应用数学和力学

1988 Vol. 9, No. 6

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Dynamic Solution of Hyperbolic Cooling Tower with Nonsymmetric Imperfections by Finite Element Method

Gao Shi-qiao, Lu Wen-da

1988, 9(6): 475-480.

Abstract(1719) PDF(577)

Abstract:
In this paper, an apprf dmate method is established to solve the couple problem between different harmonic waves in terms of the needs of nonsymmetric imperfections of cooling tower. By means of this method, the frequencies and response of rotational shell with local geometric imperfections are analysed and calculated.

Transient Spherical Flow of Non-Newtonian Power-Law Fluids in Porous Media

Liu Ci-qun

1988, 9(6): 481-485.

Abstract(1797) PDF(583)

Abstract:
The transient spherical flow behavior of a slightly compressible, non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.

Properties of a Half Space Including a Twisted Shaft of Revolution

Yun Tian-quan

1988, 9(6): 487-490.

Abstract(1620) PDF(505)

Abstract:
The properties of an elastic half space including a partly embedded twisting shaft of revolution are studied. Without knowing the exact solution of the torsion problem of a given embedded shaft, these properties can indicate some features of the displacement or stress field of the half space and can sometimes be used for checking a numerical solution. An example for checking the correct stress distribution on surfaces of twisted rigid cylindrical shaft embedded in a half space is given.

Stress Functions for Central Straight Cracked Anisotropic Plates

Duan shu-jin, Nakagawa Ken-ji

1988, 9(6): 491-498.

Abstract(1972) PDF(546)

Abstract:
In this paper, the plane problem for an anisotropic plate with a central straight crack in any direction is solved. The stress functions are given to represent the finite stress concentrations near the crack tips by the weight integral methcd. It shows that there is no stress singularity at the crack tip. The model can be used to appropriate to fracture mechanics for non-metallic materials.

Fourier Series of Rational Fractions of Jacobian Elliptic Functions

Wan Shi-dong, Li Ji-bin

1988, 9(6): 499-513.

Abstract(2135) PDF(671)

Abstract:
In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic functions sn(u.k), cn(u.k) and dn(u.k) are listed, which cannot be found in the, handbook and Ref. [2]. For the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method, and for study of some problems of physical science and engineering, these formulas can be used.

A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure

Shen Hui-shen, Chen Tie-yun

1988, 9(6): 515-528.

Abstract(2296) PDF(751)

Abstract:
Based on the boundary layer theory for the buckling of thin elastic shells-suggested in ref. [14], the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.

The Bending, Stability and Vibrations of Rectangular Plates with Free Edges on Elastic Foundations

Cheng Xiang-sheng

1988, 9(6): 529-533.

Abstract(1770) PDF(678)

Abstract:
This paper discusses the problems of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations. In the present paper we select a flexural function, which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.

The Bounded Solution of a Class of Differential-Difference Equation of Advanced Type and Its Asymptotic Behavior

Lin Yi-zhong

1988, 9(6): 534-542.

Abstract(1782) PDF(611)

Abstract:
In this paper, we consider the differential-difference equation of advanced type with perturbation term. It is shown that if the bounded solution of the reduced equation has negative exponential order and the perturbation term f satisfies certain condition, then the bounded solution of the perturbation equation has negative exponential order.

The Study of Applicability for PLK Method

Tan Jun-yu

1988, 9(6): 543-551.

Abstract(1711) PDF(440)

Abstract:
This paper researches the applicability of the PLK method. We give the general formulae of the asymptotic solution and strained coordinates, and we establish necessary conditions for the applicability PLK method. Besides, the applicability of the approach is also exemplified by means of examples in this paper.

The Axial Symmetrical Problems of a/r₂>1 Toroidal Shells with Constant Thickness

Chen Guo-dong

1988, 9(6): 553-558.

Abstract(1612) PDF(478)

Abstract:
In this paper, the uniformly valid asymptotic solutions for the complex equation of the axial symmetrical problems of a/r₂>0 toroidal shells with constant thickness in bending theory are given.

Analysis to the Stress Construction at the Vicinity of Crack Tip for Mode I Fracture in 3-D State Using Finite Element Method

Chen Xiao-ming, Guan Zhong-xin, Zhuang Jia-lin

1988, 9(6): 559-566.

Abstract(1788) PDF(508)

Abstract:
The stresses and strains are calculated for CT specimen of power hardening material in 3-D deformation state using ADINAfinite element program, and the stress distribution at the vicinity of crack tip for Mode I fracture is analysed according to the results of calculation. It is found that the expression of stress can be written as the form of separation of variables of r and θ, then the function of r can be expanded in Laurant series. It is still found that the three normal stresses have the same order of magnitude. The conclusions offer two suppositions to obtain the theoretical expression of stress at the vicinity of crack tip for Mode I fracture with good ground, and the procedure of solution will be greatly simplified.