Applied Mathematics and Mechanics (English Edition)

杨凌;刘曾荣

1998, 19(1): 1-8.

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OGY method is the most important method of controlling chaos. It stabilizes ahyperbolic periodic orbit by making small perturbations for a system parameter. Thispaper improves the method of choosing parameter, and gives a mathematics proof ofit.

IMPERFECTION SENSITIVITY ANALYSIS OF A RECTANGULAR COLUMN COMPRESSED INTO THE PLASTIC RANGE

程尧舜;方红;卢文达

1998, 19(1): 9-14.

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The effect of small geometrical imperfections on the buckling of a rectangularcolumn compressed into the plastic range is studied in this paper. In the analysis. theeffect of elastic unloading is taken into account. An asymptotically exact relation isobtained among the load. the amplitude of imperfections and the amplitude of thebifurcation mode. The results show that foe maximum supported load is very sensitiveto small imperfections, and that, however, there may not be a maxim am load if theimperfection amplitude is greater than some magnitude.

FINITE ELEMENT ANALYSIS OF TEMPERATURE FIELD WITH PHASE TRANSFORMATION AND NON-LINEAR SURFACE HEAT-TRANSFER COEFFICIENT DURING QUENCHING

程赫明;张曙红;王洪纲;李剑云

1998, 19(1): 15-20.

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The calculation of temperature field has a great influence upon the analysis of thethermal stresses and strains during quenching, and also upon the residual stresses andmicrostructure of the workpiece after quenching, too. In this paper. a 42CrMo steelcylinder was taken as an investigating example. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and thevolume fraction of phase constituents was calculated. The thermal physical propertieswere treated as the functions of temperature and the volume fraction of phaseconstitutents. Finally, the temperature field with phase transformation and non-linearsurface heat-transfer coefficients was calculated with finite element method. and thecorresponding functional of temperature was established.

PRESSURE-TRANSIENT ANALYSIS OF TWO-LAYERS FRACTAL RESERVOIRS

李凡华;刘慈群

1998, 19(1): 21-26.

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In this article based on the discussion on nonsteady flow of two-layers fractalreservoirs.the solution of generalized C-D equations in Laplace space, and then thesolution under different boundary conditions with considering or not consideringwellbore storage and skin effects are found out. At last. the nature of the solutionunder not considering wellbore storage and skin effects is taken under discussion.

THE EXISTENCE OF SOLUTION TO THE FINITE ELASTODYNAMICS WITH MIXED BOUNDARY CONDITIONS

郭兴明

1998, 19(1): 27-35.

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In this paper the existence of solution to finite elastodynamics constrainted bymixed boundary conditions is derived when the hyperpotential and its gradient (for Green’s strain) satisfy, adequate conditions.

THE DAMAGE PROCESS ZONE CHARACTERISTICS AT CRACK TIP IN CONCRETE

叶志明

1998, 19(1): 37-43.

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This paper presents a comprehensive derivation of fracture process zone sizewhich closely parallels similar work in fracture of metals and anisotropic solids, but istheied to conrete. Some nonlinear mechanics models of concrete materials will bediscussed by using uniaxial stress assumptions. For uniaxial stress assertion, energymodel and fracture model will be presented for nonlinear softening models. Finally, wemake a compariSon with those models.

The theory of relativistic analytical mechanics of the rotational systems

罗绍凯

1998, 19(1): 45-57.

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HAHN-BANACH THEOREM OF SET-VALUED MAP

孟志青

1998, 19(1): 59-66.

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We have proved generalized Hahn-Banach theorem by using the concept ofefficient for K-convex multifunction and K-sublinear multifunction in partially orderedlocally convex topological vector space.

CONTROL OF THE LORENZ CHAOS BY THE EXACT LINEARIZATION

陈立群;刘延柱

1998, 19(1): 67-73.

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Controlling chaos in the Lorenz systent with a controllable Rayleigh number isinvestigated by the state space exact linearization method. Based on proving the exactlinearizability,the nonlinear feedback is utilized to design the transformation changingthe original chaotic system into a linear controllable one so that the control is realized.Numerical examples of control are presented.

ON THE REGULARIZATION METHOD OF THE FIRST KIND OF FREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

尤云祥;缪国平

1998, 19(1): 75-83.

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The regularized intngrodifferential equation for the first kind of Fredholm integralequation with a complex kernel is derived by generalizing the Tikhonov regularizationmethod and the convergence of approximate regularized solutions is discussed. As anapplication of the method, an inverse problem in the two-demensional wave-makingproblem of a flat plate is solved numerically, and a practical approach of choosingoptimal regularization parameter is given.

GENERAL ANALYTIC SOLUTION FOR ELASTIC BENDING OF REISSNER PLATES

孙卫明;杨光松

1998, 19(1): 85-94.

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In this paper, by developing the complex Fourier series method to solve theboundary value problem of a system of partial differential equations with constantcoefficients, for the first time a general analytic solution satisfying an arbitraryboundary condition is presented for the elastic bending of thick Reissuer plates inengineering. The solution is simple and convenient to programming. Analysis andcomputation are performed for the uniformly loaded plates under two differentsupporting conditions (four simply. supported edges or three clamped and one freeedges), the results of which are fairly satisfactory in comparison Mwth those availablefor reference. And at the some time the analytic solution has been invesligated mainlyin three aspects: a) speed of convergence. b) reliability (rationality), c) fitting ofboundary conditions.

AN EXTENDED k-ε MODEL FOR NUMERICAL SIMULATION OF WIND FLOW AROUND BUILDINGS

陈水福;孙炳楠;唐锦春

1998, 19(1): 95-100.

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It is assumed in this paper that for a high Reynolds number nearly homogeneouswind flow, the Reynolds stresses are uniquely related to the mean velocity gradientsand the two independent turbulent scaling parameters k and E. By applying dimensionalanalysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulenceenclosure model so-called the axtended k-ε model has been developed. The coefficientsof the model expression were detemined by the wind tunnel experimental data ofhomogeneous shear turbulent flow. The model was compared with the standard k-εmodel in in composition and the prediction of the Reynold’s normal Stresses. Using thenew model the numerical simulation of wind flow around a square cross-section tallbuilding was performed. The results show that the extended k-ε model improves theprediction of wind velocities around the building the building and wind pressures on the buildingenvelope.

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