应用数学和力学

The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion

Chien Wei-zang, Chen Shan-lin

1985, 6(2): 103-119.

Abstract(1666) PDF(596)

Abstract:
In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky's membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.

On Computations of Stress Intensity Factors for Stiffened Half-Planes with Imperfections and Cracks

Ouyang Chang, Zhou Shiao-kang

1985, 6(2): 121-133.

Abstract(1487) PDF(490)

Abstract:
In this paper we consider uniform extension problems for joined two half-planes with different thickness and material behavior and one of which contains an elliptical hole, the other contains a crack. Along the boundary of these half-planes there is a stiffening stringer. Computational formulas are given in power series form by complex variahie-pertubation method. Results obtained here give extension to those of "Handbook of stress intensity factors". Numerical results of special cases in this paper coincide with those of references [1], [3].

The Creeping Motion of Multiple Spherical Liquid Drops

Wu Wang-yi, Zhang Bai-wen

1985, 6(2): 135-143.

Abstract(1731) PDF(451)

Abstract:
This paper deals with the drag factor of the multiple spherical liquid drops in the creeping motion by means of the Sampson singularities and collocation technique. The drag factors of the drops are calculated under distinct conditions: different number of liquid drops in the chain and different sphere spacing. From the results the influence of the viscosity ratio on the shielding effect and end effect are revealed. The convergence of the method is also studied in this paper.

Finite Difference Method of Transient Nonlinear Free Surface Wave Problems

Lu Yu-lin, Li Bao-yuan

1985, 6(2): 145-152.

Abstract(1774) PDF(568)

Abstract:
A finite difference method is developed for computing the two-dimensional transient potential flow generated by an impulse on the free surface. Both the dynamic and kinematic free surface conditions are considered in nonlinear version, the primary features of the present paper include the use of special coordinates transformations so that the geometry of the flow field is transformed into a time-invariant region, presents an iteration process, by which the velocity potential is computed as the solution of a Poisson equation, the application of fast Fourier transform (FFT) technique results in a tri-diagonal system of equations which can be readily solved by the Thomas algorithm, the computing time is significantly reduced. Thus an efficient technique for handling the transient potential problems is well justified. The feasibility of the present method is verified by two examples involving different initial disturbances.

The Relationship between the Stability and the Optimality of Linear Systems——Another Kind of the Inverse Problem of Linear Optimal Control

Chen Xiao-lin, Hwang Ling

1985, 6(2): 153-160.

Abstract(2164) PDF(576)

Abstract:
Different from the inverse problem put forward by R. E. Kalman, another kind ofinverse problem of linear optimal control is proposed and dicussed in this paper.

A Rigorous Solution for the Axisymmetrical Buckling of Simply Supported Cylindrical Sandwich Shells under Axial Load

Wang Zhen-ming, Dai Fu-ling

1985, 6(2): 161-173.

Abstract(1832) PDF(462)

Abstract:
In this paper, based on Ref. [1] the axisymmetrical buckling of simply supported cylindrical sandwich shells under the action of uniform axial lood is solved by a rigorous method. The classical theory of shells is used for the two face sheets and the core is considered as a three-dimensional elastic body. A series of transcendental equations are obtained, from which the critical loads can be calculated by manericai methods. Numerical examples are given to compare with the solutions of sandwich shell theories.

On the Problems of Buckling of an Annular Thin Plate

Qin Sheng-li, Zhang Ai-shu

1985, 6(2): 175-190.

Abstract(1977) PDF(569)

Abstract:
In this paper, problems of buckling of on annular thin plate under the action of in-plane pressure and transverse lood are studied by using the method of multiple scales. We obtain N-order uniformly valid asymptotic expansion of the solution. In the latter part of this paper we discuss a particular example, and calculate the critical value of in-plane pressure. We see that the asymptotic expansion obtained by the multiple scales is completely consistent with that of the exact solution.

The Antiplane Problem of Double Period Non-Uniform Distribution Crack Field

Hao Tian-hu, Cheng Ji-da, Yu Jia-sheng

1985, 6(2): 191-196.

Abstract(1851) PDF(598)

Abstract:
Originating from Robert Hooke's law and equilibrious equations, and using the theory of the complex variable function, this paper transfers the rectaugle region in which the cracks emerge into upper-half part of ζplane by means of conformal mapping. Then according to the theory of ref.[1]. We find the solution in closed form, there by the stress intensity factors are derived.

1985, 6(2): 197-197.

Abstract(1714) PDF(446)

Abstract:

1985 Vol. 6, No. 2