MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION （Ⅰ）——THE CONTINUOUS-TIME CASE

An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION ( Ⅱ )-THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

The mixed finite element (MFE) methods for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change were derived. A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established. The existence and convergence of MFE solution of the discrete current velocity, elevation of the bottom topography, thickness of fluid column, and mass rate of sediment is demonstrated.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

IntroductionThoughatransport_diffusion (orLagrange_Galerkin)method ,whichisalsocalledachar_acteristicsmethod ,isanoldone[1]andhasbeenextensivelyappliedtodealingwithPDEswithdiffusiontermand/orconvection ,ithadnotbeenmixedthefiniteelementmethodstotreatsuccessfullytheconvergenceofnumericalsolutionfortheNavier_Stokesequationsuntiltheearly198 0s[2 ].Intheearly 1 990s,Berm挷ｄｅｚｅｔａｌ.[3]appliedthismethodtodealingwiththeshallowwaterequationsonlyincludingthecurrentandthedepthofwaterandonlyderi…     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉｎｍｅｔｈｏｄｉｓａｍｕｌｔｉ＿ｌｅｖｅｌｓｃｈｅｍｅｔｏｆｉｎｄｔｈｅａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｆｏｒｔｈｅｄｉｓｓｉｐａｔｉｖｅＰＤＥ (ｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ) .Ｔｈｉｓｍｅｔｈｏｄｃｏｎｓｉｓｔｓｉｎｓｐｌｉｔｔｉｎｇｔｈｅｕｎｋｎｏｗｎｉｎｔｏｔｗｏ (ｏｒｍｏｒｅ)ｔｅｒｍｓ ,ｗｈｉｃｈｂｅｌｏｎｇｔｏｔｈｅｄｉｓｃｒｅｔｅｓｐａｃｅｓｗｉｔｈｄｉｆｆｅｒｅｎｔｍｅｓｈｓｉｚｅ .Ｔｈｅ…     

THE GENERALIZED GALERKIN’S EQUATION OF THE FINITE ELEMENT,THE BOUNDARY VARIATIONAL EQUATIONS AND THE BOUNDARY INTEGRAL EQUATIONS

Based on[1 ],we have further applied the variational princi-ple of the variable boundary to investigate the discretizationanalysis of the solid system and derived the generalized Ga-lerkin’s equations of the finite element.the boundary varia-tional equations and the boundary integral equations.These e-quations indicate that the unknown functions of the solid sys-tem must satisfy the conditions in the element S_a or on the boun-dariesГ_a.These equations are applied to establishing the discreti-zation equations in order to obtain the numerical solution ofthe unknown functions.At a time these equations can be usedas the basis for the simplified calculation in various corres-ponding cases.In this paper,the results of boundary integral equationsshow that the calculation of integration is not accurate alongthe surfaceГ_a of interior element S_a by J-integral suggestedby Rice[2].     

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables , was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.     

FINITE ELEMENT ANALYSIS FOR THE UNSTEADY NEARSHORE CIRCULATION DUE TO WAVE－CURRENT INTERACTION（II）──TWO－STEP EXPLICIT FINITE ELEMENT METHOD

ＦＩＮＩＴＥＥＬＥＭＥＮＴＡＮＡＬＹＳＩＳＦＯＲＴＨＥＵＮＳＴＥＡＤＹＮＥＡＲＳＨＯＲＥＣＩＲＣＵＬＡＴＩＯＮＤＵＥＴＯＷＡＶＥ－ＣＵＲＲＥＮＴＩＮＴＥＲＡＣＴＩＯＮ（ＩＩ）──ＴＷＯ－ＳＴＥＰＥＸＰＬＩＣＩＴＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＷ...     

THE MIXED STATE HAMILTONIAN DYNAMIC ELEMENT AND A SEMI-ANALYTICAL SOLUTION FOR THE ANALYSIS OF THICK LAMINATED COMPOSITE PLATES

Through introducing the Laplace transformation in the time direction,the mixed state Hamilton canonical equation and a semi-analytical solution arepresented for analyzing the dynamic response of laminated composite plates.Thismethod accounts for the separation of variables,the finite element discretization can beemployed in the plane of laminar,and the exact solution in the thickness direction isderived by the state space control method.To apply the transfer matrix method,therelational expression at the top and bottom surface is established.So the generalsolution in transformation space is deduced by the spot method.By the application ofinversion of Laplace transformation,the transient displacements and stresses can bederived.     

THE FINITE ELEMENT TECHNIQUE FOR PREDICTING THE NATURAL FREQUENCIES,MODE SHAPES AND DAMPING VALUES OF FILAMENTARY COMPOSITE PLATES

This article presents the numerical method for predicting the natural frequencies,mode shapes and damping values of filamentary composite plates.This method is based onfinite element technique,using damped element and allowing transverse shear deformation.For the example of this technique,the theoretical results comparing with experimentalvalues of carbon and glass fibre reinforced plastics plates(mid-plane symmetric)areprovided.The dynamic properties of these laminates are discussed.Finally,a simplegraphic technique to estimate the natural frequencies and damping values is suggested.     

