boundary condition /
- energy rate /
- incremental rate type /
- micropolar continua

[1]	匡震邦.非线性连续介质力学基础[M].西安:西安交通大学出版社,1989.
[2]	戴天民.极性连续统的增率型运动方程和边界条件[J].应用数学和力学,2000,21(3):221-225.
[3]	戴天民.广义连续统场论中新的增率型功率和能率原理[J].应用数学和力学,2001,22(12):1243-1248.
[4]	DAI Tian-min.On basic laws and principles for continuum field theories[A].In:CHIEN Wei-zang Ed.Proceedings of the 4th International Conference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press,2002,29-41.
[5]	戴天民.重建极性连续统理论的基本定律和原理(Ⅰ)——微极连续统[J].应用数学和力学,2003,24(10):991-997.
[6]	戴天民.重建极性连续统理论的基本定律和原理(Ⅱ)——微态连续统理论和偶应力理论[J].应用数学和力学,2003,24(10):998-1014.
[7]	戴天民.重建极性连续统理论的基本定律和原理(Ⅵ)——质量和惯性守恒定律[J].应用数学和力学.2003,24(12):1211-1216.