应用数学和力学

2010 Vol. 31, No. 9

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Existence and Algorithm of Solutions for a System of Generalized Mixed Implicit Equilibrium Problems in Banach Spaces

DING Xie-ping

2010, 31(9): 1001-1015. doi: 10.3879/j.issn.1000-0887.2010.09.001

Abstract(1727) PDF(822)

Abstract:
A new system of generalized mixed implicity equilibrium problems was introduced and studied in Banach spaces.First,the notion of Yosida proximal mapping for generalized mixed implicity equilibrium problems was introduced.By using the notion,a system of generalized equation problems was considered and its equivalence with the system of generalized mixed implicity equilibrium problems was also proved. Next,by applying the system of generalized equation problems,an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicity equilibrium problems was suggested and analyzed.The strong convergence of the iterative sequences generated by the algorithm was 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-yi

2010, 31(9): 1016-1026. doi: 10.3879/j.issn.1000-0887.2010.09.002

Abstract(1480) PDF(768)

Abstract:
The direct simulation Monte Carlo method(DSMC)was used to simulate rarefied aerodynamic characteristics during the aerobraking process of NASA Mars Global Surveyor(MGS)spacecraft.The research focused on the flowfield and aerodynamic characteristics distribution under various freestream densities,and the variation regularity of aerodynamic coefficients was analyzed.Also,an aerodynamics-aero-heating-trajectory integrative simulation model was developed to preliminarily calculate the aerobraking orbit transfer by combining DSMC technique and classical kinematics theory.Results show that the effect of planetary atmospheric density,spacecraft yaw and pitch attitudes on the spacecraft aerodynamics is significant.The numerical results are in good agreement with the existing results in the literature.The aerody-namics-aeroheating-trajectory integrative simulation model is proved to be able to simulate the orbit transfer in the complete aerobraking mission,and current results of spacecraft trajectory show that the aero-braking maneuvers give good performance of attitude control.

Analytic Solution for the Flow of a Micropolar Fluid Through a Semi-Porous Channel With an Expanding or Contracting Wall

SI Xin-hui, ZHENG Lian-cun, ZHANG Xin-xin, CHAO Ying

2010, 31(9): 1027-1035. doi: 10.3879/j.issn.1000-0887.2010.09.003

Abstract(1546) PDF(777)

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

A New Stabilized Method for Quasi-Newtonian Flow

XIE Chun-mei, FENG Min-fu

2010, 31(9): 1036-1049. doi: 10.3879/j.issn.1000-0887.2010.09.004

Abstract(1753) PDF(838)

Abstract:
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)was presented.A development of pressure projection stabilized method was extended from Stokes problems to quasi-Newtonian flow problems.The theoretical framework developed herein yielded an estimate bound which measured the error in the approximation of the velocity in the W^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 were special ones of the quasi-Newtonian flow problem discussed.Moreover,a residual-based posterior bound was given.Finally,numerical experiments were presented to confirm our theoretical results.

Identification of Boundary Surfaces in Flows

Blas Herrera, Jordi Pallares

2010, 31(9): 1050-1056. doi: 10.3879/j.issn.1000-0887.2010.09.005

Abstract(1333) PDF(706)

Abstract:
Boundary surfaces of a flow field as stream surfaces on which the shear rates vanish were defined and a procedure to find them was proposed.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 Media-Filled Enclosures

Y. M. Al Badawi, H. M. Duwairi

2010, 31(9): 1057-1065. doi: 10.3879/j.issn.1000-0887.2010.09.006

Abstract(1519) PDF(834)

Abstract:
In this study the magnetohydrodynamics(MHD)natural convection heat transfer with Joule and viscous heating effects inside iso-flux porous media filled inclined rectangular enclosures was studied numerically.An iso-heat flux was applied for heating and cooling the two opposing walls of the enclosure while the other walls were adiabatic.The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations were transformed into dimensionless form using a set of suitable variables than solved using 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 the viscous and Joule heating effects decrease heat transfer rates.

