应用数学和力学

1989 Vol. 10, No. 12

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Asymptotic Solution for Singular Perturbation Problems of Difference Equation

Wu Chi-kuang

1989, 10(12): 1033-1039.

Abstract(1616) PDF(422)

Abstract:
In this paper, we constructed a new asymptotic method for singular perturbation problems of difference equation with a small parameter.

Further Study on Large Deflection of Circular Sandwich Plates

Liu Rea-huai, Zhu Gao-qiu

1989, 10(12): 1041-1047.

Abstract(1977) PDF(559)

Abstract:
In this paper, a nonlinear solution is first presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account. In solving the nonlinear bending equations, a modified power series method is proposed. The uniformly distributed loading and the clamped but sliding ...

On Large Deformation Unilateral Contact Problem with Friction(Ⅰ)——Incremental Variational Equations

Shang Yong, Chen Zhi-da

1989, 10(12): 1049-1058.

Abstract(1845) PDF(453)

Abstract:
Based on the theory and technique of nonlinear geometric field theory of continuum, a more general incremental variational equation for elastic and plastic large deformation in co-moving coordinate is established in this paper. An expression for two and three-ditnensicnal continua is derived, and th...

Nonlinear Stability Analysis of a Sandwich Shallow Cylindrical Panel with Orthotropic Surfaces

Wang Ying-jian, Wang Zhen-ming

1989, 10(12): 1059-1070.

Abstract(1725) PDF(471)

Abstract:
In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthoiropic surfaces. The critical point is determined and the postbitckling behaviour of the panel is studied.

On the Lattice Path Method in Convolution Type Combinatorial ldentities(Ⅱ)——The Weighted Counting Function Method on Lattice Paths

Chu Wen-chang

1989, 10(12): 1071-1075.

Abstract(1851) PDF(556)

Abstract:
An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identiti...

The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains

Zhang Peng

1989, 10(12): 1077-1088.

Abstract(1928) PDF(433)

Abstract:
There are N domains D_j(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces S_j,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:
∇²H^(j)+K_jH^(j)=0 (j=0,1,…,N-1)
(H⁽⁰⁾-H⁽¹⁾)S_0.1=δ(S) (δ(S):generalized ...

The Dynamic Stiffness Matrix of the Finite Annular Plate Element

Zhang Yi-song, Gao De-ping, Wu Xiao-ping

1989, 10(12): 1089-1099.

Abstract(2186) PDF(475)

Abstract:
The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in clo...

The Application and Extension of Sachs Method

Song Shun-cheng

1989, 10(12): 1101-1106.

Abstract(1897) PDF(464)

Abstract:
In this paper,we present the simplification of Sachs formulas for the measurement and calculation of the residual stresses of the cylinder only with the plane stresses. Furthermore, we present the method for the measurement and calculation of the residual stresses of the cylinder not only with the f...

Vibration of Arbitrarily Shaped Membranes with Elastical Supports at Points

Zhou Ding

1989, 10(12): 1107-1113.

Abstract(1920) PDF(413)

Abstract:
This paper presents a new method for solving the vibration of arbitrarily shaped membranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given whi...

Criteria of Finite Element Algorithm for a Class of Parabolic Equation

Ouyang Hua-jiang, Xiao Ding

1989, 10(12): 1115-1121.

Abstract(1888) PDF(604)

Abstract:
In finite element analysis of transient temperature field, it is quite notorious that the numerical solution may quite likely oscillate and/or exceed the reasonable scope, which violates the natural law of heat conduction. For this reason, we put forward the concept of lime monotony and spatial mono...

The Asymptotic Properties of High Frequencies for Bars, Beams and Membranes

Ji Jian-jun, Hu Kui, Wang Da-jun

1989, 10(12): 1123-1130.

Abstract(1785) PDF(379)

Abstract:
In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the ease of discontinuous physical parameters is also discussed.