应用数学和力学

2009 Vol. 30, No. 3

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Systems of Generalized Vector Quasi-Variational Inclusions and Systems of Generalized Vector Quasi-Optimization Problems in Locally FC-Uniform Spaces

DING Xie-ping

2009, 30(3): 253-264.

Abstract(3207) PDF(720)

Abstract:
Some new systems of generalized vector quasivariational inclusion problems and system of generalized vector ideal(resp., proper, Pareto, weak) quasioptimization problems in locally FC-uniform spaces without convexity structure are introduced and studied. By using KKM type theorem and Himmelberg type fixed point theorem, some new existence theorems of solutions for the systems of generalized vector quasivariational inclusion problems were first proved. As applications, some new existence results of solutions for systems of generalized vector quasioptimization problems were obtained also.

Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

HUANG Ding-jiang, ZHANG Hong-qing

2009, 30(3): 265-281.

Abstract(3281) PDF(805)

Abstract:
Group classification of quasilinear thir dorder evolution equations is performed by using the classical infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract low-dimensional Lie algebras. It is indicated that there are three equations admitting simple Lie algebras of dimension three. What's more, all the inequivalent equations admitting simple Lie algebra are nothing but them. Further more, it is also shown that there exist two, five, twenty-nine and twenty-six inequivalent third or der nonlinear evolution equations a dmitting one-, two, three, and fourdimensional solvable Lie algebras, respectively.

Analysis of Multiple Interfacial Cracks in Three Dimensional Bimaterials Using Hypersingular Integral-Differential Equation Method

XU Chun-hui, QIN Tai-yan, YUAN Li, Noda Nao-Aki

2009, 30(3): 282-290.

Abstract(3913) PDF(621)

Abstract:
Using the finite-part integral concepts, a set of hypersingular integraldifferential equations for multiple interfacial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads was derived. In the numerical analysis, unknown displacement discontinuities were approximated by the products of the fundamental density functions and power series, where the fundamental functions were chosen to express a two-dimensional interface crack exactly. As illustrative examples, the stress intensity factors for two rectangular interface cracks were calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the increasing of crack spacing.

Characteristic-Based Finite Volume Scheme for 1D Euler Equations

GUO Yan, LIU Ru-xun

2009, 30(3): 291-300.

Abstract(3411) PDF(1367)

Abstract:
A highorder finitevolume scheme was presented for the onedimensional scalar and inviscid Euler conservation laws. The Simpson's quadrature rule was used to achieve highorder accuracy in time. To get the point value of the Simpson's quadrature, the characteristic theory was used to obtain the positions of the grid points at each sub-time stages along the characteristic curves, and the thirdorder and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction was adopted to estimate the cell point values. Several standard one-dimensional examples were used to verify highorder accuracy, convergence and capability of capturing shock.

Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities

HU Yan-hong, SONG Wen

2009, 30(3): 301-308.

Abstract(3336) PDF(769)

Abstract:
Some classes of generalized gap functions for two kinds of generalized variational inequality problems are considered. Error bounds for the underlying variational inequalities by using the generalized gap functions under the condition that the involved mapping F is gstrongly monotone with respect to the solution were obtained. It is not necessary to suppcsethat Fis continuously differential nor of local Lipschitz. with respect to the solution were obtained. It is not necessary to suppose that Fis continuously differentiable local Lipschitz.

Micromechanical Damage Model for Rocks and Concretes Under Triaxial Compression

REN Zhong-jun, PENG Xiang-he, HU Ning, YANG Chun-he

2009, 30(3): 309-317.

Abstract(3049) PDF(717)

Abstract:
Based on the analysis of the deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion were obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth was derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack was also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, was analyzed with the Taylor's scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression was obtained and experimentally verified.

Parametric Studies on the Relationships of Flutter Derivatives of Slender Bridge(Ⅱ)

XU Xu

2009, 30(3): 318-324.

Abstract(2784) PDF(609)

Abstract:
Based on the curves fitting of coefficients of three component forces of Messina Straits bridge, and the semianalytical expressions of flutter derivatives of flexible structure provided by the author(XU Xu, CAO Zhi-yuan. Linear and nonlinear aerodynamic theory of interaction between flexible long structrure and wind. Appli ed Mathem atical and Mechan ics, 2001, 22(12):1299-1308.), the changing of flutter derivatives of slender bridge cross-section with its aerodynamic center, rotational speed and angles variation was researched by parametric method. Not only comparison the calculated results of flutter derivatives with the tested ones were investigated, but also the expressions of flutter derivatives of Messina Straits bridge were formulated. The intrinsic relations existing in flutter derivatives were validated once again. It is showed that the influences of rotational speed on flutter derivatives can not be ignored; so it is really a supplementary and trial way to use the semianalytical method to analyze flutter derivatives of the bridge with streamlined cross-section for getting its aerodynamic information.

