应用数学和力学

Applications of the Extrapolation Method to the Numerical Solution of Singular Perturbation Problems

Su Yu-cheng

1985, 6(4): 289-302.

Abstract(1834) PDF(588)

Abstract:
In this paper we consider applications of extrapolation method to the numerical solution of singular perturbation problem for elliptic-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 Poincaré’s Problem of Irregular Integrals

Dong Ming-de

1985, 6(4): 303-315.

Abstract(2175) PDF(661)

Abstract:
In connection with non-Fuchsian equations Poincaré has made an important conclusion; It is impossible to obtain explicit expressions of irregular integrals. To elucidate the essence of Poincaré's problem, we establish correspondence theorem, Irregular integrals 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, not subjecting to any recursive relation at all. In contrast to the numerical solution calculated by infinite determinant of classical theory (Hill-Poincaré-von Koch),our method yields naturally exact analytic solution in explicit form, The method proposed map be used to;construct a unifying theory for general equations with variable coefficients, having varioas kinds of singularities as singular lines. The significance of Poincaré conjecture is discussed. The tree series obtained belong to higher automorphic functions.

Calculations for Circular Arc Type Corrugated Membrane

Wang Dai-yu, Zou Ding-qi, Chen Shan-lin

1985, 6(4): 317-324.

Abstract(1810) PDF(600)

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

The Warp and Stress Transmission in the Joint of an Open Thin Wall Beam

Yang Gin-liang

1985, 6(4): 325-334.

Abstract(2031) PDF(495)

Abstract:
The regularities of the warp in the sections of an 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 has 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

Meng Qing-sheng

1985, 6(4): 335-344.

Abstract(2174) PDF(513)

Abstract:
In the paper[1]for nonstationary random processes such as where here W(t,τ) is the response function of the systems to the unit pulse.This paper is continued on paper[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

Shen Hui-shen

1985, 6(4): 345-357.

Abstract(1796) PDF(636)

Abstract:
In this paper, basing on the general equations of agisymmetric plastic problems deduced in ref. [11], and employing perturbation technique, the asymptotic analysis for the necking problem is given, The result will provide knowledge of distribution of stress and strain in the whole plastic region, thus, it will lead to a better understanding of the necking phenomena in a tension specimen, such as cup-and-cone fracture.

Solution of Sector Plate by Fourier-Bessel Series

Qian Min-gang, Yan Zong-da

1985, 6(4): 359-376.

Abstract(2241) PDF(537)

Abstract:
In this paper a solution of deflection in the form of Fourier-Bessel double series with suplementary 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, convenient for calculation and it is in an analytical form, As computational examples, the distribution curves of deflection and bending moment of plates with various sector angles simply supported or clamped along the radial edges under uniform or concentrated load are obtained and the results are compared with the numerical results df related references, Thus the range of application of the Fourier series method with supple-mentary 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 McCiintock and Irwin

Wang Mao-hua

1985, 6(4): 377-381.

Abstract(1838) PDF(488)

Abstract:
In the case of quasi-brittle fracture, at the crack tip there is a small plastic region whose affection cannot be neglected, Therefore the linear elastic asymptotic fields must be corrected, In 1965 F. A. McClintock and G. R. Irwin presented a correction which since then has been adopted extensively, Here in this paper, it must be pointed out that such correction is wrong, A correct result is given.

1985, 6(4): 382-383.

Abstract(1899) PDF(441)

Abstract:

1985 Vol. 6, No. 4