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

DAI Tian-min

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(11): 1111-1118

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.

Citation:

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.

Citation:

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.

PDF( 2362 KB)

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

Received Date: 2000-05-28
Rev Recd Date: 2000-10-20
Publish Date: 2001-11-15

Abstract

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

FullText(HTML)

References(12)

References

[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.