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1.
RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅱ)-THERMOPIEZOELECTRICITY AND MAGNETOTHERMOELASTICITY 总被引:1,自引:1,他引:1
The theories of thermopiezoelectricity and magnetoelasticity for micropolar continua have been systematically developed by
W. Nowacki. In this paper, the theories are restudied. The reason why they were restricted to linear cases is analyzed. The
more general conservation principle of energy, energy balance equation and Hamilton principle of thermopiezoelectricity and
magnetoelasticity for micropolar continua are established. The corresponding complete equations of motion and boundary conditions
as well as balance equations of energy rate for local and nonlocal micropolar thermopiezoelectricity and magnetothermoelasticity
are naturally derived. By means of two new functionals and total variation the boundary conditions of displacement, microrotation,
electric potential and temperature are also given.
Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235)
and the DFG (51520001); the Research Foundation of the Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931-) 相似文献
2.
戴天民 《应用数学和力学(英文版)》2002,23(3):249-258
IntroductionTheoryofmicropoloarthermoelasticitypresentedbyW .Nowackiisrestudiedinourpaper[1].Thispaperisadirectcontinuationofreference [1 ] .Theproblemsoccurringinthetheoriesofthermopiezoelectricityandmagnetothermoelasticityformicropolarcontinuaaresimilart… 相似文献
3.
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
4.
戴天民 《应用数学和力学(英文版)》2003,24(10)
IntroductionThemicropolarcontinuumtheoryisatypicalandwideapplicatedtheoryinthegeneralizedcontinuumtheoriesandwasgenerallyrecognizedlongago .Manymonographsandalargenumberofscientificpapersconcerningthisfieldarepublished .Wehaverestudiedtheexistingpolarcontinuumtheoriesandfoundthatsomebasicbalancelawsandprinciplesofthemareincompleteandthereexistsometheoreticaldefectswhichshouldberemoved .Forcontrastandclaritywenowlistthetraditionalbasicbalancelawsandequationsformicropolarcontinuumtheoryasfollows… 相似文献
5.
RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE 总被引:1,自引:0,他引:1
戴天民 《应用数学和力学(英文版)》2002,23(8):867-874
IntroductionUptonowtherehasbeenverymuchwrittenworkonthesubjectsofcontinuumtheoriesinwhichthedeformationisdescribednotonlybytheusualvectordisplacementfield ,butbyothervectorortensorfieldsaswell.Inafamousmonograph ,E .CosseratandF .Cosserat[1]gaveasystematic… 相似文献
6.
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
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.
WANG Lin-xiang Roderick V. N. Melnik 《应用数学和力学(英文版)》2006,27(9):1185-1196
An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case. 相似文献
9.
吴沈荣 《应用数学和力学(英文版)》1983,(2)
In order to formulate the equations for the study here,the Fourier expansions upon the system of orthonormal polynomials are used.It may be considerably convenient to obtain the expressions of dis-placements as well as stresses directly from the solutions.Based on the principle of virtual work the equilibrium equations of va-rious orders are formulated.In particular,the system of third-order is given in detail,thus providing the reference for accur-acy analysis of lower-order equations.A theorem about the differentiation of Legendre series term by term is proved as the basis of mathematical analysis.Therefore the functions used are specified and the analysis rendered is no longer a formal one.The analysis will show that the Kirchhoff-Love’s theory is merely of the first-order and the theory which includes the transverse de-formation but keeps the normal straight is essentially of the first order,too. 相似文献
10.
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
11.
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
12.
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
13.
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
14.
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
15.
Dai Tian-min 《应用数学和力学(英文版)》2005,26(3):313-318
Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified.
For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated.
Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress
and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained,
respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and
simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing
conservation laws of energy are expounded.
Contributed by DAI Tian-min, Original Member of Editorial Committe, AMM
Project supported by the National Natural Science Foundation of China (Nos. 10472041, 10072024) and the Science Research Foundation
of Liaoning Province (No. 990111001) 相似文献
16.
《应用数学和力学(英文版)》2005,(3)
IntroductionRecently ,wehaverestudiedtheconventionalconservationlawofenergy ,whichhaswidelybeenusedandisusinginliteraturesofclassicalcontinuummechanicsathomeandabroad ,andpointedoutthatitistheoreticallyincompleteeveninthetraditionalframework .Thepresentsituationoftheconservationlawsofenergyforpolarcontinuaisthesameasthatforclassicalcontinuummechanics.Inordertochangethestatusquo ,itseemstobequitenecessarythatnewprinciplesoftotalworkandenergyshouldbeproposedtotaketheplaceoftheexistingconservatio… 相似文献
17.
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
18.
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
19.
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
20.
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