INVARIANT MANIFOLDS AND THEIR STABILITY IN A THREE－DIMENSIONAL MEASURE－PRESERVING MAPPING SYSTEMS

ＩＮＶＡＲＩＡＮＴＭＡＮＩＦＯＬＤＳＡＮＤＴＨＥＩＲＳＴＡＢＩＬＩＴＹＩＮＡＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＭＥＡＳＵＲＥ－ＰＲＥＳＥＲＶＩＮＧＭＡＰＰＩＮＧＳＹＳＴＥＭＳＬｉｕＪｉｅ（刘杰）（ＲｅｃｅｉｖｅｄＤｅｃ．１．１９９４;Ｃｏｍｍｕｎｉｃ...     

FOURIER NONLINEAR GALERKIN APPROXIMATION FOR THE TWO DIMENSIONAL NAVIER－STOKES EQUATIONS

ＦＯＵＲＩＥＲＮＯＮＬＩＮＥＡＲＧＡＬＥＲＫＩＮＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＴＨＥＴＷＯＤＩＭＥＮＳＩＯＮＡＬＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＨｏｕＹａｎｒｅｎ（侯延仁）（ＲｅｃｅｉｖｅｄＪｕｎｅ１．１９９５．Ｃｏｍｍｕｎｉｃａｔｅｄ...     

FINITE ELEMENTAN ALYSIS FOR THE UNSTEADY NEARSHORECIR CULATION DUE TO WAVE－CURRENT INTER－ACTION（I）──NUMERICAL MODEL

ＦＩＮＩＴＥＥＬＥＭＥＮＴＡＮＡＬＹＳＩＳＦＯＲＴＨＥＵＮＳＴＥＡＤＹＮＥＡＲＳＨＯＲＥＣＩＲＣＵＬＡＴＩＯＮＤＵＥＴＯＷＡＶＥ－ＣＵＲＲＥＮＴＩＮＴＥＲ－ＡＣＴＩＯＮ（Ｉ）——ＮＵＭＥＲＩＣＡＬＭＯＤＥＬＷｕＷｅｉ－ｘｉｏｎｇ（吴伟雄）（Ｔｏｎｇｊ...     

THE SLIDING SURFACE ALGORITHMSINTHREE－DIMENSIONAL DYNAMIC FINITE ELEMENT CODE

ＴＨＥＳＬＩＤＩＮＧＳＵＲＦＡＣＥＡＬＧＯＲＩＴＨＭＳＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＤＹＮＡＭＩＣＦＩＮＩＴＥＥＬＥＭＥＮＴＣＯＤＥＳｏｎｇＳｈｕｎ－ｃｈｅｎｇ（宋顺成）（ＩｎｎｅｒＭｏｎｇｏｌｕａＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｏｆＭｅｔ...     

MIKUSINSKI＇S OPERATORS SOLUTION OF THREE－ORDER LINEAR DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

ＭＩＫＵＳＩＮＳＫＩ＇ＳＯＰＥＲＡＴＯＲＳＳＯＬＵＴＩＯＮＯＦＴＨＲＥＥ－ＯＲＤＥＲＬＩＮＥＡＲＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＣＯＥＦＦＩＣＩＥＮＴＳＺｈｏｕＺｈｉ－ｈｕ（周之虎）（ＡｎｈｕｉＡｒｃｈｉｔｅｃｔｕｒａｌＩ...     

A modified method of averaging for solving a class of nonlinear equations

ＡＭＯＤＩＦＩＥＤＭＥＴＨＯＤＯＦＡＶＥＲＡＧＩＮＧＦＯＲＳＯＬＶＩＮＧＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＺｈａｎｇＢａｏ－ｓｈａｎ（张宝善）（ＤｅｐａｒｉｍｅｎｔｏｆＭａｉｈ．,ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ,Ｘｕｚｈ...     

Variable structure control of indefinite-dimensional systems

ＶＡＲＩＡＢＬＥＳＴＲＵＣＴＵＲＥＣＯＮＴＲＯＬＯＦＩＮＤＥＦＩＮＩＴＥ－ＤＩＭＥＮＳＩＯＮＡＬＳＹＳＴＥＭＳＬｉＷｅｎ－ｌｉｎ（李文林）ＢｉａｎＷｅｎ－ｍｉｎｇ（边文明）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｈｅｍａｔｉｃｓ,ＨｅｎａｎＮｏｒｍａｌＵｎｉ...     

INITIAL BOUNDARY VALUE PROBLEMS FOR A CLASS OF NONLINEAR INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣｕｉＳｈａｎｇ－ｂｉｎ（崔尚斌）（Ｄｅｐｔ．ｏｆＭａｔｈ．,ＬａｎｚｈｏｕＵｎｉ...     

STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

ＳＴＵＤＩＥＳ　ＯＦ　ＭＥＬＮＩＫＯＶ　ＭＥＴＨＯＤ　ＡＮＤ　ＴＲＡＮＳＶＥＲＳＡＬ　ＨＯＭＯＣＬＩＮＩＣ　ＯＲＢＩＴＳ　ＩＮ　ＴＨＥ　ＣＩＲＣＵＬＡＲ　ＰＬＡＮＡＲ　ＲＥＳＴＲＩＣＴＥＤ　ＴＨＲＥＥ－ＢＯＤＹ　ＰＲＯＢＬＥＭＺｈｕＲｕｚｅｎｇ（朱如...     

