应用数学和力学

1987 Vol. 8, No. 8

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An Analysis of a Radial Crack in a Reinforced Hollow Cylinder

Wang Xiao-chun, Tang Ren-ji

1987, 8(8): 661-667.

Abstract(1481) PDF(355)

Abstract:
Using the Michell solution and the crack solution, the integral equation of a radial crack in a hollow cylinder reinfcreed on its outer boundary is derived. The effects of the reinforced membrane on the crack are analysed and several numerical results arc presented herein.

Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval

Kang Sheng-liang, Zhang An-jiang

1987, 8(8): 669-688.

Abstract(1577) PDF(499)

Abstract:
In this paper we study initial value problems on the infinite interval: where x, f∈E^m, y, g∈Eⁿ,εare real small positive parameters,0≤t<+∞. On condition that g_y(t) is nonsingular and under other assumptions, we have proved that there areserial (k+m*)-dimensionalmanifolds {S_R(ε)}∈E^m+n such that (1.1) degenerates regularly provided(ξ(ε),η(ε))∈S_R(ε). Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.

A General Solution of Rectangular Thin Plates in Bending

Huang Yan

1987, 8(8): 689-696.

Abstract(1691) PDF(677)

Abstract:
In this paper a general solution of rectangular plates in bending is given. The integral constants are determined by means of boundary conditions. This method is simpler and easier than the method of superposition.

Bifurcation and Stability Analysis for Liquid Surfaces

Lu Qi-shao, Jiang Zheng-xin

1987, 8(8): 697-706.

Abstract(1568) PDF(441)

Abstract:
A more comprehensive discussion on the bifurcation problems for the shape of liquid surfaces is made in this paper. The necessary conditions for bifurcation are given, and the bifurcating solutions near bifurcation points can be obtained by perturbation technique. Finally the stability of the bifurcating states is analyzed by means of the principle of minimum potential energy.

Burning of Single Carbon Particle Approached by Activation Energy Asymptotics

Xie Ding-guo

1987, 8(8): 707-718.

Abstract(1647) PDF(525)

Abstract:
The method of activation energy asymptotics is used to treat the combustion of a single carbon particle in quiescent gas mixture with high temperature. Both heterogeneous reactions 2C+O₂ →2CO, C+CO₂→2CO and homogeneous reaction 2CO+O₂ 2CO₂ are considered. It is shown that the burning of the particle principally is carried out during a diffusion-limited period. Four brief and complex periods through which the history of the particle evolves from a heat-up period to the diffusion-limited period are described. A comparison between results of activation energy asymptotics and exact numerical solutions is given. The agreement is considered satisfactory.

On Analytical-Computerized Method to Solve Nonlinear Bending Problem of Circular Plate under a Concentrated Load

Zheng Xiao-jing, Zhou You-he

1987, 8(8): 719-726.

Abstract(1374) PDF(532)

Abstract:
In this paper, we have got a procedure of the recurrence formulas of analytical solution of iteration on solving the large deflection problem of circular plate under a concentrated load by computer. By researching convergence of the method, we have got a convergent upper bound value about load p, which is a useful criterion for analytical-computerized method.

Anisotropic Plastic Stress Field Near a Singular Point

Lin Bai-song

1987, 8(8): 727-732.

Abstract(1702) PDF(611)

Abstract:
On condition that any perfectly plastic stress component near a singular point is nothing but the function of θ only, making use of equilibrium equations and Hill anisotropic yield condition, we derive the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains. Applying these general analytical expressions to the concrete cracks and the plane-strain bodies with a singular point, the anisotropic plastic stress fields at the tips of Mode Ⅰ, Mode Ⅱ, Mode Ⅲ and mixed mode Ⅰ-Ⅱ cracks, and the limit loads of anisotropic plastic plane-strain bodies with a singular point are obtained.

A Hybrid/Mixed Model Finite Element Analysis for Eigenvalue Problem of Moderately Thick Plates

Qian Yuan-yao

1987, 8(8): 733-742.

Abstract(1700) PDF(540)

Abstract:
The buckling and free vibration problems of moderately thick plate are considered in this paper by using the hybrid/mixed finite element model. A modified Reissner principle which only requires C⁰ continuity is derived. No lockling phenomenon is observed. Linear interpolation is used for all independent unknown function. Finally a displacement generalized eigenvalue equation is obtained, in which the stiffness matrix is symmetric and positively definite. The calculated results show that the method proposed is simple, reliable and satisfactory.

Thermodynamic Entropy Models of the Frozen-Wall System (I)

Zan Ting-quan

1987, 8(8): 743-749.

Abstract(1438) PDF(368)

Abstract:
In this paper, the author describes, and comments on the traditional thermal theory on artificial ground freezing, and points out its important significance and shortcomings. The frozen-wall is analysed by system analysis methods. According to matter levels, the frozen-wall is divided into three sub-systems: frozen colloid system, frozen soil system and frozen-wall system. They correspond to different characteristics. The frozen-wall system is a large open system with multi-levels and multi-aspects. The problems of stability of the system and its control are the key problems in the techniques of artificial ground freezing. Based on non-equilibrium thermodynamics and dissipative structure theory methods, the author discusses and reveals the problems of the formation and stability of the frozen-wall system and its thermodynamic nature, and proposes the thermodynamic entropy models of the system. The result is a great satisfaction.

Some Pansystems Studies on Panchaos and Strange Panattractor

Zhu Sui-cai

1987, 8(8): 751-754.

Abstract(1658) PDF(478)

Abstract:
Paper [1] discussed the relations among panchaos and strange panattractor and pansystems operators. Paper [2] gave the applications of the fixed-point pansystems theorems to these typical nonlinear problems. In this paper, we firstly present several concepts: increasing relation, maximal panchaos, etc., and discuss the relations among them. We also discuss the problems when two increasing relations have the same panchaos and when panchaos of g is panchaos of g^t as well.