应用数学和力学

1991 Vol. 12, No. 10

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The Dynamic Plastic Behavior of a Simply Supported Circular Plate in a Damping Medium with Finite-Deflections

Zhao Ya-pu, Hsueh Dah-wei

1991, 12(10): 871-878.

Abstract(1759) PDF(542)

Abstract:
A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.

Numerical Solution of Singular Perturbation Problems for the Fourth-Order Elliptic Differential Equations

Su Yu-cheng, Liu Guo-qing

1991, 12(10): 879-902.

Abstract(2140) PDF(555)

Abstract:
In this paper we construct the finite-difference scheme for the singularly perturbed boundary value problem for the fourth-order elliptic differential equation on the basis of paper [1], and prove the uniform convergence of this scheme with respect to the small parameter e in the discrete energy norm. Finally, we give a numerical example.

An Elasticity Solution for Axisymmetric Problem of Finite Circular Cylinder

Hou Yu, He Fu-bao

1991, 12(10): 903-912.

Abstract(2043) PDF(714)

Abstract:
In this paper the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transforniution and Stockes transformation. Using the double-series, a series solution for the axisyinmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example, the cylinder subjected to the axisymmetric traellens with various loaded regions is investigated and the distributions of the displacement sand stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the eylinderical coordinates for other scientific fields by use of the method presented in this paper.

The Welding Problem of Two Half-Planes with Anisotropic Media

Huang Xiao-ling

1991, 12(10): 913-916.

Abstract(1954) PDF(726)

Abstract:
In this paper, the welding problem of two half-planes with anisotropic media is considered. By means of the complex variable method, the stress distribution is given in closed forms.

A Non-Isotropic Multiple-Scale Turbulence Model

Guo Kuan-Liang, C. P. Chen

1991, 12(10): 917-925.

Abstract(2193) PDF(713)

Abstract:
This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.

Tensile Instability of Nonlinear Spherical Membrane with Large Deformation

Shang Xin-chun

1991, 12(10): 927-933.

Abstract(1899) PDF(450)

Abstract:
The problem on instability of nonlinear spherical membrane with large axisvmmelric tensile deformations is investigated by using the bifurcation theory. It is proved that all singular points of the nonlinear boundary value problem must be simple limit points. The effect of loading and material parameters on the equilibrium state and its stability is discussed.

The Stability on the Solution of the Initial Value Problem

Shao Xiao-huang

1991, 12(10): 935-941.

Abstract(2641) PDF(521)

Abstract:
In this paper, using the differentiability of the solution with respect to the initial value and the parameter, we present a method which, different from Liapunov's direct method. will determine the stability of the non-stationary solution of the initial value problem when the non-stationary solution remains unknown.

Effect of Poisson Ratio on the Perfectly Plastic Field at a Rapidly Propagating Plane-Strain Crack-Tip

Lin Bai-song

1991, 12(10): 943-950.

Abstract(1951) PDF(462)

Abstract:
All the stress components at a rapidly propagating crack-tip in elastic perfectly-plastic material are the functions of only. Making use of this condition and the equations of steady-state motion, plastic stress-strain relations, and Mises yield condition with Poisson ratio, in this paper, we derive the general expression of perfectly plastic field at a rapidly propagating plane-strain crack-tip. Applying this general expression with Poisson ratio to Mode I crack, the perfectly plastic field at the rapidly propagating tip of Mode I plane-strain crack is obtained. This perfectly plastic field contains a Poisson ratio, and thus, we can obtain the effect of Poisson ratio on the perfectly plastic field at the rapidly propagating tip of Mode I plane-strain crack.

Stability Analysis for Two Kinds of Equations in Two-Species Population Dynamics

Wang Fu-jun

1991, 12(10): 951-955.

Abstract(1798) PDF(571)

Abstract:
In this paper we study the stability for equilibrium points of equations in two-population dynamics. We discuss two predator-prey-patch models. Model 1 is described by a differential equation. Model 2 is described by an integral differential equation. We obtain the conditions for the stability of their equilibrium points. The results show that the overall population stability despite local extinction is realizable.

On Flexurar Vibration of Hemispherical Shell

Fan Shang-chun, Liu Guang-yu, Wang Zhen-jun

1991, 12(10): 957-964.

Abstract(1695) PDF(461)

Abstract:
This paper makes detailed analyses tor the flexural vibration (frequency) of the hemispherical shell and presents the varying laws of frequency with the rarving boundary angles and the wall thickness of the above shell, It is an important value to develop the instrument, such as hemispherical resonator gyro (HRG), whose sensing component is a hemispherical shell.