Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy
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摘要: 进一步阐明了现有极性连续统力学的能量守恒定律在理论上的不完整性.为能使之完整起见,提出了全功能原理及增率型全功能原理.通过对它们的全变分,即可分别得到虚位移-微转动和虚应力-偶应力原理及虚速度-角速度和虚应力率-偶应力率原理.从这些原理可以同时而且很自然推导出微极连续统力学的所有均衡方程和边界条件.所得到非传统结果与现有能量守恒定律问题存在的本质性差异作了说明.Abstract: Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Viatotal variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.
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