应用数学和力学

1997 Vol. 18, No. 3

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Investigation on the Effective Conductivities of Carbon/Carhon Fiber Composites with Inhomogeneous Interphase

He Linghui, Cheng Zhenqiang, Liu Renhuai

1997, 18(3): 193-201.

Abstract(2101) PDF(704)

Abstract:
Thermal conductivites of carbon/carbon fiber composites with in homogeneous interphase are studied in thtis paper. the inhomogeneous interphase is modeled approximately as a multilayered structure consisting of many thin layers haying homogeneous properties, and close-formed solution of the effective conductivities of the composites is obtained by using the Mori-Tanaka mean-fieid concept.

An Approximate Method of Response Analysis of Vibrations for Cracked Beams

Chen Mengcheng, Tang Renji

1997, 18(3): 203-209.

Abstract(2259) PDF(613)

Abstract:
In this paper a method based on a line-spring model was proposed to analyze approximately vibration responses of cracked beams. The method in conjumction with the Euler-Bernoulli beam theory. modal analysis and fracture mechanics principle was applied to derive a characteristic equation for the cracked beam vibration. As application examples. natural frequency responses for a cracked hinge-hinged beam and a cracked cantilever beam were examined It was shown that the present solutions obtained are quite in agreement with the solutions or experimental results in available references.

Boundary Element Method for Solving Dynamical Response of Viscoelastic Thin Plate (Ⅰ)

Ding Rui, Zhu Zhengyou, Cheng Changjun

1997, 18(3): 211-216.

Abstract(2265) PDF(555)

Abstract:
In this paper, a boundary element method for siolving dynamical response of viscoelastic thin plate is given In Laplace domain, we propose two methods to approximate the fundamental solution and develop the corresponding boundary element method Then using the improved Bellman's numerical inversion of the Laplace transform, the solution of the original problem is obtained. The numerical results show that this method has higher accuracy and faster convergence.

The Hamiltonian System and Completeness of Symglectic Orthogonal System

Zhang Hongqing, Alatancang, Zhong Wanxie

1997, 18(3): 217-221.

Abstract(2338) PDF(711)

Abstract:
In this paper,a new Banach space ZH is defined and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results ZH space can be continuously imbedded to L₂[0,1] × L₂[0, 1] but ZH≠L₂[0, 1] × L₂[0, 1].

The Existence of Solutions in Nonlinear Elastodynamics

Guo Xingming

1997, 18(3): 223-229.

Abstract(2315) PDF(486)

Abstract:
Under the small deformation assumption this paper shows the existence of solution for the system of elastic dynamics with the general nonlinear constitutive laws.and the existence of classical solution can be found under weaker conditions.

A Two-Parameter Model for Three Types of Unclepore Filtration of Leukocytes

Shao Jinyu, Yan Zongyi, Zhuang Fengyuan, Sun Ruijuan

1997, 18(3): 231-238.

Abstract(1852) PDF(539)

Abstract:
Micropore filtration of leukocytes is one of the main methods for evaluating leukocyte's deformability. Here a biofluid mechanical model was proposed for three cases: (i) firltration under gravity; (ii)constant pressure filtration; (iii) constant flow rate filtration. In previous models, constant blood cell resistance was assumed. In this paper, when evaluating the filter resistance to leukocytes, not only the effect of the change in the driving pressure but also the difference in the deformability of individual leukocytes are taken into consideration. Moreover, based on Moessmer's experimental results, a probability distribution function.for the transit time of polymorphonuclear cells (PMNs) through the filter is assumed. Finally, numerical curves are obtained for the above three types of filtration and the comparison between the theoretical andexperimental results of PMNs for case (i) turns out to be satisfactory The two parameters in the model. A and B represent leukocytes deformability under low and high pressures respectively.

On the Exact Solution to Certain Non-Linear Partial Differential Equations

Shi Weihui, Chen Daduan, Tang Yiming

1997, 18(3): 239-245.

Abstract(1770) PDF(647)

Abstract:
This paper, based on the theory of stratifications, gives a brand-new classification of partial differential equations.

Triangular Elements for Reissuer-Mindlin Plate

Chen Shaochun, Shi Dongyang

1997, 18(3): 247-253.

Abstract(7813) PDF(595)

Abstract:
A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchhoff conditions at the interpolation points as the thickness of plate tends to zero so the element is locking free. We construct two triangular elements by this method——a 3-node elenent and a 6-node element. The numerical results are provided.

A Class of Singularly Perturbed Reaction Diffusion Systems

Mo Jiaqi

1997, 18(3): 255-259.

Abstract(2252) PDF(573)

Abstract:
A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.

The Problem of the Non-Linear Unsymmetrical Bending for Cylindrically Orthotropic Circular Thin Plate with Variable Thickness

Huang Jiayin, Qin Shengli, Xu Xiaoping

1997, 18(3): 261-276.

Abstract(2258) PDF(602)

Abstract:
To begin with, in this paper the governing equations of the problem of the non linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using "the method of two-variable" and introducing four Small parameters. the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied,and the uniformly valid asymptotic solution of Nth-order for ε₁ and Mth-order for ε₂ are oblained.

Lagrangian Model on the Turbulent Motion of Small Solid Particle in Turbulent Boundary Layer Flows

Liu Xiaobing, Cheng Liangjun

1997, 18(3): 277-284.

Abstract(2244) PDF(601)

Abstract:
The Lagrangian equations of motion of small solid particle in turbulent boundary layer flows, taking into account the effects of the drag force caused by the wall presence, the Saffman and the Magus lift forces et al., is studied. Using the spectral method. anavtical expressions relating to the Lagrangian power spectra of particle velocity to that of the fluid are dereloped and the results are used to evaluate rarious response statistics. In this paper, the results clearly show that the turbulent diffusivity of the particle may be larger than that of fluid for a period of long-time.

Probabilistic Norm of Linear Operators on PN Space

Xiao Jianzhong, Jiang Xingguo

1997, 18(3): 285-290.

Abstract(1852) PDF(632)

Abstract:
In this paper, the new definition of probabilistic norm of linear operators on a PN space is giren. In virtue of this, the boundedness of linear operators is described and the completeness of the PN space composed of all bounded linear operators is given.