应用数学和力学

1998 Vol. 19, No. 1

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Yang Ling, Liu Zengrong

1998, 19(1): 1-7.

Abstract(2371) PDF(687)

Abstract:
OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.

Imperfection Sensitivity Analysis of a Rectangular Column Compressed into the Plastic Range

Cheng Yaoshun, Fang Hong, Lu Wenda

1998, 19(1): 8-14.

Abstract(2193) PDF(602)

Abstract:
The effect of small geometrical imperfections on the buckling of a rectangular column compressed into the plastic range is studied. In the analysis, the effect of ealstic unloading is taken into account. An asymptotically exact relation is abtained among the load, the amplitude of imperfections and the amplitude of bifurcation mode. The results show that the maximum supported load is very sensitive to small imperfections, and that, however, there may not be maximum load if the imperfection amplitude is greater than some magnitude.

Finite Element Analysis of Temperature Field with Phase Transformation and Non-Linear Surface Heat-Trasfer Coefficeint during Quenching

Cheng Heming, Zhang Shuhong, Wang Honggang, Li Jianyun

1998, 19(1): 15-20.

Abstract(2473) PDF(599)

Abstract:
The calculation of temperature field has a great influence upon the analysis of the thermal stresses and stains during quenching, and also upon the residual stresses and microstructure of the workpiece after quenching, too. In this paper, a 42CrMo steel cylinder was taken as an investigating example. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mat hematical transformation, and the volume fraction of phase constit uents was calculated. The thermal physical properties were treated as the functions of temperature and the volume fraction of phase constit utents. Finally, the temperature field with phase transformation and non-linear surface heattransfer coefficeints was calculated with finite element method, and the corresponding functional of temperature was established.

Pressure-Transient Analysis of Two-Lagered Fractal Reservoirs

Li Fanhua, Liu Ciqun

1998, 19(1): 21-26.

Abstract(2032) PDF(608)

Abstract:
In this article we discuss nonsteady flow of two-lagered fractal reservoirs, and get the solution of generalized C-D equation in Laplace space and then get the solution under different boundary conditions with considering or not considering wellbore storage and skin effects, and at last we analyse the nature of the solution under not considering wellbore storage and skin effects.

The Existence of Solution to the Finite Elastodynamics With Mixed Boundary Conditions

Guo Xingming

1998, 19(1): 27-34.

Abstract(2110) PDF(675)

Abstract:
In this paper the existence of solution to finite elastodynamics constrainted by mixed boundary conditions is derived when the hyperpotential and its gradient(for Green' strain) satisfy adequate conditions.

The Damage Process Zone Characteristics at Crack Tip in Concrete

Ye Zhiming

1998, 19(1): 35-41.

Abstract(2165) PDF(500)

Abstract:
This paper presents a comprehensive derivation of fracture process zone size which closely parallels similar work in fracture of metals and anisotropic solids but is adapted to conrete. Some nonlinear mechanics models of concrete materials will be discussed by using uniaxial stress assumptions. For uniaxial stress assumption, energy model and fracture model will be presented for nonlinear softening models. Finally, a comparison of those models is provided.

The Theory of Relativistic Analytical Mechanics of the Rotational Systems

Luo Shaokai

1998, 19(1): 42-53.

Abstract(2802) PDF(926)

Abstract:
The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems T_r^*= and the generalized acceleration energy function S_r^*= are constructed and further, the Hamilton 27 principle and three kinds of Dc Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; and the relativistic Noether conservation law of the rotational systems are given too

Hahn-Banach Theorem of Set-Valued Map

Meng Zhiqing

1998, 19(1): 54-61.

Abstract(1985) PDF(782)

Abstract:
We have proved generalized Hahn-Banach theorem by using the concept of efficinet for K-convex multifunction and K-sublinear multifunction in partially ordered locally convex topological vector space.

Control of the Lorenz Chaos by the Exact Linearization

Chen Liqun, Lin Yanzhu

1998, 19(1): 62-69.

Abstract(1847) PDF(608)

Abstract:
Controlling chaos in the Lorenz system with a controllable Rayleigh number is investigated by the sate space exact linearization method. Based on proving the exact linearizability, the nonlinear feedback is utilized to design the transformation changing the original chaotic system into a linear controllable one so that the control is realized. A numerical example of control is prsented.

On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application

You Yunxiang, Miao Guoping

1998, 19(1): 70-78.

Abstract(2483) PDF(618)

Abstract:
The regularized integrodifferential equation for the first kind Fredholm integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate rgeularized solutions is discussed. As an application of the method, an inverse problem in the two-demensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.

General Analytic Solution for Elastic Bending of Reissner Plates

Sun Weiming, Yang Guangsong

1998, 19(1): 79-87.

Abstract(2466) PDF(706)

Abstract:
In this paper, by developing the complex Fourier series method to solve the boundary value problem of a system of partial differential equations with constant coefficients, for the first time a general analytic solution satisfying an arbitrary boundary condition is presented for the elastic bending of thick Reissner plates in engineering. The solution is simple and convenient to programming. Analysis and computation are performed for the uniformly loaded plates under two different supporting conditions(four simply supported edges or three clamped and one free edges), the results of which are fairly satisfactory in comparison wit h those available for reference. And at the same time the analytic solution has been investigated mainly in three aspects:a) speed of convergence; b) reliability(rationality); c)fitting of boundary conditions.

An Extended k-ε Model for Numerical Simulation of Wind Flow Around Buildings

Chen Shuifu, Sun Bingnan, Tang Jinchun

1998, 19(1): 88-94.

Abstract(2226) PDF(644)

Abstract:
It is assumed in this paper that for a high Reynolds number nearly homogeneous wind flow, the Reynolds stresses are uniquely related to the mean velocity gradients and the two independent turbulent scaling parameters k and ε. By applying dimensional analysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulence enclosure model so called the extended k-ε model has been developed. The coefficients of the model expression were determined by the wind tunnel experimental data of homogeneous shear turbulent flow. The model was compared with the standard k-ε model in its composition and the prediction of the Reynolds normal stresses. Using the new model the numerical simulation of wind flow around a square cross-section tall building, was perfoumed. The results show that the extended k-ε model improves the prediction of wind velocities around the building and wind pressures on the building envelope.