应用数学和力学

1996 Vol. 17, No. 8

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Non-Symmetrical Large Deformation of a Shallow Thin Spherical Shell

Wang Xinzhi, Ren Dongyun, Wang Linxiang, Yeh Kaiyuan

1996, 17(8): 667-683.

Abstract(1574) PDF(778)

Abstract:
By the modified iteration method,in this paper,nonsymmetrical large deflection of a shallow spherical shell is discussed.We solve the second-order approximate analytical solution of the deflection of a shallow spherical shell subjected to linearliquid loads.and portray the characteristic curves of load-deflection on a perturbing point.With this paper's method,the similar questions of other kind of shell can bediscussed.Through the examples.we discuss the large defection of a plane and shallow spherical shells with different initial deflections.

A Study of the Elasto-Plastic Axially Tensile Properties of Metal Matrix Composites with Fiber-End Debonding

Su Xiaofeng, Chen Haoran

1996, 17(8): 685-688.

Abstract(1515) PDF(516)

Abstract:
Bused on the generalized self-consistent finite element iterative averaging method.this paper studied the effects of the fiber-end debonding on the axially tensile elasto-plastic properties of SiC whiskers reinforced Aluminium matrix composite for variouscases of different.fiber's fiber's aspect ratios and volume fractions Compared with the casesof perfect interface,it could be concluded that the effects of fiber-end debonding willbecome weaker with the fiber aspect ratio increasing and greater as the fiber volumefraction increases.

Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation

Cai Chongxi, Lin Changhao

1996, 17(8): 689-698.

Abstract(2139) PDF(436)

Abstract:
In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation,i.e.we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentially wilh axial distance from the end of a semi-infinite strip.For the case of decay,we alsoestablish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.

The Law of the Iterated Logarithm of Random Weighting Approximation for Mean Error-Non.I.I.D.Situation

Wang Bingzhang, Peng Jianping

1996, 17(8): 699-707.

Abstract(1536) PDF(529)

Abstract:
For the dislribulion if mean error under independent but not identically dislribuled conditions,its approximating dislribution whose precision reach O(√lnlnn/n) is obtained.

Newtonian Mechanics on Kähler Manifold

Zhang Rongye

1996, 17(8): 709-719.

Abstract(2020) PDF(498)

Abstract:
In this paper we discuss Newtonian Mechanics on Kähler Manifold,and also givefoe complex mathematical aspects of Newton's law,the law of kinetic energy,the lawof kinetic quantity,the equation of motion and the "general equation of dynamics",and so on.

Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material

Wang Zhenqing, Shi Shouxia

1996, 17(8): 721-727.

Abstract(2088) PDF(509)

Abstract:
This paper contains an asymptotic.finite-deformation analysis about theelastostatic field near the,crack-tip in an incompress rubber-like material.The eracktip.field is divided into two narrowing sectors and one expanding seclor.By the newstyain energy funcion and deformation pattern,we derive and solve the asymptoticequations.for each sector of the tip.field.The singularity of the crack-tip field isdiscussed.The curves of stress-strain of foe crack-tip.field.for an incompress rubber-like material are given and the dominant behaviors of stress and strain near the,cracktip are revealed.

An Analytical Solution of Transverse Vibration of Rectangular Plates Simply Supported at Two opposite Edges with Arbitrary Number of Elastic Line Supports in one Way

Zhou Ding

1996, 17(8): 729-734.

Abstract(1923) PDF(446)

Abstract:
This paper presents presents a new analytical solution of transverse vibration of rectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way.The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate.The analytical solution of the differential equation of motion of the rectangular plate,which includes the unknown reaction forces.is gained.The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and the transverse displacements of the plale along the elastic line supports.There presentations of foe frequency equation and the mode shape functions are different from those obtained by other methods.

Elastic Pulse Buckling of Cylindrical Shells under Radial Impulsive Loading

Huang Chengyi, Liu Tuguang, Zheng Jijia

1996, 17(8): 735-741.

Abstract(1666) PDF(669)

Abstract:
When a cylindrical shell is subjected to dynamic implusive loading in radialdirection and foe ratio of radius-to-thickness exceeds a special value.the cylindricalshell will produce elastic dynamic buckling.This paper which is based on foe results ofsome relative experiments,assumes deformation mode and utilizes Lagrange method toanalyse the elastic pluse buckling of a thin cylindrical shell with a finite length under acosine impulse.The dynamic buckling equations are derived and solved by numericalmethod.The results of calculation are compared with some relative calculation resultswhich were obtained by other authors.

Zhang Shenxue

1996, 17(8): 743-747.

Abstract(2014) PDF(543)

Abstract:

A Group of Isoparametric Elements Suitable for St.Venant's Torsion of a Bar with Cracks

Fan Xiuchang, Wu Yueming

1996, 17(8): 749-757.

Abstract(2155) PDF(569)

Abstract:
In this paper,we shall give a group of new isoparametric elements suitable.for St.Wenant's torsion of a bar with vertical cracks.These elements are eight-point isoparametric element,quarter eight-Point isoparametric element and eight-point isoparametric transition element.Among these elements,the second and the third elements possess the singularity of order r^-1/2 at crack tip.Using these elements,wehave completed the calculations of St.Venant's torsion for a cylinder with a radial vertical crack.The calculated results show that the isoparametric elements given bythis paper have ideal accuracy,good convergence.high speed of convergence,low freedom and little computational time,and so they can be widely applied to practice.

1996, 17(8): 758-760.

Abstract(1542) PDF(542)

Abstract: