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(1627) 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(1992) 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 boundary condition are also assumed. Then our results are compared with those from Liu Ren-huai and Shi-Yun-fang^[15]. The present solution can be used ax a more accurate basis in engineering applications.

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

Shang Yong, Chen Zhi-da

1989, 10(12): 1049-1058.

Abstract(1871) PDF(454)

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 the incremental variational equation for large deformation of changing boundary contact and the variational inequality in rate form tire obtained, which provides the theoretical basis for the computation of elastic-plastic large deformation contact problem with friction.

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

Wang Ying-jian, Wang Zhen-ming

1989, 10(12): 1059-1070.

Abstract(1743) 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(1869) 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 identities for multinomial and q-multinomial coefficients.

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

Zhang Peng

1989, 10(12): 1077-1088.

Abstract(1958) 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 function)
(H⁽¹⁾-H⁽ⁱ⁺¹⁾)S_j,j+1=0 (j=0,1,…,N-2)
The analytical solution of the above problem is given in this paper.

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(2206) 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 closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

The Application and Extension of Sachs Method

Song Shun-cheng

1989, 10(12): 1101-1106.

Abstract(1922) 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 finite length but with the longitudinal stress. These can be applied to the investigation on the residual stresses of the autofretted gun tube.

Vibration of Arbitrarily Shaped Membranes with Elastical Supports at Points

Zhou Ding

1989, 10(12): 1107-1113.

Abstract(1940) PDF(414)

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 which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.

Criteria of Finite Element Algorithm for a Class of Parabolic Equation

Ouyang Hua-jiang, Xiao Ding

1989, 10(12): 1115-1121.

Abstract(1901) 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 monotony, and then derive several sufficient conditions for nionotonic solutions in lime dimension for 3-D passive heal conduction equations with a group of finite difference schemes. For some special boundary conditions and regular element meshes, the lower and upper bounds for Δt/Δx² can be obtained from those conditions so that reasonable numerical solutions are guaranteed. Spatial monotony is also discussed. Finally, the lumped mass method is analyzed.We creatively give several new criteria for the finite element solutions of a class of parabolic equation represented by heal conduction equation.

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(1809) 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.