| 广义连续流场论中新的功能及功率能率原理 |
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| 引用本文： | 戴天民.广义连续流场论中新的功能及功率能率原理[J].应用数学和力学,2001,22(11):1111-1118. |
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| 作者姓名： | 戴天民 |
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| 作者单位： | 辽宁大学数学应用中心和数学系, |
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| 基金项目： | 国家自然科学基金资助项目(19672023);国家自然科学基金委员会(10011130235)德意志研究联合会(51520001)资助的国际合作项目;辽宁省教委(A类)科研项目(990111001) |
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| 摘 要： | 提出极性和非局部极性连续统场论中具有交叉项的新的功能及功率能率原理，并据此和广义的Piola定理一次性地而且无需其它要求地推导出所有相应的运动方程和边界条件以及新的能量和能率均衡方程。同时，建立起广义连续统力学中的新的能量和能率均衡原理。给出的新的功能及能率原理纠正了现有文献中所有有关不带交叉项的能量和能率原理的不完整性。
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| 关 键 词： | 功率能率原理 Piol定理 能率均衡方程 广义连续统场论 能量均衡方程 功能原理 连续统力学 |
| 文章编号： | 1000-0887(2001)11-1111-08 |
| 修稿时间： | 2000年5月28日 |
New Principles of Work and Energy as well as Power and Energy Rate for Continuum Field Theories |
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| DAI Tian-min.New Principles of Work and Energy as well as Power and Energy Rate for Continuum Field Theories[J].Applied Mathematics and Mechanics,2001,22(11):1111-1118. |
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| Authors: | DAI Tian-min |
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| Abstract: | New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally,some new balance laws of energy and energy rate for generalized continuum mechanics were established.The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories. |
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| Keywords: | principles of work and energy power and energy rate generalized Piola's theorem equations of energy and energy rate generalized continua |
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