THE BOUNDED EXTERMINATION AND STABILITY OF MUTUAL INTERFERENCE SYSTEM OF FOUR－DIMENSIONAL SPECIES

ＴＨＥＢＯＵＮＤＥＤＥＸＴＥＲＭＩＮＡＴＩＯＮＡＮＤＳＴＡＢＩＬＩＴＹＯＦＭＵＴＵＡＬＩＮＴＥＲＦＥＲＥＮＣＥＳＹＳＴＥＭＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＳＰＥＣＩＥＳＨｏｕＧａｎ－ｓｈｅｎｇ（侯赣生）（Ｄｅｐｌ．ｏｆＰｈｙｓｉｃｓ,Ｊｉａｎｇｘ...     

THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

IntroductionNumerical manifold method is a new numerical method established on the basis of finitecover of manifold[1,2].By using continuous and non-continuous finite cover system,thenumerical manifold method includes the continuous and non-continuous as …     

复合材料层合板的三维研究

本文提出了固支复合材料各向异性层合圆板受均布横向载荷作用下的满足三维弹性力学基本微分方程和边界条件的解析解答。文中采用一种发展的摄动方法进行求解，板中的每个应力和位移都展开为无量纲厚度参数ε的摄动级数，并采用二维板理论解答作为其相应三维摄动解答的一个基本解的形式，通过摄动方法逐级求解而获得完整的三维解答。文中以解析形式和数值形式给出了高精确度的三维应力和位移结果，结果表明，本文求解三维问题的解析方法是合理有效的。     

Mechanism of three-dimensional boundary-layer receptivity

Boundary-layer receptivity is always a hot issue in laminar-turbulent transition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept flat-plate boundary layer is a typical three-dimensional flow. Study of its receptivity is important both in theory and applications. In this paper, a freestream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space discretization. On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer(the infinite back-swept flat-plate boundary layer) by free-stream turbulence is studied numerically. If so, effects of the level and the direction of free-stream turbulence on the three-dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.     

膜-基复合材料界面剪应力的三维半解析计算

 采用影响系数法对膜-基复合材料的界面剪应力三维半解析进行 了分析研究.利用三维有限元方法对薄膜的影响系数进行了计算. 将 基体作为半无限大体，利用其平面边界作用单位力时的位移场解析 解，得到基体的影响系数. 结果表明，对膜-基复合材料界面剪应力 进行三维半解析计算，克服了完全用三维有限元对其进行计算的限 制，为该类问题的分析提供了新的途径.     

A practical implementation of turbulence models for the computation of three-dimensional separated flows

An upwind MUSCL-type implicit scheme for the three-dimensional Navier-Stokes equations is presented and details on the implementation for three-dimensional flows of a ‘diagonal’ upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson-King non-equilibrium model. Good predictions of separated two- and three-dimensional flows are demonstrated.     

Nonlinear dynamical stability analysis of the circular three-dimensional frame

The three-dimensional frame is simplified into flat plate by the method of quasiplate. The nonlinear relationships between the surface strain and the midst plane displacement are established. According to the thin plate nonlinear dynamical theory, the nonlinear dynamical equations of three-dimensional frame in the orthogonal coordinates system are obtained. Then the equations are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundary conditions of fixed edges, then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimensional frame are studied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artificial method.     

Nonlinear dynamics of three-dimensional belt drives using the finite-element method

In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.     

An algorithm of finite element grid generation for three-dimensional complex connected domain

An automated quasi three-dimensional finite element grid generation method is presented for particular three-dimensional complex connected domain, across which some are simply connected two-dimensional.regions and some are multiply connected two-dimensional regions. A subdivision algorithm based on the variational principle has been developed to ascertain the smoothness and orthogonality of the generated grid in any cross sections. Smooth transition between the simply and multiply connected regions is maintained. For illustration, the method is applied to generate a finite element three-dimensional grid for human above knee stump.     

Construction of Equivalent Axisymmetric Bodies for Calculating Heat Transfer and Viscous Stress on Three-Dimensional Bodies at Incidence

An effective approximate technique for calculating heat transfer, viscous stress, and species components on the windward side of three-dimensional bodies at incidence in hypersonic flow is developed. Using the similarity method, the solution of the three-dimensional problem is reduced to the solution of an axisymmetric problem. For determining the heat flux on a real body, modified two-dimensional equations are solved for equivalent axisymmetric bodies, specially constructed for meridional planes of the original body. For an arbitrary three-dimensional geometry and angle of attack formulas are derived and a conversion program is developed. These make it possible to determine all the parameters of the equivalent body corresponding to a given meridional plane of the original body; then these parameters are used as input data for calculating the viscous flow past the body. The solutions of the two-dimensional equations for the equivalent bodies are in good agreement with more exact solutions of the three-dimensional equations.     

Three-dimensional disturbances of planar viscometric flow

This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.