应用数学和力学

1984 Vol. 5, No. 2

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

Ouyang Chang, Zhu Han

1984, 5(2): 153-158.

Abstract(1500) PDF(494)

Abstract:
This work is the continuation of the discussion of [1J by C.Ouyang (Appl.Math.&Mech,Vol,1, No,2, 1980).Here computations for boundary notches are made by using the method of [1], Numerical results show that the method presented here is quite workable in practical computations.

Phenomenological Theory of Failure Criterion for Composite Materials

Zhou Cheng-ti

1984, 5(2): 159-166.

Abstract(1956) PDF(470)

Abstract:
In this paper, some current anisotropic failure criteria in the forms of tensor polynomials are investigated. In order to deterumne the interaction coefficients of the failure criteria, a nonlinear optimization method is proposed. The results obtained by different theories as well as the optimization are compared with the test data of some composite materials. The comparison shows that the optimization method for the materials considered in this paper is effective.

New Method of Solving Lame-Helmholtz Equation and Ellipsoidal Wave Functions

Dong Ming-de

1984, 5(2): 167-178.

Abstract(2255) PDF(562)

Abstract:
Despite the great significance of equations with doubly-periodic coefficients in the methods of mathematical physics, the problem of solving Lamb-Helmholtz equation still remains to be tackled; Arscott and Möeglich's method of double-series expansion as well as Malurkar's non-linear integral equation are unable to reach the final solution, Our main result consists in obtaining analytic expression for ellipsoidal wave funcdons of four species ε_ci(sna),ε_si(sna)(i=1,2,3,4) by deriving a couple of linear integral equations and solving these by integral transform, including the well-known Lamé function E_ci(sna),E_si(sna) as special case.Generalizing Riemann's idea of P-function, we introduce D-function to eapress their transformation properties.

On the Dynamical Structure of the Wind Field of Jupiter’s Great Red Spot

Yue Zeng-yuan, Zhang Bin

1984, 5(2): 179-189.

Abstract(1748) PDF(502)

Abstract:
Basing on the geostrophic approximation, the two-dimensional dynamical structure of the wind fields of Jupiter's Great Red Spot and White Oval BC is obtained.The results of calculation are in good agreement with the observations Thus, an explanation of the observed dispersion of the velocities along the horizontal streamline is given, The major physical mechanism of this dispersion is as follows The distance between two adjacent elliptical streamlines varies along the elliptical streamline, leading to the variance of the normal pressure gradient, Thus, the horizontal velocity V_T has to vary correspondingly so that the, Coriolis force can approximately balance the normal pressure gradient, Another less important factor, i,e, the change of the Coriolis force parameter f with the latitude,is also taken into account The distributions of the vorticities of GRS and White Oval BC are also calculated.

Unsymmetrical Bending of Annular and Circular Thin Plates under Various Supports (Ⅱ)

Jiang Fu-ru

1984, 5(2): 191-203.

Abstract(1615) PDF(682)

Abstract:
In this paper we study the unsymmetrical bending of elastic flexible plates under various supports in case the tensile force acting on its boundary is zero.

Extended Variational Principle in Non-Linear Theory of Elasticity

Zheng Quan-shui

1984, 5(2): 205-216.

Abstract(1840) PDF(774)

Abstract:
From the extended energy functional,a unified variational rinciple an extended variational principle^*, is given and proved in this aher. It is about the nonconservative, abrupt and divuied domains static (or kinetic) system, Using the undetermined energy functional, we can immediately deduce various variational princiales.

The Vibration Problem of Rod System in the Continuous Elastic Medium

Gu Xiang-zhen, Zhao Yu-xiang, Chien Er-xuan

1984, 5(2): 217-228.

Abstract(1708) PDF(542)

Abstract:
The vibration of rod system in the elastic continuous medium is a problem which is often met and also a composite solution problem of elastic dynamics and structural dynamics It seems rather difficult and complex to find solutions by general method. Using Lagrangian method of multipliers, we give here the generalized functionals concerning this kind of plane problem and show how to apply the method presented here through examples.

Fatigue Crack Propagation under Mixed Mode Loading

Cao Gui-xin, Ju Ding-yi

1984, 5(2): 229-238.

