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1985年 第6卷 第4期    刊出日期：1985-04-18

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论文

APPLICATIONS OF THE EXTRAPOLATION METHOD TO THE NUMERICAL SOLUTION OF SINGULAR PERTURBATION PROBLEMS

苏煜城

1985, 6(4):  293-360. 

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In this paper we consider applications of extrapolation method to the numerical solution of singular perturbation problem for etliptic-parabolic equation in order to manifesting accuracy of approximations and estimate the order of accuracy.Concerning the uniform convergence in ref.[1].its proof is given in the appendix.

NEW DEVELOPMENT IN POINCAR'S PROBLEM OF IRREGULAR INTEGRALS

董明德

1985, 6(4):  307-320. 

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In connection with non-Fuchsian equations Pnincare has made an important conclusion.It is impossible to obiain explicit expressions of irregular integrals To elucidate the essence of Pomcare’s problem, we establish correspondence theorem.Irregular inlegrals are analytic functions of new kind, possessing tree structure; part of which can be represented by conventional recursive series, while its remaining part is expressed by the so-called tree series, nol subjecting to any recursive relation at all.In contrast to the numerical solution calculated by infinite determinant of classical theory (Hill-Poincare-von Koch), our method yields naturally exact analytic soiution in explicit form.The method proposed may be used lo construct a unifying theory for general equations wilh variahle coefficients, having various kinds of singularities as singular lines.The significance of Poincare conjecture is discussed, the tree series obtained belong to higher automorphic functions.

CALCULATIONS FOR CIRCULAR ARC TYPE CORRUGATED MEMBRANE

王玳瑜;邹定祺;陈山林

1985, 6(4):  321-329. 

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Using Chien Wei-zang’s general Solutions of axial symmetrical ring shells, we calculate the stress and displacement of circular are type corrugated membrane under axial loads in this paper.According to the results of calculation, we plot the usable graphs for engineering.Scientists and lechnicians can keep these graphs for easy reference.

THE WARP AND STRESS TRANSMISSION IN THE JOINT OF AN OPEN THIN WALL BEAM

杨钦梁

1985, 6(4):  331-342. 

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The regularities of the war p in the sections of on open thin-wall beam have been discussed using the MODERN ENGINEERING THEORY OF BEAM.Thus, the transmission relationship between the warp displacements and the double-moments in the joints of open thin-wall beams which are connected in different ways hos been deduced.Meanwhile.experiments conducted by the author and some conclusions reached from these experiments as well as the tentative idea for further perfection are briefly presented here.

NONSTATIONARY RANDOM VIBRATION OF ONE-DEGREE AND MULTIDEGREE OF FREEDOM SYSTEMS

孟庆生

1985, 6(4):  343-352. 

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In ref.[1] for nonstationary random processes such as we defined the spectral densi Sξ(t, ω)=|t,ω|²S(ω) tywhere Z(A) is an orthogonal random measure, S(ω) is the spectral density of the stationary random processf(t,ω) is a complex function with two real variables, it is called modulation function and it is satisfied byIn ref.[1] we obtained the main results: for the linear dynamic systems which is described by such equationswe obtained under certain conditions thatwherehere W(t,τ) ir the response function of the systems to the unit pulse.This paper is continued on ref.[1].We obtain some results for the one-degree and multidegree of freedom systems.

PERTURBATION SOLUTION OF AXISYMMETRIC PLASTIC PROBLEM I-NECKING OF A BAR

沈惠申

1985, 6(4):  353-365. 

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In this paper, basing on the general equations of axisymmetric plastic problems deducedin ref.[11], and employing perturbation technique, the asymptotic analysis for the necking problem is given.The result will pro vide knowledge of distribution of stress and strain in whole plastic region, thus, il will lead to a beller understanding of the necking phenomena in a tension specimen, such as the cup-cone type fracture.

SOLUTION OF SECTOR PLATE BY FOURIER-BESSEL SERIES

钱民刚;严宗达

1985, 6(4):  367-385. 

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In this paper a solution of deflection in the form of Fourier-Bessel double series with supplementary terms is proposed to analyse bending and vibration problems of thin elastic sector plate with various edge conditions.This solution is suitable to a wider range, conventent for calculation and it is in on analytical form.As computational examples, the distribution curves of deflection and bending moment of plates with various sector angles.simply supported or damped along the radial edges under uniform ar concentrated load are obtained and the result are compared with the numerical results of related references.Thus the range of application of the Fourier series method with supplementary terms is extended.Frequencies and nodal lines in free vibration of plates with various sector angles simply supported along the radial edges are also given in this paper.

ON THE CORRECTION BY MCCLINTOCK AND IRWIN

汪懋骅

1985, 6(4):  387-391. 

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In the case of quasi-brittle fracture, at the crack tip there is a small plastic region whose affection cannot be neglected.Therefore the Imar elaslic asympotone fields must be corrected.In 1965 F.A.MoClintock and G.R.Irwin presented a correction which since then has been adopted extensively.Here in this paper, u must be pomted out that such correction is wrong.A correct result is given.