应用数学和力学

1986 Vol. 7, No. 1

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Unified Definition of Divergence, Curl, and Gradient

Tai Zhen-duo

1986, 7(1): 1-5.

Abstract(2411) PDF(1568)

Abstract:
In this note the differential expressions of divergence, curl, and gradient are derived based on one common model. Each of them involves the limiting value of a differential quantity per unit volume. By taking advantage of some differential relations of the unit vectors weighted by the metric coefficients, the full expressions of these three quantities in vector analysis can be readily derived.

On a Class of Method for Solving Problems with Random Boundary Notches and/or Cracks-(IV) Computations for Deep Boundary Notches and/or Cracks

Ou Yang-chang, Zhu Han

1986, 7(1): 7-16.

Abstract(1707) PDF(631)

Abstract:
This paper continues the discussions to a class of method for solving problems with random boundary notches and/or cracks in references by C. Ouyang in [1] (See also [2] and [3]). Using the basic met hod given in this reference as well as some further developments. We develop here a new effective computational method for solving random deep boundary notches and/or cracks. The actual numerical computations given in this paper show that the present method is quite workable and the results obtained have enlarged the contents of "Handbook of Stress Intensity Factors" given by G. C. Sih.

The Computation of Nonlinear Instability for Multilayer Composite Cylindrical Shells

Zhou Cheng-ti, Zhou Chien-bin

1986, 7(1): 17-23.

Abstract(1989) PDF(561)

Abstract:
In this paper, energy method and finite difference method are used to Compute the instability behavior ofmultilayeredfiber reinforced composite cylindrical shells under axial compression, hydrostatic pressure and torsion. The influences of initial imperfections, geometrical nonlinearities of shells and physical nonlinearities of the materials to the buckling and postbuckling behavior of the shells are considered. The effect of transverse shear is also discussed. The computational results of this paper are well agreed with the experimental data.

Diffraction of Elastic Waves in the Plane Multiply-Connected Region and Dynamic Stress Concentration

Gai Bing-zheng

1986, 7(1): 25-36.

Abstract(2074) PDF(652)

Abstract:
This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions. The complete function series which approach the solution of the problem and general expressions for boundary conditions are given. Then the problem is reduced to the solution to infinite series of algebraic equations and the solution can be directly obtained by using electronic computer. In particular, for the case of weak interaction, an asymptotic method is presented here, by which the problem ofp waves diffracted by a circular cavities is discussed in detail. Based on the solution of the diffracted wave field the general formulas for calculating dynamic stress concentration factor for a cavity of arbitrary shape in multiply-connected region are given.

Random Common Fixed Point Theorems of Set-Valued Mappings

Ding Xie-ping

1986, 7(1): 37-42.

Abstract(1883) PDF(529)

Abstract:
In this paper, we prove several random common fixed point theorems to general set-valued contractive mappings. These theorems improve and generalize the corresponding results in [1-18].

Chaotic Phenomenon in Catalytic Reaction

Liu Zheng-rong, Li Ji-bin, Lin Chang

1986, 7(1): 43-49.

Abstract(1955) PDF(642)

Abstract:
In this pqper, Melnikov's method is used to discuss a kind of equation governed by flickering on catalytic wires (gauzes) and in chemical reactor. By analysis on mathematics, we point out flickering phenomenon described by this kind of system has chaotic behavior.

Nielsen’s and Euler’s Operators of Higher Order in Analytical Mechanics

Liu Zheng-fu, Jin Fu-sheng, Mei Feng-xiang

1986, 7(1): 51-60.

Abstract(2028) PDF(694)

Abstract:
In this paper, the definitions of Nielsen's and Euler's operators of higher order are presented. These operators are concerned in analysis for systems with holonomic constraints and non-holonomic constraints of higher order. Some theorems that indicating relation between the two operators are established. Moreover, using the theorems, the new equations of mechanical systems with constraints of higher order are derived. Finally, an example is given.

On the General Equations, Double Hormonic Equation and Eigen-Equation in the Problems of Ideal Plasticity

Shen Hui-chuan

1986, 7(1): 61-72.

Abstract(1617) PDF(708)

Abstract:
In this paper the outcome of axisymmetric problems of ideal plasticity in paper [39], [19] and [37] is directly extended to the three-dimensional problems of ideal plasticity, and get at the general equation in it. The problem of plane strain for material of ideal rigid-plasticity can be solved by putting into double harmonic equation by famous Pauli matrices of quantum electrodynamics different from the method in paper [7]. We lead to the eigen equation in the problems of ideal plasticity, taking partial tenson of stress-increment as eigenfunctions, and we are to transform from nonlinear equations into linear equation in this paper.

The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response

Chen Jun-ping, Zhang Hong-de

1986, 7(1): 73-80.

Abstract(1869) PDF(706)

Abstract:
This paper is denoted to the qualitative analysis of two species predator-prey model with Boiling's type Ⅲ functional response. Conditions for the global stability ofnontrivial equilibrium points and conditions for the existence and uniqueness of limit cycles around the positive equilibrium point are obtained. The biological interpretations of these conditions are discussed. The authors believe that the conditions established in this paper are new to literature.

Approximate Solution for Bending of Rectangular Plates Kantorovich-Galerkin’s Method

Wang Lei, Li Jia-bao

1986, 7(1): 81-94.

Abstract(2257) PDF(709)

Abstract:
This paper derives the cubic spline beam function from the generalized beam differential equation and obtains the solution of the discontinuous polynomial under concentrated loads, concentrated moment and uniform distributed by using delta function. By means of Kantorovich method of the partial differential equation of elastic plates which is transformed by the generalized function (δ function and σ function), whether concentrated load, concentrated moment, uniform distributed load or small-square load can be shown as the discontinuous polynomial deformed curve in the x-direction and the y-direction. We change the partial differential equation into the ordinary equation by using Kantorovich method and then obtain a good approximate solution by using Glerkin's method. In this paper there are more calculation examples involving elastic plates with various boundary-conditions, various loads and various section plates, and the classical differential problems such as cantilever plates are shown.

An Estimation Method of Bearing Strength of Bolted Joints in Fibre Reinforced Composite

Yang Ling

1986, 7(1): 95-101.

Abstract(1832) PDF(583)

Abstract:
Some researchers have estimated the strength of bolted joints in fibre reinforced composite, using simple and efficient engineering procedures. However, for these procedures the effect of clamping due to the strength of bolted joints is not considered. In this paper, a method is presented for predicating critical bearing strength of single-hole bolted joints in composite on the basis of observing and analysing the results of experiments. The clamping effect of bolts is considered. The calculated results correspond to the test data on Glaphic/Epoxy laminates.