应用数学和力学

2003 Vol. 24, No. 9

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Analysis of Elastic Layers with Dilative Eigenstrains Varying Through the Thickness

HE Ling-hui, LIM Chee-wah, LIU Ren-huai

2003, 24(9): 881-891.

Abstract(2114) PDF(624)

Abstract:
Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state-space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid-plane, which are governed by a set of two-dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two-dimensional equations immediately gives the three-dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.

Cavity Formation at the Center of a Sphere Composed of Two Compressible Hyper-Elastic Materials

REN Jiu-sheng, CHENG Chang-jun, ZHU Zheng-you

2003, 24(9): 892-898.

Abstract(2222) PDF(623)

Abstract:
The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials under a uniform boundary radial stretch was examined. The solutions, including the trivial solution and the cavitated solutions, were obtained. The bifurcation curves and the stress contributions subsequent to cavitation were discussed. The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.

Maximal Elements for G_B-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅱ)

DING Xie-ping

2003, 24(9): 899-905.

Abstract(2337) PDF(800)

Abstract:
By applying existence theorems of maximal elements for a family of G_B-majorized map-pings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature.

Suarface Effects of Internal Wave Generated by a Moving Source in a Two-Layer Fluid of Finite Depth

WEI Gang, LE Jia-Chun, DAI Shi-qiang

2003, 24(9): 906-918.

Abstract(2605) PDF(740)

Abstract:
Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green. s function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr₂. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.

Controllability of a Class of Hybrid Dynamic Systems(Ⅰ)—Basic Properties and Preliminary Results

XIE Guang-ming, WANG Long, YE Qing-kai

2003, 24(9): 919-928.

Abstract(2538) PDF(766)

Abstract:
The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. First, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitoins and lemmas are necessary research tools for controllability analysis.

Controllability of a Class of Hybrid Dynamic Systems(Ⅱ) Single Time-Delay Case

XIE Guang-ming, WANG Long, YE Qing-kai

2003, 24(9): 929-939.

Abstract(2590) PDF(670)

Abstract:
The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the 1-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively.

Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case

XIE Guang-ming, WANG Long, YE Qing-kai

2003, 24(9): 940-950.

Abstract(2417) PDF(518)

Abstract:
The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the 1-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.

Numerical Simulation for Formed Projectile of Depleted Uranium Alloy

SONG Shun-cheng, GAO Ping, CAI Hong-nian

2003, 24(9): 951-955.

Abstract(2269) PDF(565)

Abstract:
The numerical simulation for forming projectile of depleted uranium alloy with the SPH (Smooth Particle Hydrodynamic) algorithm was presented. In the computations the artificial pressures of detonation were used, i. e. the spatial distribution and time distribution were given artificially. To describe the deformed behaviors of the depleted uranium alloy under high pressure and high strain rate, the Johnson-Cook model of materials was introduced. From the numerical simulation the formed projectile velocity, projectile geometry and the minimum of the height of detonation are obtained.

Hybrid Finite Analytic Solutions of Shallow Water Circulation

HUAI Wen-xin, Y. Peter Sheng, T. Komatsu

2003, 24(9): 956-962.

Abstract(2288) PDF(542)

Abstract:
The hybrid finite analytic(HFA) method is a kind of numerical scheme in rectangular element. In order to simulate the shallow circulation in irregular bathymetry by HFA scheme, the model in sigma coordinate system was obtained. The model has been tested against three cases: 1) wind induced circulation, 2) density driven circulation and 3) seiche oscillation. The results obtained in the present study compare well with those obtained from the corresponding analytical solutions under idealized for the above three cases. The hybrid finite analytic method and the circulation model in sigma coordinate system can be used calculate the flow and water quality in estuaries and coastal waters.

Visco-Elastic Systems Under Both Deterministic and Bound Random Parametric Excitation

XU Wei, RONG Hai-wu, FANG Tong

2003, 24(9): 963-972.

Abstract(2757) PDF(496)

Abstract:
The principal resonance of a visco-elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analyses. The contributions from the visco-elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, band-width, and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses are verified by numerical results.

Difference Scheme and Numerical Simulation Based on Mixed Finite Element Method for Natural Convection Problem

LUO Zhen-dong, ZHU Jiang, XIE Zheng-hui, ZHANG Gui-fang

2003, 24(9): 973-983.

Abstract(2568) PDF(499)

Abstract:
The non stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.

Post-Buckling of a Cantilever Rod with Variable Cross-Sections Under Combined Load

WU Ying, LI Shi-rong, TENG Zhao-chun

2003, 24(9): 984-990.

Abstract(2174) PDF(602)

Abstract:
Based on the geometrically non-linear theory of axially extensible elastic rods, the governing equations of post-buckling of a clamped-free rod with variable cross-sections, subjected to a combined load, a concentrated axial load P at the free end and a non-uniformly distributed axial load q,are established. By using shooting method, the strong nonlinear boundary value problems are numerically solved. The secondary equilibrium paths and the post-buckling configurations of the rod with linearly varied cross-sections are presented.