Table of Content

01 September 2010, Volume 31 Issue 09

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Articles

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

DING Xie-Ping

2010, 31(09):  1049-1062.  doi:10.1007/s10483-010-1341-z

Abstract ( 742 )   PDF (224KB) ( 1189 )  

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A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

Spacecraft aerodynamics and trajectory simulation during aerobraking

ZHANG Wen-Pu;HAN Bo;ZHANG Cheng-Xi

2010, 31(09):  1063-1072.  doi:10.1007/s10483-010-1342-x

Abstract ( 676 )   PDF (696KB) ( 1860 )  

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This paper uses a direct simulation Monte Carlo (DSMC) approach to simulate rarefied aerodynamic characteristics during the aerobraking process of the NASA Mars Global Surveyor (MGS) spacecraft. The research focuses on the flowfield and aerodynamic characteristics distribution under various free stream densities. The variation regularity of aerodynamic coefficients is analyzed. The paper also develops an aerodynamics-aeroheating-trajectory integrative simulation model to preliminarily calculate the aerobraking orbit transfer by combining the DSMC technique and the classical kinematics theory. The results show that the effect of the planetary atmospheric density, the spacecraft yaw, and the pitch attitudes on the spacecraft aerodynamics is significant. The numerical results are in good agreement with the existing results reported in the literature. The aerodynamics-aeroheating-trajectory integrative simulation model can simulate the orbit transfer in the complete aerobraking mission. The current results of the spacecraft trajectory show that the aerobraking maneuvers have good performance of attitude control.

Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall

SI Xin-Hui;ZHENG Lian-Cun;ZHANG Xin-Xin;CHAO Ying

2010, 31(09):  1073-1080.  doi:10.1007/s10483-010-1343-6

Abstract ( 716 )   PDF (464KB) ( 1673 )  

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The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields.

A new stabilized method for quasi-Newtonian flows

XIE Chun-Mei;FENG Min-Fu

2010, 31(09):  1081-1096.  doi:10.1007/s10483-010-1344-z

Abstract ( 601 )   PDF (251KB) ( 885 )  

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For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in theW^1,r(Ω) norm and that of the pressure in the L^r´(Ω) (1/r +1/r´ = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.

Identification of boundary surfaces in flows

B.HERRERA;J.PALLARES

2010, 31(09):  1097-1104.  doi:10.1007/s10483-010-1345-7

Abstract ( 509 )   PDF (207KB) ( 889 )  

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In this study, boundary surfaces of a flow field are defined as stream surfaces, on which the shear rates vanish, and a procedure is proposed to find them. The method, based on calculations using the velocity vector field, is independent of the coordinate system adopted.

MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures

Y.M.AL-BADAWI;H.M.DUWAIRI

2010, 31(09):  1105-1112.  doi:10.1007/s10483-010-1346-6

Abstract ( 773 )   PDF (500KB) ( 1421 )  

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In this study, the magnetohydrodynamics (MHD) natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically. An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adiabatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a finite difference scheme. The governing parameters are the magnetic influence number, the modified Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates.

Lamb’s integral formulas of two-phase saturated medium for soil dynamic with drainage

DING Bo-Yang;DANG Gai-Hong;YUAN Jin-Hua

2010, 31(09):  1113-1124.  doi:10.1007/s10483-010-1347-9

Abstract ( 823 )   PDF (381KB) ( 818 )  

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When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb’s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot’s equation and Betti’s theorem (the reciprocal theorem). According to the basic solution to Biot’s equation, Green’s function G_ij and three terms of Green’s function G_4i, G_i4, and G₄₄ of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe’s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.

Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote mode III uniform load and concentrated load

LIU You-Wen;XIE Chao;JIANG Chun-Zhi;FANG Qi-Hong

2010, 31(09):  1125-1140.  doi:10.1007/s10483-010-1348-7

Abstract ( 765 )   PDF (580KB) ( 839 )  

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In this paper, the analytical solution of stress field for a strained reinforcement layer bonded to a lip-shaped crack under a remote mode III uniform load and a concentrated load is obtained explicitly in the series form by using the technical of conformal mapping and the method of analytic continuation. The effects of material combinations, bond of interface and geometric configurations on interfacial stresses generated by eigenstrain, remote load and concentrated load are studied. The results show that the stress concentration and interfacial stresses can be reduced by rational material combinations and geometric configurations designs for different load forms.

A new finite element of spatial thin-walled beams

WANG Xiao-Feng;ZHANG Qi-Lin;YANG Qing-Shan

2010, 31(09):  1141-1152.  doi:10.1007/s10483-010-1349-7

Abstract ( 710 )   PDF (565KB) ( 1156 )  

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Based on the theories of Timoshenko’s beams and Vlasov’s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space

Rajneesh KUMAR;Rajeev KUMAR

2010, 31(09):  1153-1172.  doi:10.1007/s10483-010-1350-6

Abstract ( 715 )   PDF (561KB) ( 1032 )  

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The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of a transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived after developing a mathematical model for welded and smooth contact boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficient via wave number are plotted graphically to depict the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction field, the normal stress, and the temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.

Screw theoretic view on dynamics of spatially compliant beam

DING Xi-Lun;J.M.SELIG

2010, 31(09):  1173-1188.  doi:10.1007/s10483-010-1351-9

Abstract ( 826 )   PDF (295KB) ( 1044 )  

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Beams with spatial compliance can be deformed as bending in a plane, twisting, and extending. In terms of the screw theory on rigid body motions, the concept of “deflection screw” is introduced, a spatial compliant beam theory via the deflection screw is proposed, and the spatial compliance of such a beam system is presented and analysed based on the material theory and fundamental kinematic assumptions. To study the dynamics of the spatially compliant beam, the potential energy and the kinetic energy of the beam are discussed by using the screw theory to obtain the Lagrangian. The Rayleigh-Ritz method is used to compute the vibrational frequencies based on discussions of boundary conditions and shape functions. The eigenfrequencies of the beam with spatial compliance are compared with those of individual deformation cases, pure bending, extension, or torsion. Finally, dynamics of a robot with two spatial compliant links and perpendicular joints is studied using the spatial compliant beam theory. Coupling between the joint rigid body motions and the deformations of spatial compliant links can easily be found in dynamic simulation. The study shows the effectiveness of using the screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.

Large time asymptotics for solutions to a nonhomogeneous Burgers equation

S.R.CHIDELLA;M.K.YADAV

2010, 31(09):  1189-1196.  doi:10.1007/s10483-010-1352-9

Abstract ( 676 )   PDF (161KB) ( 937 )  

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In this article, the solutions to a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles are constructed. In an interesting study, Kloosterziel (Journal of Engineering Mathematics 24, 213–236 (1990)) represented a solution to an initial value problem (IVP) for the heat equation, with an initial data in a class of rapidly decaying functions, as a series of self-similar solutions to the heat equation. This approach quickly revealed the large time behaviour for the solution to the IVP. Inspired by Kloosterziel’s approach, the solution to the nonhomogeneous Burgers equation is expressed in terms of the self-similar solutions to the heat equation. The large time behaviour of the solutions to the nonhomogeneous Burgers equation is obtained.