Abstract(1689) PDF(608)

Abstract:
Mixed mode fatigue crack propagation is analyzed in this paper, using a center cracked plate geometry, loaded under uni-axial cyclic tension.Based on maximun principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of △K and crack angle β₀ for an inclined crack.It is also shown that it is more convenient to express the Paris equation by means of crack length projected on the x-axis, a_x rather than the actual length, a, itself.The crack trajectory due to cyclic loading is predicted. β₀ is varied from 20°to 90°. Experimental data on Type L₃ aluminium agree fairly well with predicted values when β₀ exceeds 30°.

Spatial Instability of a Swirling Flow

Ma Hui-yang

1984, 5(2): 239-247.

Abstract(1616) PDF(511)

Abstract:
The instability of a swirling flow of an inviscid and incompressible fluid is studied on the assumption that the wave number k=k_r+ik_i of the disturbance is complex while its frequency w is real, This implies that the disturbance increases with distance along the axis of the swirling flow, but it does not grow with time, The occurrence of such disturbance is called spatial instability, in contrast to the temporal instability, in which k is a real number and ω=ω_r+iω_i is complex, The results show that spatial instability analysis is a useful tool for the comprehensive understanding of the instability behaviours of a swirling flow.

The Steady Isothermal Spinning of Viscoelastic Fluids

C. F. Chan Man Fong, Fan Chun

1984, 5(2): 249-254.

Abstract(1586) PDF(776)

Abstract:
The flaw problem given in the title has been considered for a modified Mazwell fluid, The resulting spin line equation is salved both numerically and analytically.It has been found that the results obtained by the above two methods are in agreement. This confirms the accuracy of the perturbation method which we adopted.

Perturbation Method in the Problem of Large Deflections of Circular Plates with Nonuniform Thickness

Yang Chia-shih, Xie Zhi-cheng

1984, 5(2): 255-261.

Abstract(1757) PDF(406)

Abstract:
In this paper the perturbation method about two parameters is applied to the problem of large deflections of a circular plate with exponentially varying thicknesses under uniform pressure, An asymtotic solution up to the third-order is derived. In comparison with the exact solutions in special cases,the asymtotic solution shows a precise accuracy.

An Approximate Solution Considered Flow Inertia between Spherical Surfaces

Wang Zhi-qing, Liu Zhen-bei

1984, 5(2): 263-276.

Abstract(1440) PDF(450)

Abstract:
In this paper, the analytical expressions of the pressure distribution, velocity distribution and volume flue of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms in Navier-Stokes equation of the spherical coordinates are taken into consideration, Furthermore, using these egpressions, we may directly obtain the corresponding analytical expressions of the radial laminar flow between parallel disks, which are fully unified with corresponding results presented from references [3.4].

The Exponential Asymptotic Solution of Differential Equation

Liu Zheng-rong, Xu Jun-tao

1984, 5(2): 277-286.

Abstract(2358) PDF(472)

Abstract:
In this paper, the exponential asymptotic solution (E. A. S.) of differential equation is discussed Firstly, E. A. S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E. A. S. are found out.Next,E.A.S.in matched asymptotic method is discussed, Finally, some examples are give.

On the Modified Castigliano’s Theorem

Fu Bao-lian

1984, 5(2): 287-296.

Abstract(2947) PDF(534)

Abstract:
This paper gives the modified Castigliano's theorem, which is more convenient and more extensive for applications than the classical Castigliano's theorem. The modifications to the classical Castigliano's theorem are in the two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load P of the complementary energy density in the classical Castigliano's theorem is replaced by the expression with the products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano's theorem,the modification provides the theoretical fundamental for solving the problems of various boundary conditions We show also the method of how to apply the modified Castigliano's theorem to solve the problems of the surface stractural mechanics, hinally, as a calculated example of the application of the modified Castigliano's theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent built-in edges and other two adjacent free edges.

Fixed Point Theorems for Fuzzy Mappings

Chang Stuh-sen

1984, 5(2): 297-304.

Abstract(1731) PDF(463)

Abstract:
Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation This paper presents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].