应用数学和力学

1997 Vol. 18, No. 4

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A Calculation Method for Fully Developed Flows in Curved Rectangular Tubes

Lu Zhiming, Liu Yulu

1997, 18(4): 291-296.

Abstract(2353) PDF(520)

Abstract:
In this paper, A method, consisted of perturbation method, Garlerkin method andfinite-difference method, is designed to calculate fully developed flows in curved tubes ofrectangular cross-section. It costs less computation than that of direct solving N-Sequations, and prevents from building high-order difference equations and extra dealingwith the boundary conditions. Numerical results in the situation of small curvature and lowDean number is in accordance with former's numerical and experimental results in quality,and it shows the feasibility of this paper's method.

Nonlinear Theory of Multilayer Sandwich Shells and lts Application(Ⅲ)-Large Deflection and Postbuckling of Shallow Shells

Wu Jiancheng, Pan Lizhou

1997, 18(4): 297-306.

Abstract(2517) PDF(552)

Abstract:
In this paper, exact solutions of large deflection of multilayer sandwich shallow shellsunder transverse forces and different boundary conditions are presented. Exact results ofpostbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlineardeflection of general shallow shells such as spherical shells under inplane edge forcesare also obtained by the same procedure.

An Explicit Tensor Expression for the Fundamental Solutions of a Bimaterial Space Problem

Chen Mengcheng, Tang Renji

1997, 18(4): 307-315.

Abstract(2652) PDF(594)

Abstract:
In this paper, by using the method of tensor operation, the fundamental solutions,given in the references listed, for a concentrated force in a three-dimensional biphaseinfinite solid were expressed in the tensor form, which enables them to be directly appliedto the boundary integral equation and the boundary element method for solving elasticmechanics problems of the bimaterial space. The fundamental solutions for Mindlin'sproblem, Lorentz's problem and homogeneous space problem ore involved in the present results.

Bounds of the Expansion Coefficients of Composites Reinforced by Spherically Isotropic Particles

He Linghui, Liu Renhuai

1997, 18(4): 317-323.

Abstract(2069) PDF(462)

Abstract:
The present paper is devoted to the study of expansional behaviours of a compositerein forced by spherically isotropic particles. An exact relation is derived between the effective expansion coefficient and bulk modulus of the composite by using the concept ofuniform fields in the matrix which is proposed here. Through obtaining the Paul-typebounds of the bulk modulus by using the extreme principle of energy, bounds of the effective expansion coefficient are also derivded.

Normal Form of the Nonsemi-Simple Bifurcation Problem

Wu Zhiqiang, Chen Yushu, Bi Qinshen

1997, 18(4): 325-330.

Abstract(2201) PDF(635)

Abstract:
On the basis of the method proposed in[1]. the paper gives the method for finding thenormal form of nonsemi-simple bifurcation problems. As an example, it analyses thenormal form of a general nonlinear dynamical system with the nonsemi-simple double zeroeigenvalues, and gives out the expression for the coefficients in the normal form by usingthose in the original system.

Nonlinear Problems of Current-Carrying Round Plates with Varying Thickness in the Electromagnetic Field

Chang Fuqing, Xu Yaoling, Bai Xiangzhong

1997, 18(4): 331-339.

Abstract(2201) PDF(557)

Abstract:
In this paper, the equations of motion and two-dimensional magnetoelastic equationsof current-carrying round elastic plates with varying thickness in nonlinear deformation inthe unsteady electromagnetic field and mechanical field are establishied, and the numeralsolutions of round elastic plates in axisymmetrical deformation are given.

The General Solution of Second order Effects in Elastic Half-Space Acted upon by a Non-Uniform Shear Load

Liu Youwen, Gou Jianlin

1997, 18(4): 341-355.

Abstract(2557) PDF(610)

Abstract:
This paper is a continuation of [1]. A closed form solution to the second orderelasticity problem, when an isotropic compressible elastic half-space undergoes adeformation owing to a non-uniformly distributed shear load, is presented. The method ofintegral transform is employed to determine the solutions.

On One of Graffiti’s Conjecture(583)

Wang Liuxing

1997, 18(4): 357-360.

Abstract(2155) PDF(502)

Abstract:
In the paper, a counterexample of the Graffiti's conjecture(583) is given out whichproves the conjecture is false. And the best bounds of I(T)+a'(T) are got, where Tdenotes a free, I(T) denotes the inverse degree of T and a'(T) is the matching of T.

A New Solution to Structural Fuzzy Finite Element Equilibrium Equations(SFFEEE)

Lü Enling

1997, 18(4): 361-366.

Abstract(2605) PDF(737)

Abstract:
A speedy accurate solution to structural fuzzy finite element equilibrium equations(SFFEEE), by combining the definition of the solution of interval equations with themechanical meaning of the structural finite element equilibrium equations(SFEEE), wasput forward. The fuzzification of the SFFEEE, which is discussed in this paper, originatesfrom that of material property, structural conditions and external loading. Thecomputing quantity of this solution is almost equal to that of the general finite elementmethod(GFEM).

Higher Order Sensitivities in Structural Static Design

Li Shu, Feng Taihua

1997, 18(4): 367-372.

Abstract(2777) PDF(641)

Abstract:
In this paper, structural static design is considered as a kind of inverse algebraiceigenvalue problem. It is the most important task for for the inverse problem to compute thesensitivities of eigenvalues and eigenvectors. Therefore. a complete set of higher ordersensitivity expressions has been presented based on the complex variables theory. Theseexpressions have solid mathematical foundation and practical significance.

Plastic Dynamic Stability of a Column under Nonconservative Forces

Jie Min

1997, 18(4): 373-379.

Abstract(2430) PDF(475)

Abstract:
In this paper Liapunov’s second method is used to analyze the plastic dynamicstability of a column under nonconservative forces. The column is in a viscous medium, andunder the action of uniformly distributed tangential follower forces. The strain-rate effecton the stress-strain relation of materials is included in the analysis. A condition of stabilityis derived. and the critical buckling food is obtained. The strain-rate effect on the stabilityof the column is discussed.

On(g, f)-Factorizations of Graghs

Ma Runnian, Gao Hangshan

1997, 18(4): 381-384.

Abstract(2319) PDF(547)

Abstract:
Let G be a graph and g, f be two nonnegative integer-valued functions defined on thevertices set V(G) of G and g≤f, A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)≤d_F(x)≤f(x) for all x∈V(G). If G itself is a (g, f)-factor, then itis said that G is a (g, f)-graph. If the edges of G can be decomposed into some edgedisjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, onesufficient condition for a graph to be (g, f)-factorable is given.