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1984年 第5卷 第2期    刊出日期：1984-03-18

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Articles

ON A CLASS OF METHOD FOR SOLVING PROBLEMS WITH RANDOM BOUNDARY NOTCHES AND/OR CRACKS(Ⅱ) COMPUTATIONS FOR BOUNDARY NOTCHES

欧阳鬯;朱涵

1984, 5(2):  1137-1141. 

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This work is a continuation of the discussion of [1], "On a class of method for solving problems with random boundary notches and/or cracks, (I)" by C. Ouyang (Appl, Math, & Mech., Vol, 1, No, 2, 1980). Here computations for boundary notches are made by using the theory and formulas presented in [1], In the computation modification is also wade for the boundary conditions in parametric plane in [1], Numerical results for examples show that within ranges of parameter considered in the paper, for example L, the present method in quite workable in practical computations.

PHENOMENOLOGICAL THEORY OF FAILURE CRITERION FOR COMPOSITE MATERIALS

周承倜

1984, 5(2):  1143-1150. 

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

NEW METHOD OF SOLVING LAME-HELMHOLTZ EQUATION AND ELLIPSOIDAL WAVE FUNCTIONS

董明德

1984, 5(2):  1151-1162. 

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Despite the great significance of equations with doubly-periodic coefficients in the methods of mathematical physics, the problem of solving Lamé-Helmholtz equation still remains to be tackled. Arscott and Moglich method of double-series expansion as well as Malurkar nonlinear integral equation are incapable of reaching the final explicit solution.Our main result consists in obtaining analytic expressions for ellipsoidal wave functions of four species (i=1,2,3,4) including the well known Lam(α) functions E_ci(snα),E_z1(snα) as special cases. This is effected by deriving two Integra-differential equations with variable coefficients and solving them by integral transform. Generalizing Riemann’s idea of P function, we introduce D function to express their transformation properties.

ON THE DYNAMICAL STRUCTURE OF THE WIND FIELD OF JUPITER’S GREAT RED SPOT

岳曾元;张彬

1984, 5(2):  1163-1172. 

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Based on the geographic 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 follwos: 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 VT 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)

江福汝

1984, 5(2):  1173-1184. 

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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 NONLINEAR THEORY OF ELASTICITY

郑泉水

1984, 5(2):  1185-1196. 

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From the extended energy functional^**, a unified variational principle and an extended variational principle^** are given and proved in this paper. It is about the non-conservative, abrupt and divided domains static (or kinetic) system and by using the undetermined energy functional, we can immediately deduce various variational principles.

THE VIBRATION PROBLEM OF ROD SYSTEM IN THE CONTINUOUS ELASTIC MEDIUM

顾祥珍;赵玉祥;钱尔旋

1984, 5(2):  1197-1207. 

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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 through examples.

FATIGUE CRACK PROPAGAION UNDER MIXED MODE LOADING

曹桂馨;琚定一

1984, 5(2):  1209-1219. 

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Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under un-iaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β_α 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, α_x rather than the actual length, α itself. The crack trajectory due to cyclic loading is predicted, β is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β_α exceeds 30°.

SPATIAL INSTABILITY OF A SWIRLING FLOW

马晖扬

1984, 5(2):  1221-1229. 

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The instability of a swirling flow of an inviscidand incompressible fluid is studied on the assumption that the wavenumber k=k_r + ik_i of the disturbance is complex while its frequency ω is real. This implies that the disturbance grows 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 a complex one. 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

陈文芳;范椿

1984, 5(2):  1231-1236. 

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The flow problem given in the title has been considered for a modified Maxwell fluid. The resulting spin line equation is solved 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

杨嘉实;谢志成

1984, 5(2):  1237-1242. 

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

AN APPROXIMATE SOLUTION CONSIDERING FLOW INERTIA BETWEEN SPHERICAL SURFACES

王致清;刘震北

1984, 5(2):  1243-1254. 

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In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs. [3,4].

THE EXPONENTIAL ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION

刘曾荣;徐钧涛

1984, 5(2):  1255-1262. 

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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 given.

ON THE MODIFIED CASTIGLIANO’S THEOREM

付宝连

1984, 5(2):  1263-1272. 

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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 following 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 clasical Castigliano ’s theorem is replaced by the expressions with teh products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second respect 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 structural mechanics.Finally, as a calculated example of the applications of the modified Castigliano’s theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent edges built-in and other two adjacent edges free.

FIXED POINT THEOREMS FOR FUZZY MAPPING

张石生

1984, 5(2):  1273-1279. 

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Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation. This paper pressents 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].