应用数学和力学

1991 Vol. 12, No. 4

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Perturbation Solution to the Nonlinear Problem of Oblique Water Exit of an Axisymmetric Body with a Large Exit-Angle

Ye Qu-yuan, He You-sheng

1991, 12(4): 303-313.

Abstract(2522) PDF(599)

Abstract:
In this paper,a nonlinear,unsteady 3-D free surface problem of the oblique water exit of an axisymmetric body with a large water exit-angle was investigated by means of the perturbation method in which the complementary angle a of the water exit angle was chosen as a small parameter.The original 3-D problem was solved by expanding it into a power series of a and reduced to a number of 2-D problems.The integral expressions for the first three order solutions were given in terms of the complete elliptic functions of the first and second kinds.The zeroth-order solution didn't turn out to be a linear problem as usual but a nonlinear one corresponding to the vertical water exit for the same body.Computational results were presented for the free surface shapes and the forces exerted up to the second order during the oblique water exit of a series of ellipsoids with various rat ios of length to diameter at different Froude numbers.

Why Can the Major Planets Have Their Satellites Moving in Direct and Retrograde Orbits As Well?

Wong Chia-ho

1991, 12(4): 315-319.

Abstract(2715) PDF(606)

Abstract:
Now we use the Jacobian integral of circular restricted three-body problem to establish a testing function of the stability of satellites.This method of criterion may be applied to the stability problem of satellites when the six elements of the instantaneous orbit of the satellite with respect to its parent planet are known.By means of an electronic computer,we can find the stable region of a satellite with a quasi-circular orbit.The boundary surface of this region is a nearly oblate ellipsoid.The volume of this enclosed space is much smaller than that of binding by Hill surface and that of "sphere of action".As the expressions of relative kinetic energy of a satellite with respect to its parent planet have the same form for the direct as well as the retrograde orbits,they can coexist in the same region at the same time.

The Theory of Static Decay in Computational Mechanics

Wu Jian-xun

1991, 12(4): 321-330.

Abstract(2801) PDF(764)

Abstract:
In this paper,a new mathematical form,matrix,continued fraction(MCF) is introduced to describe the decay of effects of an equilibrant system of forces acting on a sphere of an elastic body.By this way,the famous Saint-Venant's principle is proved often but not always valid in computational mechanics.

Elastic Instability of an Orthotropic Elliptic Plate

Cheng Chang-jun, Ning Jian-guo

1991, 12(4): 331-338.

Abstract(2633) PDF(709)

Abstract:
On the basis of von Karman equations and using the general bifurcation theory,the elastic instability of an orthotropic elliptic plate whose edge is subjected to a uniform plane compression is discussed.Following the well-known Liapunov-Schmidt process the existance of bifurcation solution at a simple eigenvalue is shown and the asymptotic expression is obtained by means of the perturbation expansion with a small parameter.Finally,by using the finite element method,the critical loads of the plate are computed and the post-buckling behavior is analysed.And also the effect of material and geome trie parameters on the stability is studied.

Fixed Point Theorems of Local Contraction Mappings on Menger Spaces

Fang Jin-xuan

1991, 12(4): 339-347.

Abstract(2414) PDF(703)

Abstract:
In this paper,we introduce the concept of ε-chainable PM-space,and give several fixed point theorems of one-valued and multivalued local contraction mapping on the kind of spaces.

Navier Solution for the Elastic Equilibrium Problems of Anisotropic Skew Thin Plate with Variable Thickness in Nonlinear Theories

Zhou Qing-qing

1991, 12(4): 349-358.

Abstract(2272) PDF(650)

Abstract:
This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories,and uses the Navier method to seek an approach to the problem,and to illustrate the solution with the examples.In conclusion,the mention is made of the scope of application and the convergency of the solution.

A New Displacement-Type Stability Equation and General Stability Analysis of Laminated Composite Circular Conical Shells with Triangular Grid Stiffeners

Wang Hu, Tsun-kuei

1991, 12(4): 359-368.

Abstract(2640) PDF(710)

Abstract:
In this paper,based on the theory of Donnell-type shallow shell,a new displacement-type stability equations is first developed for laminated composite circular conical shells with triangular grid stiffeners by using the variational calculus and generalized smeared-stiffener theory.The most general bending stretching couplings,the effect of eccentricity of stiffeners are considered.Then,for general stability of composite triangular grid stiffened conical shells without twist coupling terms,the approximate formulas are obtained for critical external pressure by using Galerkin's procedure.Numerical examples for a certain C/E composite conical shells with inside triangular grid stiffeners are calculated and the results are in good agreement with the experimental data.Finally,the influence of some parameters on critical external pressure is studied.The stability equations developed and the formulas for critical external pressure obtained in this paper should be very useful in the astronautical engineering design.

Plane-Stress Crack-Tip Stress Fields for Orthotropic Perfectly-Plastic Materials

Fan Ji-xia, Yuan Zu-pei

1991, 12(4): 369-374.

Abstract(2169) PDF(581)

Abstract:
Under the hypothesis that the stress components of crack-tip fields are only the functions of θ,the differential equations of plane-stress crack-tip stress fields for orthotropic perfectly-plastic materials are obtained by using Hill's yield condition and equilibrium equations.By combining the general analytical expression with the numerical method the crack-tip stress fields for orthotropic perfectly-plastic materials for plane stress are presented.

Singular Perturbation of Initial-Boundary Value Problems for a Class of Reaction Diffusion Systems

Mo Jia-qi

1991, 12(4): 375-384.

Abstract(2199) PDF(639)

Abstract:
In this paper,a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered.Using the theory of differential inequality,we prove that the initial-boundary value problems have a solution and obtain their asymptotic expansion.

Iterative Approximation of the Solution of a Locally Lipschitzian Equation

Zou Bao-kang

1991, 12(4): 385-389.

Abstract(2727) PDF(541)

Abstract:
Suppose X=L_p(or l_p),p>2,T:D(T)→X is a locally Lipschitzian and strictly accretive operator.In this paper,the iterative approximation of the solution of nonlinear equation Tx=y is given and the iterative approximation of a fixed point of a locally Lipschitzian and strictly pseudo-contractive mapping is discussed.

Remarks of Some Problems for Rectangular Thin Plates with Free Edges on Elastic Foundations

Tan Jun-yu

1991, 12(4): 391-396.

Abstract(2028) PDF(645)

Abstract:
For the bending,stability and vibrations of rectangular thin plates with free edges on elastic foundations,in this paper we give a flexural function which exactly satisfies not only all the boundary conditions on free edges but also the conditions at free corner points.Applying energy variation principle,we give equations defining parameters in flexural function,stability equation,frequency equation,and general formulae of minimum critical force and minimum eigenfrequency as well.