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1.
《应用数学和力学(英文版)》2005,(3)
IntroductionRecently ,wehaverestudiedtheconventionalconservationlawofenergy ,whichhaswidelybeenusedandisusinginliteraturesofclassicalcontinuummechanicsathomeandabroad ,andpointedoutthatitistheoreticallyincompleteeveninthetraditionalframework .Thepresentsituationoftheconservationlawsofenergyforpolarcontinuaisthesameasthatforclassicalcontinuummechanics.Inordertochangethestatusquo ,itseemstobequitenecessarythatnewprinciplesoftotalworkandenergyshouldbeproposedtotaketheplaceoftheexistingconservatio… 相似文献
2.
戴天民 《应用数学和力学(英文版)》2005,26(6):709-715
The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified. 相似文献
3.
戴天民 《应用数学和力学(英文版)》2006,27(2):167-174
Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether's theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases. 相似文献
4.
戴天民 《应用数学和力学(英文版)》2005,(6)
The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified. 相似文献
5.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1119-1125
Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for
micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and
body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity
produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy
are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can
be clearly seen that the new results are believed to be rather general and complete.
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: Dupai Tian-min (1931≈) 相似文献
6.
戴天民 《应用数学和力学(英文版)》2003,24(11)
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization . 相似文献
7.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(11):1253-1258
The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua
based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations
of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete
principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived
from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different
from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics
may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results
of micropolar thermopiezoelectricity are directly given.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931-) 相似文献
8.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(12):1369-1374
The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass
and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the
line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented.
Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived
in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories
is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum
and energy may be obtained by the usual localization.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931≈) 相似文献
9.
戴安民 《应用数学和力学(英文版)》2003,24(12)
IntroductionThisworkisadirectcontinuationandasupplementofRefs .[1~8] .InRefs.[1~8]thecoupledbalancelawsandequationsofmomentum ,angularmomentumandenergyaswellasthenewHamiltonprinciple,principleofvirtualpowerandNoethertheoremhavebeenpresented .However,thecoupledconservationlawsofmassandinertiahavenotbeenreestablishedyet.Thepurposeofthispaperistoreestablishtheconservationlawsandequationsofmassandinertiaandtocombinethemwiththecoupledbalancelawsandequationsofmomentum ,angularmomentum ,energyand… 相似文献
10.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(12):1375-1380
The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental
rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse
are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations
of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as
a special case.
Contributed by Dai Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education
Committee (990111001)
Biography: Dai Tian-min (1931≈) 相似文献
11.
戴天民 《应用数学和力学(英文版)》2003,24(10)
IntroductionThispaperisadirectcontinuationofthepreviouspapers [1 ,2 ] .ThefieldequationsoflinearcouplestresselasticityweredevelopedbyMindlinandTiersten[3].AgeneralcouplestresstheorywaspresentedbyToupin[4 ].Eringen[5 ,6 ]haspointedoutthatthecouplestresstheoriesofelasticmediafluidsmaybededucedfromthemicropolarelasticityandfluidmechanicswhenthemicrorotationsiandψiareconstrainedbytherotationvectorωiofclassicalelasticityandvorticityvectorrioffluidmechanics,respectively .AnexpressionoftheJ_int… 相似文献
12.
戴天民 《应用数学和力学(英文版)》2003,24(10)
IntroductionThemicropolarcontinuumtheoryisatypicalandwideapplicatedtheoryinthegeneralizedcontinuumtheoriesandwasgenerallyrecognizedlongago .Manymonographsandalargenumberofscientificpapersconcerningthisfieldarepublished .Wehaverestudiedtheexistingpolarcontinuumtheoriesandfoundthatsomebasicbalancelawsandprinciplesofthemareincompleteandthereexistsometheoreticaldefectswhichshouldberemoved .Forcontrastandclaritywenowlistthetraditionalbasicbalancelawsandequationsformicropolarcontinuumtheoryasfollows… 相似文献
13.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(11):1245-1252
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the
translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of
momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are
derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The
incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface
conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931 ~) 相似文献
14.
戴安民 《应用数学和力学(英文版)》2003,24(12)
IntroductionTherelationsbetweenvariousstresstensors,theequationofmomentumandtheboundaryconditionsofincrementalratetypeforclassicalcontinuummechanicshavebeensystematicallyderivedbyKuanginRef.[1 ] .InRef.[2 ]wehavederivedtherelationsbetweenvariouscouplestresstensorsandtheirratesandpresentedtheequationsofmotionandtheboundaryconditionsofincrementalratetypeofCauchyform ,PiolaformandKirchhoffformforpolarcontinua .InRef.[3 ]wehavepresentednewprinciplesofpowerandenergyrateofincrementalratetypeformi… 相似文献
15.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)--POLAR THERMOMECHANICAL CONTINUA 总被引:3,自引:3,他引:0
戴天民 《应用数学和力学(英文版)》2003,24(11):1253-1258
The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity . The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle . The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case , respectively . Finally , the results of micropolar thermopiezoelectricity are directly given . 相似文献
16.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1134-1140
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. 相似文献
17.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(10):1126-1133
The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local
and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic
continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled
conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic
continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation
laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum
theories are clarified. Finally, some special cases are conveniently derived.
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931≈) 相似文献
18.
戴天民 《应用数学和力学(英文版)》2003,24(10)
IntroductionThispaperisadirectcontinuationofRef.[1 ] .InitthecoupledconservationlawofenergypresentedinRef.[2 ]wasextendedandtherathercompletesystemsofbasicbalancelawsandequationsformicropolarcontinuumtheoryhavebeenconstitutedbycombiningtherenewedresultsandthetraditionalconservationlawsofmassandmicroinertiaandtheentropyinequality .Thepurposeofthispaperistorestablishthesystemsofbasicbalancelawsandequationsformicromorphiccontinuumtheoryandcouplestresstheoryviadirecttransitionsandreductionsfromth… 相似文献
19.
云天铨 《应用数学和力学(英文版)》2000,(8)
IntroductionThepriceofgoodsvaryingarounditsvalueisconsideredtobeabasicruleofgoods,i.e .,thelawofvalueofgoods.Astockisakindofgoods ,itnatuallyobeysthelawofvalueofgoods.Sothatthepriceofstockvariesarounditsvalue.Todeterminethevalueofstockisveryimportantforth… 相似文献
20.
云天铨 《应用数学和力学(英文版)》2000,21(8):861-868
By basic equations, two basic theories are presented: 1. Theory of stock’s value v*(t)=v*(0) exp (ar2*t);2. Theory of conservation of stock’s energy. Let stock’s energy Φbe defined as a quadratic function of stock’s price v and its derivative v, Φ=Av2+Bv+Cv2+Dv, under the constraint of basic equation, the problem was reduced to a problem of constrained optimization along optimal path. Using Lagrange multiplier and Euler equation of variation method, it can be proved that Φkeeps conservation for any v,v. The application of these equations and theories on judgement and analysis of tendency of stock market are given, and the judgement is checked to be correct by the recorded tendency of Shenzhen and Shanghai stock markets. 相似文献