Study on Velocity Distribution of Flow With Submerged Flexible Vegetations Based on Mixing-Length Approach

HUAI Wen-xin, HAN Jie, ZENG Yu-hong, AN Xiang, QIAN Zhong-dong

2009, 30(3): 325-332.

Abstract(4418) PDF(798)

Abstract:
Choosing PVC slice to simulate the flexible vegetation, the laboratory experiments were carried out in an open channel with submerged flexible vegetation, and 3D acoustic Doppler velocimeter (Micro ADV) was introduced to measure the local flow velocities and Reynolds stress. The result showed that the hydraulic characteristics in the non-vegetation layer and the vegetation layer are totally different. In the region above the vegetation, Reynolds stress's distribution is linear; meanwhile, measured velocity's profile is a classical logarithmic one. Based on the concept of nwe/riverbed0, the river compress parameter which represented the impact of vegetation on river was given for the first time and a new mixing length expression was assumed with reason. The formula of time-averaged velocity deduced from the mixing length expression had advantages of less parameters needed, simple calculation and useful application.

Elastodynamic Analysis at an Interface of Viscous Fluid/Thermoelastic Micropolar Honeycomb Medium due to Inclined Load

Rajneesh Kumar, Rajani Rani Gupta

2009, 30(3): 333-344.

Abstract(3272) PDF(615)

Abstract:
The effect of angle of inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load was assumed to be a linear combination of normal load and tangential load. The Laplace transform with respect to time variable and Fourier transform with respect to space variable were applied to solve the problem. The expressions in transformed domain of stresses, temperature distribution and pressures were obtained by introducing potential functions. The numerical inversion technique was used to obtain the solution in the physical domain. The expressions in frequency domain and for steady state situation were also obtained with the appropriate change of variables. Graphical representation due to the response of different sources and change of angle of inclination were shown. Some particular cases were also discussed.

Engineering Analysis of Penetration of a Metal Ball Into Fibre-Reinforced Composite Targets

LI Yong-chi, WANG Zhi-hai, WANG Xiao-jun, HU Xiu-zhang

2009, 30(3): 345-352.

Abstract(3003) PDF(567)

Abstract:
An engineering analysis method of computing the penetration problem of a steel ball penetrating into fibre-reinforced composite targets is presented. The metal ball was assumed to be a rigid body, and the composite target was regarded as a transversely isotropic elasto-plastic material. In the analysis, the spherical cavity dilatation model is coupled with the cylindrical cavity penetration method. The simulation results based on the modified model are in good agreement with the results for the 3D Kevlar woven composite (3DKW) antipenetration experiments. Furthermore, the effects of the target material parameters and impact parameters on the penetration problem were also studied.

Thermal Criticality for a Reactive Gravity Driven Thin Film Flow of a Third Grade Fluid With Adiabatic Free Surface Down an Inclined Plane

Oluwole Daniel Makinde

2009, 30(3): 353-359.

Abstract(2800) PDF(640)

Abstract:
The thermal criticality for a reactive gravity driven thin film flow of a third grade fluid with adiabatic free surface down an inclined isothermal plane is investigated. It was assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy were obtained and solved using a new computational approach based on a special type of Hermite-Pad approximation technique implemented on MAPLE. This seminumerical scheme offers some advantages over solutions obtained by using traditional methods such as finite differences, spectral method, shooting method, etc. It reveals the analytical structure of the solution function and the important properties of overall flow structure including velocity field, temperature field, thermal criticality and bifurcations were discussed.

Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes

LIN Zheng-yan, CHENG Zong-mao

2009, 30(3): 360-368.

Abstract(2578) PDF(670)

Abstract:
The definition of multiparameter fractional Lvy process which more general than that studied by Xiao and Zhang was introduced firstly, and then a decomposition for it was given and shown. Later using this decomposition, existence and joint continuity of its local time were proved.

Initial Value Problem for a Class of Nonlinear Wave Equations of Fourth Order

CHEN Guo-wang, HOU Chang-shun

2009, 30(3): 369-378.

Abstract(3467) PDF(970)

Abstract:
The existence and the uniqueness of the global generalized solution and the global classical solution to the initial value problem for a class of nonlinear wave equation of fourth order are studied in the fractional order Sobolev space by the contraction mapping principle and the extension theorem. The sufficient conditions for blow up of the solution to the above initial value problem are given.