| 重建极性连续统理论的基本定律和原理(Ⅲ)--Noether定理 |
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| 引用本文： | 戴天民. 重建极性连续统理论的基本定律和原理(Ⅲ)--Noether定理[J]. 应用数学和力学, 2003, 24(10): 1005-1011 |
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| 作者姓名： | 戴天民 |
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| 作者单位： | 辽宁大学,数学系和数学应用中心,沈阳,110036 |
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| 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) |
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| 摘 要： | 对现有的各种偶应力理论进行了认真的再研究，目的是要提出一个耦合型的Noether定理并由此重新建立偶应力弹性动力学的较为完整的守恒定律和相应的均衡方程．这里给出了新的各种守恒定律和均衡方程的具体形式，并建立起从给定的不变性要求所得到的这类守恒定律的确切属性．最后，由这里的结果自然地推导出各种特殊情形；并可自然地过渡到微极连续统的结果．
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| 关 键 词： | Noether定理 偶应力弹性动力学 偶应力弹性静力学 守恒定律 |
| 文章编号： | 1000-0887(2003)10-1005-07 |
| 修稿时间： | 2002-05-19 |
Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether''s Theorem |
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| DAI Tian|min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether''s Theorem[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1005-1011 |
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| Authors: | DAI Tian|min |
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| Abstract: | The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether's theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper. |
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| Keywords: | Noether's theorem couple stress elastodynamics couple stress elastostatics conservation law |
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