应用数学和力学

1989 Vol. 10, No. 3

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The General Solution on Nonliear Deformation of Axial-Symmetrical Nonuniform and Variable Thickness Cylinderical Shells

Ye Kai-yuan, Ji Zhen-yi

1989, 10(3): 187-193.

Abstract(1710) PDF(524)

Abstract:
The aonuniform cylindrical shells are widely used as structural configuration in engineeriag, In this paper, the general solution on nonlinear deformation of axial-symmetrical nonuniform and variable thickness cylindrical shells is obtained by step reduction method^[1].The displasement and stress resultants of shells can be expressed is analytic form is arbitrary axial-symmetrical load and boundary conditions, Its convergence is proved, Finally, it is only necessary to solve one set of binary linear algebraic equation, A numerical example is given at the end of the paper which indicates satisfactory results of stress resultants, moments and displacement can be obtained by step reduction method.

Some Coincidence Theorems of Set-Valued Mappings

Ding Xie-ping

1989, 10(3): 195-201.

Abstract(1738) PDF(586)

Abstract:
Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder's results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder's theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems of set-valued mappings. They improve and generalize the important results in [1,2,3].

Quasi-Periodic Waves and Quasi-Solitary Waves in Stratified Fluid of Slowly Varying Depth

Zhu Yong, Dai Shi-qiang

1989, 10(3): 203-210.

Abstract(1868) PDF(540)

Abstract:
The nonlinear waves in a stratifiiedfiuid of slowly varying depth are inrestigated in this paper. The model considered here consists of a two-layer incompressible constant-density inviscid fiuid confined by a slightly uneren bottom and a horizontal rigid vrall. The Korteweg-de Vries (KdV) eguation with varving coeffieients is derived with the aid of the reductive perturbation method. By using the method of multiple scales, the upproximate solutions of this eguation are obtained. It is found that the uneve nness of bottom may lead to the generation of so-called quasi-periodic waves quasi-solitary waves, whose periods propugation velocities and wave profiles vary slowly. The relations of the period of guasi-periodic waves and of the amplitude, propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented. The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.

Asymptotic Method for Singular Perturbation Problem of Ordinary Difference Equations

Wu Chi-guang, Su Yu-cheng, Sun Zhi-zhong

1989, 10(3): 211-220.

Abstract(1765) PDF(557)

Abstract:
This paper is taken up for the following difference equation problem (P_ε):(L.y)_k≡εy(k+1)+a(k,ε)y(k)+b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1)B₁y≡-y(0)+c₁y(1)=a,B₂y≡-c₂y(N-1)+y(N)=β where e is a small parameter, c₁, c₂,α,β constants and a(kε),b(kε),ƒ(kε)(1≤k≤N) functions of k and ε. Firstly, the case with constant coefficients is considered. Secondly, a general method based on extended transformation is given to handle (P_a) where the coefficients may be variable and uniform asymptotic expansions are obtained. Finally, a numerical example is provided to illustrate the proposed method.

A Uniformly Convergent Second Order Difference Scheme for a Singularly Perturbed Self-Adjoint Ordinary Differential Equation in Conservation Form

Guo Wen, Lin Peng-cheng

1989, 10(3): 221-230.

Abstract(1844) PDF(472)

Abstract:
In this paper, based on the idea of El-Mistikawy and Werle we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.

On the Stability of Distorted Laminar Flow(Ⅱ)——The Linear Stability Analysis of Distorted Parallel Shear Flow

Zhou Zhe-wei

1989, 10(3): 231-238.

Abstract(1900) PDF(446)

Abstract:
Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.

The Order of a Damage Tensor

Lü Yun-bing, Chen Xing-fu

1989, 10(3): 239-246.

Abstract(1998) PDF(657)

Abstract:
In this paper, the stress deformation constitutive relations for continua are discussed and a stress deformation constitutive relation expressed by functional tensorial expression is found. When we study the anisotropic damage of anisotropic materials either from a macroscopic continuum mechanics model or from a micro-defect model, there exists a limit to the order of a damage tensor, and the condition under which the damage variable may be described by a tensor lower than those of the highest order is found.

Flow Field at Collapse of a Cavity

Huang Jing-quan

1989, 10(3): 247-251.

Abstract(1919) PDF(647)

Abstract:
Employing Rayleigh's method, the collapse of a vaporous bubble in an incompressible liquid with surface tension is analysed. The expressions of time versus radius, bubble-wall velocity and pressure developed at collapse are thus introduced.Finally, the numerical solution of velocity and pressure field in the liquid surrounding the cavity is also given.

The Reciprocal Theorem and Linear Elastic Variational Principles

Fu Bao-lian

1989, 10(3): 253-258.

Abstract(1951) PDF(652)

Abstract:
In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.

Several New Types of Finite-Difference Schemes for Shallow-Water Equation with Initial-Boundary Value and Their Numerical Experiment

Lü Qiu-qiang, Zhou Gang, Liu Ying-zhong

1989, 10(3): 259-269.

Abstract(1734) PDF(620)

Abstract:
This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. At last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.

On Some Problems for Unsymmetrically Lateral Buckling of Rectangular Plates

Cheng Xiang-sheng

1989, 10(3): 271-275.

Abstract(1656) PDF(541)

Abstract:
The present paper investigates several problems for unsymmetrically lateral instability of rectangular plates by the energy method. In the text we discuss the minimum critical load of rectangular plates which possess the unsymmetrical supporters and to which the lateral buckling occurs unsymmetrically under a concentrated force, uniformly distributed load and the concentrated couples respectively.