应用数学和力学

1992 Vol. 13, No. 3

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Studies on the Torsional Buckling of Elastic Cylindrical Shells

Wang De-yu, Ma Hong-wei, Yang Gui-tong

1992, 13(3): 193-197.

Abstract(2399) PDF(775)

Abstract:
The experimental phenomenon and theoretical analysis are given for the torsional buckling of elastic cylindrical shells. From the experiment, it is found that the postbuckling deformation doesn't occupy the whole length when the shell is longer. In the theoretical calculation, only the normal displacement boundary condition is taken into account. By comparing the present calculation results with the accurate result of Yamakis theory and the results of the present experiment, it is shown that the influence of the axial and circumference boundary condition is less important.

Heteroclinic Orbit and Subharmonic Bifurcations and Chaos of Nonlinear Oscillator

Zhang Wei, Huo Quan-zhong, Li Li

1992, 13(3): 199-208.

Abstract(2475) PDF(771)

Abstract:
Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.

Minimal and Maximal Fixed Point Theorems and Iterative Technique for Nonlinear Operators in Product Spaces

Lan Kun-quan, Ding Xie-ping

1992, 13(3): 209-213.

Abstract(1809) PDF(529)

Abstract:
In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham^[2] and the results obtained by Lan in [4] and [6].

The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems

Liu Ru-xun

1992, 13(3): 215-222.

Abstract(2337) PDF(531)

Abstract:
In this paper a new approach for designing upwind type schemes-the characterizing-integral method and its applied skills are introduced. The method is simple, convenient and eff ective. And the method isn't only limited to conservation laws unlike other methods and maybe easily extended to multi-dimension problems. Furthermore, the numerical dissipation of the method can be flexibly regulated, so that it is especially suitable for solving various discontinuity problems.The paper shows us now to use this approach to simulate deformation and breaking of a nonlinear shallow water wave on a gentle slope, and to compute two-dimensional dam failure problem.

On the Throughflow with Swirling Inflow in Annular Diffuser

Yu Ji-lun, Yang Zhao-gang, Wang Ming-de

1992, 13(3): 223-235.

Abstract(1844) PDF(485)

Abstract:
In this paper, a throughflow with swirling in flow in an annular diffuser is calculated. Under the assumption of small cross-flow, the flow near inner and outer wall surfaces is calculated based on the three-dimensional momentum integral equation of the boundary layer. The potential flow outside the boundary layer is computed by means of the iteration method based on the velocity gradient equation along the quasi-orthogonal direction of the meridional projection of the stream-line on the meridional surface and the constancy of flux equation^[1]. The numerical results agree with the experiments quite well. This method is useful for analyzing the through flow with pre-swirl in the annular diffuser.

On Nonlinear Hyperbolic Equation in Unbounded Domain

Geng Di, Qu Chang-zheng

1992, 13(3): 237-243.

Abstract(2202) PDF(491)

Abstract:
The following nonlinear hyperbolic equation is discussed in this paper:u_tt+A²u+M(x,||A^1/2u||₂²)Au=0, where A=-Δ+I and x∈Rⁿ. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.

Perturbation Solution of Non-Newtonian Fluid Axial Laminar Flow through Eccentric Annuli

Yue Xiang-an, Kong Xiang-yan, Chen Jia-lang

1992, 13(3): 245-254.

Abstract(2642) PDF(544)

Abstract:
Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity ε is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.

An Extremum Theory of the Residual Functional in Sobolev Spaces W^{m, p}(Ω)

Ling Yong-yong

1992, 13(3): 255-262.

Abstract(2492) PDF(531)

Abstract:
In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.

On J-lntegrals in the Plane Fracture of Composite Materials

Yang Wei-yang, Zhang Shao-qin, Jia Yuan-duo

1992, 13(3): 263-269.

Abstract(2616) PDF(616)

Abstract:
By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.

Effect of the Poisson Ratio on the Perfectly Plastic Stress Field at a Stationary Plane-Strain Crack Tip

Lin Bai-song

1992, 13(3): 271-278.

Abstract(2635) PDF(568)

Abstract:
Under the condition that all the perfectly plastic stress components at a crack tip are the functions of θ only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode Ⅰ, Mode Ⅱ and Mixed-Mode Ⅰ-Ⅱ plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.