广义连续统场论中新的功能及功率能率原理

戴天民

广义连续统场论中新的功能及功率能率原理

戴天民

辽宁大学数学应用中心和数学系, 沈阳, 110036

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)

详细信息

作者简介:
戴天民(1931- ),男,满族,辽宁开原人,博士,教授,博士生导师,已发表专著12部,论文50余篇.

中图分类号: 033
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- 被引次数: 0
出版历程
- 收稿日期: 2000-05-28
- 修回日期: 2000-10-20
- 刊出日期: 2001-11-15

New Principles of Work and Energy as well as Power and Energy Rate for Continuum Field Theories

DAI Tian-min

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

摘要

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。
- 功能及功率能率原理 /
- 广义的Piola定理 /
- 能量和能率均衡方程 /
- 广义连续统场论
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 the mall corre sponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of gener alized Piola.s the orems were naturally derive dinall 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 incom-pleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.
- principles of work and energy /
- power and energy rate /
- generalized Piola.s the orem /
- equations of energy and energy rate

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参考文献(12)

[1]	Cosserat E F. Theorie des Corps Deformable[M]. Paris: Hermann, 1909.
[2]	Ericksen J L,Truesdell C. Exact theory of stress and strain in rods and shells [J]. Arch Rational Mech Anal,1958,2:298.
[3]	Guenther W, Zur statik and kinematik des cosseratschen kontinuums [J]. Abh Braunschw Wiss Ges,1958,10:195.
[4]	Kroener E. Mechanics of Generalized Continua[M]. Berlin, Heidelberg, New York: Springer-Verlag,1967.
[5]	Edelen, D G B. Nonlocal Variations and Local Invariance of Fields[M]. New York: Elsevier,1969.
[6]	Stojanovic R.Mechanics of Polar Continuum[M]. Udine: Int Center Mech Sci, 1969.
[7]	Eringen A C. Continuum Physics[M].Vol.IV, New York: Academic Press,1976.
[8]	Kunin I A.Elastic Media with Microstructure[M]. Berlin, Heidlberg, New York: Springer-Verlag,1982.
[9]	Nowacki W. Theory of Asymmetric Elasticity[M]. Oxford: Pergamon Press,1986.
[10]	Ciarletta M,Iesan D.Non-classical Elastic Solids[M].Pitman Research Notes 293,Boston, London, Melbourne: Longman Scientific & Technical,1993.
[11]	Eringen A C. Balance laws of micromorphic continua revisited [J].Int J Engng Sci, 1992,30(6):805-810.
[12]	Stojanovic R. On the principle of virtual work in the theory of oriented elastic media[J].Z Angew Math Mech,1973,53:79-82.