A NEW SOLUTION TO STRUCTURAL FUZZY FINITE ELEMENT EQUILIBRIUM EQUATIONS (SFFEEE)

I.IntroductionInthefieldofthefuzzyfiniteelementmethod(FFEM),tostudynow,tosolvetheequilibriumequationsisofmomentoussignificance.EspeciallyfortheapplicationoftheFFEMtoengineeringproblems,thekeyworktodoistoexplorehigh-speedandhigh-effeciencysolutionstoequili…     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

InPartl,anonlineartheoryformultilayersand`"ichshellsundergoingsmallstrainsandmoderaterotatiol1sisgiven-inwhichtranst'ersesheardeformationisconsidered.Thesimplifiedtheoryfortheshellsundergoingmoderateormoderate/smallrotationsisalsoPresented.Theexpressionsi…     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)-NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed. Foundation items: the National Natural Science Foundation of China (59678003); Special Research Plan of the Education Department of Shaanxi Province (01JK178) Biographies: HUANG Yi (1936-) ZHANG Yin-ke (1964-)     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｌｌｏｗｓ,ａｓｈｅｌｌｏｆｗｒｉｎｋｌｅｄｍｅｒｉｄｉａｎｏｆｒｅｖｏｌｕｔｉｏｎ ,ｈａｓｂｅｉｎｇｉｎｃｒｅａｓｉｎｇｌｙｕｓｅｄｉｎｍｏｄｅｒｎｅｑｕｉｐｍｅｎｔａｓａｎｅｌａｓｔｉｃ＿ｓｅｎｓｉｔｉｖｅｅｌｅｍｅｎｔａｎｄａｆｌｅｘｉｂｌｅｊｏｉｎｔ.Ｔｈｅｆｏｒｍｅｒｉｓｕｓｕａｌｌｙｓｕｂｊｅｃｔｅｄｔｏｌａｒｇｅｄｉｓｐｌａｃｅｍｅｎｔｓａｔｉｔｓｅｎｄｓ,ａｎｄｔｈｅｌａｔｔｅｒｍａｙｐａｒｔｌｙｅｎｔｅｒｉｎｔｏｐｌａｓｔｉｃｓｔａｔｅ .Ｈｅｎｃｅ ,ｂ…     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)—NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

IntroductionSoilisthemostcommonlyusedconstructionmaterialincivilengineeringandhydraulicengineering .Thecharacteristicsofsoilhavebeeninvestigatingfornearlyonehundredyears.Butbecauseofitscomplexstructure,changeableenvironmentandbeingsensitivetotheoutsideconditions,thesoiloftenshowsvariedproperties[1,2 ].Themaindifficultytothedevelopmentofgeotechnicalmechanicsishowtosetupconstitutiveequationswhichcouldsatisfactorilyaccountforengineeringpropertiesofsoil[3].Manyconstitutivemodelshavebeenformedinth…     

DISSIPATION MECHANICS AND EXACT SOLUTIONS FOR NONLINEAR EQUATIONS OF DISSIPATIVE TYPE—PRINCIPLE AND APPLICATION OF DISSIPATION MECHANICS(Ⅰ)

This work is the continuation and the distillation of the discussion of Refs. [1-4].(A)From complementarity principle we build up dissipation mechanics in this paper.It is a dissipative theory of correspondence with the quantum mechanics.From this theorywe can unitedly handle problems of macroscopic non-equilibrium thermodynamics andviscous hydrodynamics. and handle each dissipative and irreversible problems in quantummechanics.We prove the basic equations of dissipation mechanics to eigenvalues equationsof correspondence with the Schr(?)dinger equation or Dirac equation in this paper.(B)We unitedly merge the basic nonlinear equations of dissipative type, especially theNavier-Stokes equation as a basic equation for macroscopic non-equilibrium ther-modynamics and viscous hydrodynamics into integrability condition of basic equation ofdissipation mechanics. And we can obtain their exact solutions by the inverse scatteringmethod in this paper.     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID (Ⅰ)

1　IntroductionandSignsForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1- 3].Andthereislessdiscussiononitsillposedness[4 ,5 ].Inthedifferentialfunctionclasses,BaouondiandGoulaouicprovedthattheCauchyproblemonthecompactmanifoldofEulerequationshasuniquesolutionwellexpectaconstant[4 ].InthebooktitledSolutionsAnalytiquesdeQuelquesEquationsauxDerivesPartiellesenMecaniquedesFluides,thest…     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R⁴, and explain that the problem has more than one solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)