GENERALIZED REYNOLDS EQUATION AND VARIATIONAL INEQUALITY IN LUBRICATION THEORY

This paper has derived generalized Reynolds equationin lubrication theorg in terms of tensor analgsis and S-coordinate system, and has provided corresponding varia-tional inequality. The curved effect of flow of lubri-cant fluid is considered. and the influence of intrinsicproperties of surfaces of axis and axle sleeve on floware counted.     

VARIATIONAL PRINCIPLE AND GENERALIZED VARIATIONAL PRINCIPLE IN HYDRODYNAMICS OF A CLASS OF NON－NEWTONIAN FLUID

ＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＩＮＨＹＤＲＯＤＹＮＡＭＩＣＳＯＦＡＣＬＡＳＳＯＦＮＯＮ－ＮＥＷＴＯＮＩＡＮＦＬＵＩＤＳｈｅｎＭｉｎ（沈敏）,ＳｕｎＱｉ－ｒｅｎ（孙其仁）（Ｓ...     

A NEW VARIATIONAL INEQUALITY FORMULATION FOR SEEPAGE PROBLEMS WITH FREE SURFACES

IntroductionTherearetwoclassesofsolutionsforseepageproblemswithfreesurfaces ,i.e .,theadaptivemeshmethodsandthefixedmeshmethods.Theadaptivemeshmethodsinvolvetoolargeamountofcomputationforinhomogeneoussoilsandoftenleadtodivergentcalculations,andhence,arenowbeingsupercededbythefixedmeshmethods.Thefixedmeshmethodsfallintotwocategories,theintuitivemethodsandthevariationalinequalitymethods.Theintuitivemethods[1- 3]establishusuallytheiterativeproceduresbaseduponthefactthatthereisnodischargebetweenth…     

EXTENDED VARIATIONAL PRINCIPLE IN NONLINEAR THEORY OF ELASTICITY

From the extended energy functional, a unified variational principle and an extended variational principle are given and proved in this paper. It is about the non-conservative, abrupt and divided domains static (or kinetic) system and by using the undetermined energy functional, we can immediately deduce various variational principles.     

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.     

SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES

The purpose of this paper is to introduce the concept of generalized KKM mapping andto obtain some general version of the famous KKM theorem and Ky Fan’s minimaxinequality.As applications,we utilize the results presented in this paper to study the saddlepoint problem and the existence problem of solutions for a class of quasi-variationalinequalities.The results obtained in this paper extend and improve some recent results of[1-6].     

ON VARIOUS VARIATIONAL PRINCIPLES IN NONLINEAR THEORY OF ELASTICITY

In the present paper functionals for the various possiblemain variational principles in the nonlinear theory of e-lasticity are derived from the“full energy principle” andseveral of them are not found yet in the literatures avail-able. Through the derivation of this paper we suggest aconjecture on the nonexistence of the eleventh and thesixth classes for the variational principles in Table 6.1of H. C. Hu’s monograph [1].     

A SEMI－ANALYTICAL AND SEMI－NUMERICAL METHOD FOR SOLVING 2－D SOUND－STRUCTURE INTERACTION PROBLEMS

Based on the transfer matrix method and the virtual source simulation technique,this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound-structure interaction problems under a harmonic excitation. Within any integration segment,as long as its length is small enough, along the circumferential curvilinear coordinate, the nonhomogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper. For the exterior fluid domain, the multi-circular virtual source simulation technique is adopted. The source density distributed on each virtual circular curve may be ex-panded as the Fourier‘‘s series. Combining with the inverse fast Fourier transformation, a higher accuracy and efficiency method for solving 2-D exterior Helmholtz‘s problems is presented in this paper. In the aspect of solution to the coupling equations, the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper. According to the superposition principle and compatibility conditions at the interface between the elastic ring and fluid, the algebraic equation of system can be directly constructed by using the least square approximation. Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented. Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.     

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS

In this paper, the variational principles of hgdrodynamic problems for the incompressibleand compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.     

DUAL CHARACTERS OF INTERACTION BETWEEN PARTICLES AND FLUID

The unique characteristics of gas-solids two-phase flow and fluidization in terms of the flow structures and the apparent behavior of particles and fluid-particle interactions are closely linked to physical properties of the particles, operating conditions and bed configurations. Fluidized beds behave quite differently when solid properties, gas velocities or vessel geometries are vaded. An understanding of hydrodynamic changes and how they, in turn, influence the transfer and reaction characteristics of chemical and thermal operations by variations in gas-solid contact, residence time, solid circulation and mixing and gas distribution is very important for the proper design and scale-up of fluidized bed reactors. In this paper, rather than attempting a comprehensive survey, we concentrate on examining some important positive and negative impacts of particle sizes, bubbles, clusters and column walls on the physical and chemical aspects of chemical reactor performance from the engineering application point of view with the aim of forming an adequate concept for guiding the design of multiphase fluidized bed chemical reactors.     

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir including the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The non-linear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.     

Boundary mixed variational inequality in friction problem

IntroductionThestaticffichonProblemdiscussedinthespaperisakindofnonlinearunilateralboundalvaluePIDbleth.Itiswell-knownthatordinarylinearelliphcboundaryvalueProblemoftencormspondstOCertainlinearvariahonalequahon,theexistenceanduniquenessofitssolutioncanbeobtainedbyusingthein-MilgramtheoremorBabuskatheorem.HoweverthisunilateralboundalvallueProblemcormSPOndstoakindof"dxedvariahonalinequality['J.Sinceitcontainsthenonlinearindifferentialfunchonal,theusuallinearizationmethodsareuseless.Thereby…     

The variational inequality formulation for the deformation theory in plasticity and its non-iterative solution

In this paper,the deformation theory in plasticity is formulated in the variational inequality,which can relax the constraint conditions of the constitutive equations.The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis.Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods.And the solutions can be made in one step without any diversion of the load.     

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.     

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

Hybrid projection method for generalized mixed equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

接触问题的互补变分原理及非线性互补模型

给出了接触问题的互补虚功原理,互补能量原理及变分不等式等变分提法,并讨论了三类提法的关系。其此建立了有限维非线性互补模型并给出解的存在唯一性定理。文中还阐明了有,无摩擦接触问题之间以及二维和三维有摩擦接触问题之间的本质区别。     

UZAWA TYPE ALGORITHM BASED ON DUAL MIXED VARIATIONAL FORMULATION

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｔｈｅｓｏｌｕｔｉｏｎｏｆｔｈｅｅｌａｓｔｉｃｐｒｏｂｌｅｍ ,ｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔａｄｖａｎｔａｇｅｏｆｔｈｅｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｌｉｅｓｉｎｔｈｅｃｏｍｐｕｔｉｎｇｏｆｓｔｒｅｓｓａｎｄｄｉｓｐｌａｃｅｍｅｎｔａｎｄｓｏｏｎｓｉｍｕｌｔａｎｅｏｕｓｌｙ .Ｆｏｒｔｈｅｃｏｎｔａｃｔｐｒｏｂｌｅｍｉｎｅｌａｓｔｉｃｉｔｙ ,ａｎｅｗｄｕａｌｍｉｘｅｄｖａｒｉａｔｉｏｎａｌｆｏｒｍｕｌａｔｉｏｎａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎ…     

Asymptotic approximation method for elliptic variational inequality of first kind简

An asymptotic approximation method is proposed to solve a particular elliptic variational inequality of first kind associated with unilateral obstacle problems. In this method, the free boundary is first captured, and then the method of the fundamental solution (MFS) is used to find the solution of the Dirichlet problem for Laplace’s equation in the non-coincidence set. Numerical examples are given to show the efficiency of the method.