应用数学和力学

1990 Vol. 11, No. 4

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A Weighted Penalty Finite Element Method for the Analysis of Power-Law Fluid Flow Problems

Chen Da-peng, Zhao Zhong

1990, 11(4): 279-282.

Abstract(1778) PDF(553)

Abstract:
In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

Uniform Difference Scheme for a Singularly Perturbed Linear 2nd Order Hyperbolic Problem with Zeroth Order Reduced Equation

Su Yu-cheng, Lin Ping

1990, 11(4): 283-294.

Abstract(2064) PDF(583)

Abstract:
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.

A New Element for Thin Plate of Bending with Curvilinear Boundary——Curvilinear Boundary Quadrilateral Element

Chien Wei-zang, Wang Gang

1990, 11(4): 295-300.

Abstract(1906) PDF(711)

Abstract:
This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.

The Analytical Solutions Based on the Concept of Finite Element Methods

Sui Yun-kang, Guo Tian-fu

1990, 11(4): 301-310.

Abstract(1817) PDF(667)

Abstract:
On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.

Lubrication Analysis of a Cell Sliding into a Circular Pore

Yan Zong-yi, Pan Chun-hui

1990, 11(4): 311-318.

Abstract(1788) PDF(617)

Abstract:
The resistance to the blood cells at the entrance to capillaries and membrane pores contributes considerably to the peripheral resistance in the blood circulation. This paper proposes, for the first lime, a simplified mechanical model in an attempt to treat the axisymmetric motion of a cell sliding into a circular pore. In this model, the shape of the cell is taken as given according to the microvideograph and the cell membrane is assumed to slide over its surface. The lubrication theory is applied to the thin layers of plasma between the membrane and the pore wall, yielding the pressure and shear stress distributions over the membrane as well as the resultant drag exerted on the cell. Our computations have simulated the process of the cell entering the pore, which is in qualitative agreement with the microvideographic observations.

Large Deflection Problem of Thin Orthotropic Circular Plate with Variable Thickness under Uniform Pressure

Wang Ying-jian

1990, 11(4): 319-328.

Abstract(1953) PDF(652)

Abstract:
Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.

Free Vibration of a Class of Hill’s Equation Having a Small Parameter

Shao Xiao-huang, Wang Xin-zhi

1990, 11(4): 329-335.

Abstract(1699) PDF(567)

Abstract:
In this paper, we consider the initial value problem of a class of Hill's equation having a small parameter. Using the solvable condition of boundary value problem and the stretched parameter method in the perturbation techniques, we present the method which can be applied to obtain asymptotic periodic solution of the initial value problem. As an example, we consider Mathieu equation and present its computational result.

An Approach to the Elastic-Plastic Analysis of the Plane Strain Mode-Ⅰ Crack

Zhao Xue-ren

1990, 11(4): 337-340.

Abstract(1861) PDF(570)

Abstract:
This paper presents an approach to the solution of the approximate elastic-plastic analysis for the plane strain mode-Ⅰ crack.

Buckling and Postbuckling of Moderately Thick Plates

Shen Hui-shen

1990, 11(4): 341-350.

Abstract(2133) PDF(889)

Abstract:
This paper gives the basic differential equations for finite deflections of elastic plates according to Reissner's approximate stress distributions. The buckling and postbuckling problems of elastic rectangular plates, including the effect of transverse shear deformation, are solved and discussed, by using perturbation method suggested in ref. [8]. The postbuckling equilibrium paths of perfect and imperfect moderately thick rectangular plates are presented and compared with the results based on thin plate theory.

On Buckling of Cantilever Rectangular Plates under Symmetrical Edge Loading

Cheng Xiang-sheng

1990, 11(4): 351-356.

Abstract(1848) PDF(592)

Abstract:
The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by lite varialional calculus. We are going to find out the minimum critical loading for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We'll discuss the least critical loadings when the buckling of rectangular plates acted on bv a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.

Rates of Strong Uniform Convergence of Nearest Neighbor Density Estimates on Any Compact Set

Zhang Di-xin

1990, 11(4): 357-364.

Abstract(1850) PDF(556)

Abstract:
In this paper, we propose the concept of rates of strong uniform convergence of nearest neighbor density estimates on any compact set and obtain some better convergence rates. Hence the problem of the strong uniform convergence rates predetermined is its special example. The applied region of the estimate is extended.

The Rationalism Theory and Its Finite Element Analysis Method of Shell Structures

Li Long-yuan

1990, 11(4): 365-372.

Abstract(1838) PDF(639)

Abstract:
In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.