Lamb’s Integral Formulas of Two-Phase Saturated Medium for Soil Dynamic Problems With Drainage

DING Bo-yang, DANG Gai-hong, YUAN Jin-hua

2010, 31(9): 1066-1074. doi: 10.3879/j.issn.1000-0887.2010.09.007

Abstract(1516) PDF(987)

Abstract:
It's an ordinary phenomenon to vibration response with drainage when the dynamic force acts upon the saturated soil in the project site.The saturated soil was simulated with the two-phase saturated medium in theory,the Lamb's integral formulas(representative theorem)with drainage and the stress formulas on the two-phase saturated medium had been shown based on Biot's equation and Betti's theorem(reciprocal theorem).According to the basic solution of Green's function and three items of Green's function on the flow-phase of the two-phase saturated medium subjected to a concentrated force,the displacement field with drainage,the magnitude of drainage and the pore pressure of the center explosion source and so on were computed.Moreover,the comparative results of classical Sharpe's solutions and calculated solutions that the two-phase saturated medium decays to the single-phase medium had giverout.A good agreement can be observed from the figures.

Analytical Solution for a Strained Reinforcement Layer Bonded to a Lip-Shaped Crack Under Remote Mode Ⅲ Uniform Load and a Concentrated Load

LIU You-wen, XIE Chao, JIANG Chun-zhi, FANG Qi-hong

2010, 31(9): 1075-1088. doi: 10.3879/j.issn.1000-0887.2010.09.008

Abstract(1507) PDF(737)

Abstract:
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 was obtained explicitly in the series form by using the technique of conformal mapping and the method of analytic continuation.The effect of material combinations,bond of interface and geometric configurations on interfacial stresses generated by eigenstrain,remote load and concentrated load were studied.The results show that the stress concentration and interfacial stresses could be reduced by rational material combinations and geometric configurations designs for different load forms.

New Finite Element of Spatial Thin-Walled Beams

WANG Xiao-feng, ZHANG Qi-lin, YANG Qing-shan

2010, 31(9): 1089-1100. doi: 10.3879/j.issn.1000-0887.2010.09.009

Abstract(1809) PDF(823)

Abstract:
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 was 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 were all considered.According to the generalized variational theory of Hellinger-Reissner,the element stiffness matrix was deduced.Examples manifest that the developed model is accurate and can be applied in the finite element analysis of thin-walled 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(9): 1101-1117. doi: 10.3879/j.issn.1000-0887.2010.09.010

Abstract(1953) PDF(670)

Abstract:
The purpose of this research was to study the effect of voids on the surface wave propagation in a layer of transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space.The frequency equation was derived after developing the mathematical model for welded and smooth contact boundary conditions.The dispersion curves giving the phase velocity and attenuation coefficient verses wave number were plotting graphically to depict the effects of voids and anisotropy for welded contact boundary conditions.The specific loss and amplitudes of volume fraction field,normal stress,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

2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011

Abstract(1744) PDF(963)

Abstract:
Beam with spatial compliance can be deformed as bending in the plane,twisting and extending. In terms of the screw theory on rigid body motion,the concept of‘deflection screw' was introduced,spatial compliant beam theory via the deflection screw was then proposed,and the spatial compliance of such a beam system was presented and analysed based on material theory and fundamental kinematic assumptions. To study the dynamics of spatially compliant beam,the potential energy and the kinetic energy of the beam were discussed using screw theory,and then,the lagrangian was obtained.The Rayleigh-Ritz method was further used to compute the vibrational frequencies after a discussion of boundary conditions and shape functions.The eigenfrequencies of the beam with spatial compliance were compared with that of individual deformation cases,pure bending,extension or torsion.Finally,dynamics of a robot with two spatial compliant links and perpendicular joints was studied using the spatial compliant beam theory,and the coupling effects between the joint rigid body motions and the deformations of spatial compliant links can be easily found by our dynamic simulation.The study convinces that the effectiveness of using screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.

Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation

Ch. Srinivasa Rao, Manoj K Yadav

2010, 31(9): 1133-1139. doi: 10.3879/j.issn.1000-0887.2010.09.012

Abstract(1346) PDF(704)

Abstract:
Solutions of a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles were constructed.In an interesting study,Kloosterziel(Kloosterziel R C.J Engrg Math,1990, 24(3):213-236)represented the solution of an initial value problem(IVP)for the heat equation,with initial data in(L²(R,e^x²/2),as a series of the self-similar solutions of the heat equation.This approach quickly revealed the large time behaviour for the solution of the IVP.Inspired by Kloosterziel's approach, the solution of the nonhomogeneous Burgers equation in terms of the self-similar solutions of the heat equation was expressed.Finally,the large time behaviour of the solutions of the nonhomogeneous Burgers equation is obtained.