应用数学和力学

1998 Vol. 19, No. 10

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Non-Symmetrical Large Deformation of a Shallow Thin Conical Shell

Wang Xinzhi, Zhao Yonggang, Yeh Kaiyuan

1998, 19(10): 847-857.

Abstract(2056) PDF(617)

Abstract:
In this peper, non-symmetrical large deformation problem of a shallow conical shell is studied by two-parameter perturbation method. The third-order approximate analytical solution of the deformation of a shallow conical shell subjected to linear loads is abtained and the characteristic curves of loaddeflection on a perturbin point are portrayed. The similar questions of other kind of shell and plate can be disscussed by using this paper's method. As the examples, the large deflection of plate and shallow conical shells with different initial deflections is discussed.

The Wavelet Aanalysis Method of Stationary Random Processes

Luo Shaoming, Zhang Xiangwei

1998, 19(10): 859-864.

Abstract(2289) PDF(802)

Abstract:
The spectral analysis of stationary random processes is studied by using wavelet transform method.On the basis of wavelet transform, the conception of time-frequency pewer spectral density of random processes and time-frequency cross-spectral density of jointly stationary random processes are presented. The characters of the timefrequency power spectral density and its relationship with traditional power spectral density are also studied in details.

Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅰ)

Bissanga Gabriel, Jiang Furu

1998, 19(10): 865-877.

Abstract(2153) PDF(538)

Abstract:
In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions. Theseries solutions are constructed, the boundary layer effects are analysed and their asymptotics are proved.

The Discussion on Algebraic Properties of Polynomial Matrices

Liang Zhian, Ye Qingkai

1998, 19(10): 879-884.

Abstract(1944) PDF(727)

Abstract:
By using the results about polynomial matrix in the system and control theory,this paper gives some discussions about the algebraic properties of polynomial matrices. The obtained main results include that the ringof n×n polynomial matrices is a principal ideal and principal one-sided ideal ring.

Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems

Liao Shijun

1998, 19(10): 885-890.

Abstract(2848) PDF(1612)

Abstract:
In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Differem from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.

Variational Principles in Hydrodynamics of a Non-Newtonian Fluid

Shen Min

1998, 19(10): 891-896.

Abstract(3104) PDF(1367)

Abstract:
In this paper, the principle of maximum power losses for the incompressible visous fluid proposed by professor Chien Weizang in reference[1]is further extended to the hydrodynamic problem of the non-Newtonian fluid with constive law expressed as ε_ij=∂τ/∂σ'_ij. The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.

A Nonclassical Constitutive Model for Crystal Plasticity and Its Application

Peng Xianghe, Zeng Xiangguo, Fan Jinghong

1998, 19(10): 897-906.

Abstract(1910) PDF(614)

Abstract:
A nonclassical constitutive description for a slip system is formulated by using a simple mechanical model consisting of a spring and a plastic dashpot-like block. The corresponding constitutive model for a single crystal and the analysis for polycrystalline response is proposed based on the KVW's self-consistent theory. The constitutive model contains no yield criterion, so the corresponding numerical analysis is greatly simplified because it involves no additional process to search for the activation of slip systems and slip direction. A mixed averaging approach is proposed to obtain the response of polycrystalline material, which consists of the Gaussian integral mean for the ω which varies continuously within each face of the isosahedron and the arithmetic mean for the spatially uniformly distributed twenty sets of θ and φ determined by the normal of each face of the isosahedron. The main features 316 stainless steel subjected to typical biaxial nonproportional cyclic strain paths are well described. Calculation also shows that the developed model and the corresponding analytical approach are of good accuracy and efficiency.

Using Wavelet Transform to Study the Lipschitz Local Singular Exponent in Wall Turbulence

Jiang Nan, Wang Zhendong, Shu Wei

1998, 19(10): 907-913.

Abstract(2001) PDF(508)

Abstract:
In this paper, wavelet transform is introduced to study the Lipschitz local singular exponent for characterizing the local singularity behavior of fluctuating velocity in wall turbulence. It is found that the local singular exponent is negative when the ejections and sweeps of coherent structures occur in a turbulent boundary layer.

The Homology Classes of Large-Scale Periodic Orbits on Nonlinear Space

Gu Zhiming

1998, 19(10): 915-920.

Abstract(1923) PDF(646)

Abstract:
The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface are determined by the that of the phase space and the large-scale properties of the Hamiltonian. These properties are used for estimate of the rank of first homology group of energy level surfaces in the paper.

The Effective Moduli of Composite Reinforced by Spherical Coating Particles

Lu Zixing

1998, 19(10): 921-929.

Abstract(2094) PDF(572)

Abstract:
The effective moduli of composite reinforced by spherical coating particles are investigated by the four phase spheroidal model and the theory of equivalent media.The theoretical predicting formulae of bulk modulus and shear modulus have been derived for this kind of composite in this paper. These formulae can reduce to the results of three phase spheroidal model which had been obtained by others for composite reinforced by particles.

Flow of Robertson-Stiff Fluids Through an Eccentric Annulus

Wang Haige, Su Yinao

1998, 19(10): 931-940.

Abstract(2356) PDF(609)

Abstract:
Flow of drilling fluids, cement slurries and completion fluids through and eccentric annulus is an everyday event in petroleum drilling and completing enginering. While Robertson-Stiff(RS) rheological model on the basis of its proven success for describing various non-Newtonian fluids is more accurate than over other rheological models. In this paper, based on the RS fluid rheological equation and the geometrical relationship of eccentric annular clearance with other parameters, the axial-flow velocity distribution, the annular average velocity, the volumtrical flow rate and the frictional pressure drop are worked out as RS fluid flowing through an eccentric annulus where purely laminar flow is assumed. Results show that the main difference between concentric annular flow and eccentric annular flow lies in that the velocity profile is substantially altered in the annulus when the inner pipe is no longer concentric and the velocity in the reduced region of eccentric annulus is much smaller than that of the increased region. Moreover, the paper also compares the computed results by the use of RS model with that of Bingham model and Power-Law model.