应用数学和力学

1997 Vol. 18, No. 6

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On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks

A. N. Guz, V. M. Nazarenko, Ⅰ. P. Starodubtsev

1997, 18(6): 483-494.

Abstract(1911) PDF(447)

Abstract:
The frqcture of materials under the action of compressive forces, directed along cracks which are parallel in plere cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type,used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening[1,2].The problems of such a class may be described only by using new approaches.One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics[3, 4, 5]. It should be remarked here that this approach has been widely used inproblems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.

The Exact Solution of Stress Distribution in Fillet Welds

Xue Dawei

1997, 18(6): 495-498.

Abstract(2205) PDF(493)

Abstract:
The exact solution of stress distribution in fillet welds under the action of bending moment M is presented in this paper. Together with the exact solution of stress distribution in fillel welds under the action of concentrated force P given in an earlier paper[1], designers of weldments can improve their work on the foundation of exact analytical solutions.

An Analytical Solution and Analysis of Characters for Viscoelastic Fluid Flow in Annular Pipe

Huang Junqi, Liu Ciqun

1997, 18(6): 499-506.

Abstract(1838) PDF(627)

Abstract:
In this paper an analytical solution to flow of second order and Maxwell fluid in annular pipe by using Hankel integral transform is presented A derived formula can be used to analyze the behavior of rotatory velocity and shear stress: since the parameters of material and the gap size of annular pipe explicitly appear in the analytical formula one can easily analyze their effection on the flow behavior. This solution can provide a theoretical base to drilling engineering and polymer shaping techniques. In addition, it can be used to analyze the flow characters in concentric cylinder rheometer and obtain material constants with curve fitting procedure.By investigation it is found that when outer cylinder makes uniform rotatory the history curve of velocity and stress of Maxwell fluid exhibit obliquerectangle wave and rawwave oscillation respectively. The wave period and amplitude increase with material constant Ha. This conclusion may be of significance in practice.

Effect of Suspended Solid Particles on Unstability of Two-Dimension Mixing Layer

Zhou Zexuan, Lin Jianzhong

1997, 18(6): 507-512.

Abstract(2267) PDF(513)

Abstract:
By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified R ayleigh equation are obtained.And then, by solving the corresponding eigen-value equations with nu merical vo mputational method, the relation curves between perturbation frequency and spacial gro wth rate of the mixing layer for the varying particle loading, ratio of particle velocity to fluid velocity and Stokes number are got .Several important conclusions on the effect of suspended solid particles on unstability of the mixing layer are presented in the end by analyzing all the relation curves.

An Equivalent Nonlinearization Method for Analysing Response of Nonlinear Systems to Random Excitations

Zhao Lei, Chen Qiu

1997, 18(6): 513-521.

Abstract(2140) PDF(1094)

Abstract:
In this paper, a hew equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian white noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method several kinds of usual nonlinear random vibration systems are analyzed The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.

The Illustration Calculations of Second Order Effects in Elastic Half-Space Acted upon By A Non-Uniform Shear Load

Liu Youwen, Guo Jianlin

1997, 18(6): 523-530.

Abstract(2412) PDF(465)

Abstract:
This paper is a continuation of [1]. An example is discussed in detail to illustrate the second order effects. Numerical calculations for the second order elastic material for the z-direction displacement and the stress t_rz, are carried out. It is found that the second order effect is to reduce z-direction displacement and to decrease t_rz inside the circle but to increase its value outside the circle.

The Extended Jordan’s Lemma and the Relation between Laplace Transform and Fourier Transform

Wei Zhiyong, Zhu Yongtai

1997, 18(6): 531-534.

Abstract(4833) PDF(859)

Abstract:
Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>0, if =0 where z=Re^iφ and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.

Boundary Value Problem for a Singularly Perturbed Nonlinear System

Huang Weizhang

1997, 18(6): 535-544.

Abstract(2278) PDF(527)

Abstract:
In this paper, by the technique and the method of deagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with:εy"=f(t,y,y',ε),y(0,ε)=a(ε),y(1,ε)=b(ε) The existance of the solution and its asymptotic properties are discussed when the eigenvaslues of Jacobi matrix fy' has K negative real parts and N-K positve real parts.

Nonlinear Free Vibration of Orthotropic Shallow Shells of Revolution under the Static Loads

Wang Yonggang, Wang Xinzhi, Song Huifang

1997, 18(6): 545-550.

Abstract(2075) PDF(451)

Abstract:
In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthoiropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method. from which, the characteristic relation between frequency ratio and amplitude is obtsained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.

The Equations of External lmpacted Dynamics between Multi-Rigidbody Systems

Zhang Dingguo

1997, 18(6): 551-555.

Abstract(2346) PDF(560)

Abstract:
This paper discusses the problem of impact dynamics between two multi-rigidbody systems, and presents the mathematical model of this kind of impact problem. In this model the impact impulses at collision points are not coupled with the increments of the velocities, and they are also suitable for computer coding. So the model obtained in this paper is of practical value.

Existence of Periodic Traveling Wave Solutions for a Class of Generalized BBM Equation

Huang Nanjing

1997, 18(6): 557-561.

Abstract(2289) PDF(538)

Abstract:
In this paper. a new kind of generalized BBM equation is introduced and discussed Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.

Group Theory Analysis of Mixed Convection over a Horizontal Moving Plate

Xu Xuezi, Shi Junmei, Fan Jianren

1997, 18(6): 563-571.

Abstract(2151) PDF(413)

Abstract:
In the present paper, the investigation to the mixed convective boundary-layer behavior over a horizontal plate is carried out. By applying transformation group theory, the analysis of the governing equations of continuity, momentum. energy and diffusion shows the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x^4/(7-5n) and that the moving speed of the plate is proportional to x^(3-n)/(7-5n), furthermore, a set of similarity equations is obtained. The similarity equations are solved numerically by a fourth-order Runge-Kutta scheme. The numerical results obtained for velocity,temperature and concentration distributions for Pr=0.72 and various values of the parameters Sc, K₁, K₂ and K₃ reveals the influence of these parameters on the flow,and heat and mass transfer behavior.