应用数学和力学

1988 Vol. 9, No. 2

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On the Nonlinear Stability of a Truncated Shallow Spherical Shell under a Concentrated Load

Liu Ren-huai, Cheng Zhen-qiang

1988, 9(2): 95-106.

Abstract(1692) PDF(547)

Abstract:
In this paper, the axisymmetric nonlinear stability of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is investigated by use of the modified iteration method. The analytic formulas of second approximation for determining the upper and lower critical buckling loads are obtained.

Uniform Strength Design of Beams with Non-Zero Minimum Flexural Rigidity under Multiple Loadings

Yeh Kai-yuan, Tang Xie-li

1988, 9(2): 107-115.

Abstract(1757) PDF(556)

Abstract:
The analytical method for uniform strength design (U.S.D.) of statically indeterminate beams is extended to deal with a preassigned constraint of non-zero minimum flexural rigidity and multiple load cases. And a numerical method of finding the U.S.D. is presented. Therefore we have a uniform procedure of solution of U.S.D. to beams with arbitrary cross-sectional shape and acted upon by several loadings and subjected to the constraint of minimum flexural rigidity.

Basic Theory and Applications of Probabilistic Metric Spaces (Ⅰ)

Zhang Shi-sheng

1988, 9(2): 117-126.

Abstract(2119) PDF(602)

Abstract:
This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.

On the Embedding and Compact Properties of Finite Element Spaces

Wang Ming, Zhang Hong-qing

1988, 9(2): 127-134.

Abstract(2022) PDF(539)

Abstract:
In this paper, the generalized Sobolev embedding theorem and the generalized Rellich-Kondrachov compact theorem for finite element spaces with multiple sets of functions are established. Specially, they are true for nonconforming, hybrid and quasi-conforming element spaces with certain conditions.

General Solutions of Axisymmetric Problems in Transversely Isotropic Body

Ding Hao-jiang, Xu Bo-hou

1988, 9(2): 135-142.

Abstract(1965) PDF(560)

Abstract:
In this paper we solve axisymmetric problems by stress and deduce a series of valuable general solutions by unified method. Some of them are well-known solutions, and others have not appeared in the literature. We also prove the completeness of these general solutions.

Nonlinear Axisymmetric Bending and Stability of Thin Spherical Shallow Shell with Variable Thickness under Uniformly Distributed Loads

Ye Zhi-ming

1988, 9(2): 143-148.

Abstract(1788) PDF(635)

Abstract:
In this paper, the nonlinear bending and stability of thin spherical shallow shell with variable thickness under uniformly distributed loads are investigated by a new modified iteration method proposed by Prof. Yeh Kai-yuan and the author^[1]. Deflections and critical loads have been calculated and the numerical results obtained have been given in figures and tabular forms. It is shown that the final equation determining the central deflection and the load obtained coincides with the cusp catastrophe manifold.

A Finite Element Method on the Plane Elastic Material Analysis

Jiang You-liang

1988, 9(2): 149-154.

Abstract(1560) PDF(502)

Abstract:
Based on the finite element displacement method, a finite element method on the analysis of mechanical behaviour of plane elastic materials is proposed in this paper. By using this method and the corresponding computational program, the material behaviour of any unknown plane elastic material can be determined and all the elastic constants can be calculated.

Problems on Collinear Cracks between Bonded Dissimilar Materials under Concentrated Loads

Jiang Chi-ping, Liu You-wen

1988, 9(2): 155-164.

Abstract(1957) PDF(495)

Abstract:
Following Ref. [6], this paper deals with the problem on collinear cracks between bonded dissimilar materials under a concentrated force and moment at an arbitrary point. Several typical solutions of complex stress functions in closed form are formulated and the stress intensity factors are given. These solutions include a series of results of previous researchers, and redress some errors in the researches of problems containing semi-infinite cracks^[3][4].

On General Form of Navier-Stokes Equations and Implicit Factored Scheme

Wang Bao-guo

1988, 9(2): 165-172.

Abstract(2526) PDF(694)

Abstract:
A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam-Warming's implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.

Slip-Line Field Theory of Plane Plastic Strain Dealing with Mohr’s Criterion Expressed by Quadratic Limiting Curves

Chen Qiang

1988, 9(2): 173-182.

Abstract(2037) PDF(480)

Abstract:
In this paper, the slip-line field theory of plane plastic strain dealing with Mohr's criterion expressed by quadratic limiting curves is preliminarily established. It takes the classical slip-line field theory as its special case, and it can be applied to the analysis of plane-strain problems in metal processing, rock and soil mechanics and tectonomechanics. As preliminary application, the slip-line field and limiting loads of flat punch indenting problem are determined by numerical solution, and the slip-line field of bedded medium gravity-sliding problem is determined and discussed.

Axisymmetric Spherical Shell with Variable Wall Thickness

Wang Shen-xing

1988, 9(2): 183-188.

Abstract(1720) PDF(575)

Abstract:
This paper is engaged in research of the problem of axisymmetric spherical shell with variable wall thickness. The solutions for the problem are given for the spherical shell segment which does not contain the pole of sphere and the point of zero wall thickness.