Applied Mathematics and Mechanics (English Edition)

Systems of variational inclusions and optimization problems in locally FC-uniform spaces

丁协平

2009, 30(3): 263-274. doi:10.1007/s10483-009-0301-z

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In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

Preliminary group classification of quasilinear third-order evolution equations

黄定江;张鸿庆

2009, 30(3): 275-292. doi:10.1007/s10483-009-0302-z

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Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three.
Furthermore, we also show that there exist two, five, twenty-nine and twenty-six nonequivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

徐春晖;秦太验;袁丽;野田尚昭

2009, 30(3): 293-301. doi:10.1007/s10483-009-0303-z

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By using the concept of finite-part integral, a set of hypersingular integrodifferential equations for multiple interfacial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

Characteristic-based finite volume scheme for 1D Euler equations

郭彦;刘儒勋

2009, 30(3): 303-312. doi:10.1007/s10483-009-0304-6

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In this paper, a high-order finite-volume scheme is presented for the onedimensional scalar and inviscid Euler conservation laws. The Simpson,s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson,s quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifthorder central weighted essentially non-oscillatory (CWENO) reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.

Generalized gap functions and error bounds for generalized variational inequalities

胡艳红;宋文

2009, 30(3): 313-321. doi:10.1007/s10483-009-0305-x

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We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

A micromechanical damage model for rocks and concretes under triaxial compression

任中俊;彭向和;胡宁;杨春和

2009, 30(3): 323-333. doi:10.1007/s10483-009-0306-z

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Based on analysis of 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 are 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 is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.

Parametric studies on relationships between flutter derivatives of slender bridge (II)

徐旭

2009, 30(3): 335-341. doi:10.1007/s10483-009-0307-x

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Based on curve fitting of coefficients of three component forces of the Messina Straits Bridge, and the previously proposed semi-analytical expressions of flutter derivatives of flexible structure, the change of flutter derivatives of slender bridge cross-section with respect to its aerodynamic center, rotational speed and angle variation is studied using a parametric method. The calculated results are compared with the measured ones, and expressions of flutter derivatives of the Messina Straits Bridge are derived. The intrinsic relationships existing in flutter derivatives are validated again. It is shown that the influence of the rotational speed on flutter derivatives is not negligible. Therefore, it provides an additional semi-analytical approach for analyzing flutter derivatives of the bridge with streamlined cross-section to get its aerodynamic information.

Velocity distribution of flow with submerged flexible vegetations based on mixing-length approach

槐文信;韩杰;曾玉红;安翔;钱忠东

2009, 30(3): 343-351. doi:10.1007/s10483-009-0308-1

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By choosing a PVC slice to simulate flexible vegetation, we carried out experiments in an open channel with submerged flexible vegetation. A 3D acoustic Doppler velocimeter (micro ADV) was used to measure local flow velocities and Reynolds stress. The results show that hydraulic characteristics in non-vegetation and vegetation layers are totally different. In a region above the vegetation, Reynolds stress distribution is linear,
and the measured velocity profile is a classical logarithmic one. Based on the concept of new-riverbed, the river compression parameter representing the impact of vegetation on river is given, and a new assumption of mixing length expression is made. The formula for time-averaged velocity derived from the expression requires less parameters and simple calculation, and is useful in applications.

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

Rajneesh Kumar;Rajani Rani Gupta

2009, 30(3): 353-364. doi:10.1007/s10483-009-0309-6

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

An engineering analysis of penetration of metal ball into fibre-reinforced composite targets

李永池;王志海;王肖钧;胡秀章

2009, 30(3): 365-372. doi:10.1007/s10483-009-0310-y

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An engineering analysis of computing the penetration problem of a steel ball penetrating into fibre-reinforced composite targets is presented. Assume the metal ball is a rigid body, and the composite target is a transversely isotropic elasto-plastic material. In the analysis, a spherical cavity dilatation model is incorporated in the cylindrical cavity penetration method. Simulation results based on the modified model are in good
agreement with the results for 3-D Kevlar woven (3DKW) composite anti-penetration experiments. Effects of the target material parameters and impact parameters on the penetration problem are 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): 373-380. doi:10.1007/s10483-009-0311-6

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This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is 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 are obtained and solved by using a new computational approach based on a special type of Hermite-Pad´e approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.

Existence and joint continuity of local time of multi-parameter fractional L´evy processes

林正炎;程宗毛

2009, 30(3): 381-390. doi:10.1007/s10483-009-0312-y

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In this paper, we introduce the definition of a multi-parameter fractional L´evy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

Initial value problem for a class of fourth-order nonlinear wave equations

陈国旺;侯长顺

2009, 30(3): 391-401. doi:10.1007/s10483-009-0313-x

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In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

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