应用数学和力学

1992 Vol. 13, No. 10

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Large Deflection Problem of a Clamped Elliptical Plate Subjected to Uniform Pressure

Chien Wei-zang, Pan Li-zhou, Liu Xiao-ming

1992, 13(10): 857-871.

Abstract(2416) PDF(569)

Abstract:
In this paper,the perturbation solution of large deflection problem of clampedelliptical plate subjected to uniform pressure is given on the basis of the perturbationsolution of large deflection problem of similar clamped circular plate (1948)^[1],(1954)^[2].The analytical solution of this problem was obtained in 1957.However,due to social difficulties,these results have never been published.Nash and Cooley (1959)^[3] published a brief note of similar nature,in which only the case λ=a/b=2 is given.In this paper,the analytical solution is given in detail up to the 2nd approximation.The numerical solutions are given for various Poisson ratios ν =0.25,0.30,0.35 and for various eccentricities λ=1,2,3,4,5,which can be used in the calculation of engineering designs.

A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form

Wu Qi-guang, Sun Xiao-di

1992, 13(10): 873-880.

Abstract(2389) PDF(533)

Abstract:
A uniform high-order method is.presented for the numerical solution of a singular perturbation problem in conservative form.We firest replace the original second-order problem (1.1) by two equivalent first-order problems (1.4),i.e.,the solution of (1.1) is a linear combination of the solutions of (1.4).Then we derive a uniformly O(^hm+1) accurate scheme for the first-order problems (1.4),where m is an arbitrary nonnegative integer,so we can get a uniformly O(^hm+1) accurate solution of the original problem (1.1) by relation (1.3).Some illustrative numerical results are also given.

Finite Layer Analysis for Semi-Infinite Soils (Ⅰ)——General Theory

Yang Zheng-wen, Loo Wen-da

1992, 13(10): 881-890.

Abstract(2325) PDF(609)

Abstract:
In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies.With this method,semi-infinite soils can be considered as an transverse isotropic half-space,its material functions varying with depth.Dividing the half-space into a scries of layers in the direction of depth,the material junctions in each layer are simulated by exponential functions Consequently,the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used.We have obtained the relationship between the "layer forces" and "layer displacements".This finite layer method,in fact,can also be called a semi-analytical method.It possesses those advantages as the usual semi-analytical methods do,and can be used to analyse the problem of the interaction between soils and structures.

Finite Element Analysis for Consolidation in Interaction between Structure and Saturated Soil Foundation

Zhang Hong-wu, Zhong Wan-xie, Qian Ling-xi

1992, 13(10): 891-899.

Abstract(2051) PDF(573)

Abstract:
The consolidation analysis of interaction between structure and saturated soil foundation is discussed.With the use of substructure technique,the structure is condensed onto the interface of the soil,and then the consolidation governing equations to describe the interaction between soil and structure are derived,The solution with non-iterative algorithm is proposed in this paper.The pressure Master-Slave relation method is used to deal with the non-permeability conditions on soil boundaries.A numerical example is illustrated.Based on this paper,the interactive consolidation analysis between large structure and soil has been more practical.

An Engineering Formula on the Calculation of Oblique Penetration by Long-Rod Projectile

Wang Li-ren

1992, 13(10): 901-906.

Abstract(2191) PDF(487)

Abstract:
Based on the concept supposed in this paper that damage of a target is determined by momentum rather than by stress,an engineering formula on the calculation of oblique penetration by long-rod projectile is established.The results calculated from this formula show good agreements with experimental data.

Applications of the Signs of Melnikov’s Function

Shen Jia-qi

1992, 13(10): 907-910.

Abstract(2164) PDF(551)

Abstract:
The existence and stability ol periodic solutions for the two-dimensional system x'=f(x)+εg(x,a),0<ε<<1,a∈R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function.The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.

On the Coupled Vibration of an Ideal Fluid with a Linear Elastic Structure

Huang Zheng-ming

1992, 13(10): 911-924.

Abstract(2015) PDF(617)

Abstract:
The purpose of this paper is to analyse theoretically and numerically the coupled vibration of an ideal fluid with a linear elastic structure,It is proved in the paper that the natural frequencies of the coupled vibration do exist and are all real positive.The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the vibrational analysis of the former is replaced by the latter in vacuum only.Numerical solution is outlined for the transformed problem and a compact jrequeney equation is derived in which fluid variables do not appear.This simplifies the analysis significantly.A convergent proof has been given to guarantee the reliability of the solution.The paper also offers a general algorithm combined with Ritz method,boundary element method,and finite element method to analyse the transformed problem.Based on this algorithm,one can apply a known structural analysing program,with a little modification,to solve many different kinds of fluid-structure coupling problems.Some numerical results are given to show the efficiency of the algorithm.

A Fully Elliptic Calculating Procedure for Three Dimensional Thermal Pollution

Li Jia, Zhao Wen-qian, Luo Lin

1992, 13(10): 925-933.

Abstract(1929) PDF(510)

Abstract:
The use of the mathematical models so far for three-dimensional flow has some limitations because of their simplifications.Many characteristics of the flow field can not be predicted by these models.In this paper the three dimensional elliptic governing equations are solved by finite-volume methods;the buoyancy extensions of the widely tested k-ε.model is adapted.The method is first applied to calculate the field of side discharge into open channel flow.The results are in good agreement with those of ref.[7].Then it is further used to the intake discharge problem which is of a typical layout in cooling-water projects,and the calculated results,which predict in detail the charactreistics of flow field,are reasonable.

A Free Rectangular Plate on Elastic Foundation

Cheng Xiang-sheng

1992, 13(10): 935-940.

Abstract(2278) PDF(630)

Abstract:
This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations.We talk over the two cases,that is,the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively.We select a flexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces.We apply the variational method meanwhile and then obtain better approximate solutions.

The Existence of Solution of a Class of Two-Order Quasilinear Boundary Value Problem

He Qing, Ji Chun-ci

1992, 13(10): 941-944.

Abstract(1637) PDF(445)

Abstract:
Ref.[1] discussed the existence of positive solutions of quasilinear two-point boundary problems: but it restricts 0<α<1<β.This article proves the existence of positive solution to this equation: