应用数学和力学

2011 Vol. 32, No. 2

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Linear Instability of Ultra-Thin Liquid Films Flowing Down a Cylindrical Fibre

ZHAO Lu-hai-bo, HU Guo-hui, ZHOU Zhe-wei

2011, 32(2): 127-134. doi: 10.3879/j.issn.1000-0887.2011.02.001

Abstract(1742) PDF(795)

Abstract:
The stability characteristics of an ultra-thin layer of viscous liquid flowing down a cylindrical fibre were investigated by linear theory. The film with a thickness less than 100 nm was driven by an external force,and under the influence of van der Waals forces. Results show that when the relative film thickness decreases,the curvature of the fibre depresses the development of the linear perturbations,whereas the van der Waals forces promote instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from absolute to convective instability,which demonstrates that the van der Waals forces have the role of enlarging the absolutely unstable region. Furthermore,the surface tension is benefitial for the development of the absolute instability,whereas the external force plays an opposite effect.

Computations of Wall Distances by Solving a Transport Equation

XU Jing-lei, YAN Chao, FAN Jing-jing

2011, 32(2): 135-143. doi: 10.3879/j.issn.1000-0887.2011.02.002

Abstract(2105) PDF(805)

Abstract:
Motivated by the large expense to compute wall distances which still play a key role in modern turbulence modeling,the approach of solving partial differential equations is considered. An Euler-like transport equation was proposed based on Eikonal equation so that efficient algorithms and code components developed for solving transport equations such as Euler and Navier-Stokes can be reused. A detailed implementation of the transport equation in Cartesian Coordinates was provided based on code MI-CFD of BUAA. The transport equation was found to have robust and rapid convergence using implicit LUSGS time advancement and upwind spatial discretization. Geometric derivatives must also be upwind determined for accuracy assurance. Special treatments on initial and boundary conditions were discussed. This distance solving approach is successfully applied on several complex geometries with 1-1 blocking or overset grids.

Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness

JIANG Jin-ping, HOU Yan-ren, WANG Xiao-xia

2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003

Abstract(1645) PDF(966)

Abstract:
The pullback attractors for the 2D non-autonomous g-Navier-Stokes equations with linear dampness on some unbounded domains were investigated. The existence of the pullback attractors was proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore,the estimation of the fractal dimensions for the 2Dg-Navier-Stokes equations was given.

Time-Dependent Three-Dimensional Flow and Mass Transfer of an Elastico-Viscous Fluid Over an Unsteady Stretching Sheet

T. Hayat, M. Mustafa

2011, 32(2): 158-170. doi: 10.3879/j.issn.1000-0887.2011.02.004

Abstract(1535) PDF(733)

Abstract:
The three-dimensional boundary layer flow of an elastico-viscous fluid over a stretching surface was looked at. Velocity of the stretching sheet was assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction was further considered. Computations were made by homptopy analysis method(HAM). The convergence of the obtained series solutions was explicitly analyzed. The variations of embedding parameters on the velocity and concentration were graphically discussed. Numerical computations of surface mass transfer were reported. Comparison of the present results with the numerical solutions was also seen.

Natural Convection of Non-Newtonian Power-Law Fluid Over Axisymmetric and Two-Dimensional Bodies of Arbitrary Shape in a Fluid-Saturated Porous Medium

S. M. Abdel-Gaied, M. R. Eid

2011, 32(2): 171-179. doi: 10.3879/j.issn.1000-0887.2011.02.005

Abstract(1871) PDF(764)

Abstract:
Numerical analysis of free convection coupled heat and mass transfer was presented for nonNewtonian power-law fluids with yield stress flowing over two-dimensional or axisymmetric body of arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions were cast into a dimensionless form by similarity transformation and the resulting system of equations was solved by a finite difference method. The parameters studied were the rheological constants, the buoyancy ratio,and the Lewis number. Representative velocity as well as temperature and concentration profiles were presented and discussed. It was found that the result depend strongly on the values of the yield stress parameter,and the power-law index of non-Newtonian fluid.

Elastodynamic Solution for Plane-Strain Response of Functionally Graded Thick Hollow Cylinders by Analytical Method

Mehdi Nikkhah, Farhang Honarvar, Ehsan Dehghan

2011, 32(2): 180-193. doi: 10.3879/j.issn.1000-0887.2011.02.006

Abstract(1585) PDF(763)

Abstract:
An elastodynamic solution for the plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at the boundary surfaces,was presented. The material properties,except Poisson's ratio,were assumed to vary through the thickness following a power law function. To achieve an exact solution,the dynamic radial displacement was divided into two quasistatic and dynamic parts. For each part,an analytical solution was derived. Firstly,the quasi-static solution was obtained by means of Euler's equation,and then the dynamic solution was derived by utilizing the separation of variables method and the orthogonal expansion technique. Radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were discussed. The presented analytical solution was suitable for analyzing various arrangements of FGM hollow cylinders with arbitrary thickness and arbitrary initial conditions, subjected to arbitrary form of dynamic pressures distributed uniformly at the boundary surfaces. Finally, radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were considered.

Analysis of Dynamic Stress Intensity Factors of Three-Point Bend Specimen Containing Crack

CHEN Ai-jun, CAO Jun-jun

2011, 32(2): 194-201. doi: 10.3879/j.issn.1000-0887.2011.02.007

Abstract(1931) PDF(858)

Abstract:
A new formula was produced to calculate dynamic stress intensity factors of three-point bend specimen containing a single edge crack. Firstly,the weight function for three-point bend specimen containing a single edge crack was derived from a general weight function form and two reference stress intensity factors. The coefficients of the weight function were given. Secondly,the history and distribution of dynamic stresses in unflawed three-point bend specimen which takes account of the effects of rotator inertia and shear deformation were inferred according to vibration theory. Finally,the dynamic stress intensity factor equations for three-point bend specimen with a single edge crack subjected to impact loadings were obtained by weight function method. The new formula was verified by the comparison with the numerical results of FEM(finite element method). Good agreement was achieved. And the law of dynamic stress intensity factors of three-point bend specimen under impact loadings changing with crack depths and loading rates was studied.

On the Instability of Equilibrium of Nonholonomic Systems With Dissipation and Circulatory Forces

M. Vesković, V. Čović, A. Obradović

2011, 32(2): 202-212. doi: 10.3879/j.issn.1000-0887.2011.02.008

Abstract(1864) PDF(767)

Abstract:
The equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative,conservative,circulatory forces was discussed. The applied methodology was based on the existence of solutions of differential equations of motion which asymptotically tend to the equilibrium state of the system,as t→-∞. It was assumed that the kinetic energy,the Rayleigh dissipation function,the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained,which partially generalize results from[V V Kozlov. On the asymptotic motions of systems with dissipation. Prikl Math Mekh,1994,58 (4):31-36. (in Russian);D R Merkin. Introduction to the Theory of the Stability of Motion. 1987,Moscow:Nauka. (in Russian);W Thomson,P Tait. Treatise on Natural Philosophy. Part Ⅰ. Cambridge University Press,1879],are illustrated by an example.

Exploring Human Rhythmic Gait Movement in the Role of Cerebral Cortex Signal

DONG Wei, WANG Ru-bin, ZHANG Zhi-kang

2011, 32(2): 213-220. doi: 10.3879/j.issn.1000-0887.2011.02.009

Abstract(1415) PDF(954)

Abstract:
The rhythmic movement was a spontaneous behavior generated by central pattern generator (CPG). At present,the CPG model only showed the spontaneous behavior,it did not refer to the instruction regulation role of cerebral cortex. A revised model based on Matsuoka Neural oscillator theory was presented to better show the regulation role of cerebral cortex signal to CPG neuronal network. The complex interaction between input signal and other parameters in CPG network was established,making the every parameter of CPG itself vary with the input signal. It enhanced the effect of input signal to CPG network to make the CPG network express the self-regulation movement state instead of being limited to the spontaneous behavior,reflecting the regulation role of cerebral cortex signal. The numerical simulation showed that the revised model could generate various movement forms with different modes and frequencies,and their interchanges. It was theoretically revealed that the cerebral cortex signal could regulate the mode and frequency of gait in the course of gait movement.

Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

DING Xie-ping

2011, 32(2): 221-231. doi: 10.3879/j.issn.1000-0887.2011.02.010

Abstract(1705) PDF(776)

Abstract:
A system of new generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems (SGMEP) was introduced and studied in reflexive Banach spaces. First,a system of auxiliary generalized mixed equilibrium problems (SAGMEP) for solving the SGMEP was introduced. The existence and uniqueness of the solutions of the SAGMEP was proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Next,by using the auxiliary principle technique,a new iterative algorithm for solving the SGMEP was suggested and analyzed. Finally,the strong convergence of the iterative sequences generated by the algorithm was also proved under quite mild assumptions without any coercive conditions. These results improve,unify and generalize some recent results in this field.

Viscosity Method for Hierarchical Fixed Point and Variational Inequalities With Applications

ZHANG Shi-sheng, WANG Xiong-rui, H. W. Joseph LEE, Chi Kin CHAN

2011, 32(2): 231-240. doi: 10.3879/j.issn.1000-0887.2011.02.011

Abstract(1882) PDF(942)

Abstract:
A viscosity method for a hierarchical fixed point approach to variational inequality problems was presented,which was used to solve variational inequalities where the involving mappings were nonexpansive and the solutions were sought in the set of the fixed points of another nonexpansive mapping. As applications,the results were utilized to study the monotone variational inequality problem,convex programming problem,hierarchical minimization problem and quadratic minimization problem over fixed point sets.

Hybrid Projection Method for Generalized Mixed Equilibrium Problems,Variational Inequality Problems and Fixed Point Problems in Banach Spaces

WANG Ya-qin, ZENG Lu-chuan

2011, 32(2): 241-252. doi: 10.3879/j.issn.1000-0887.2011.02.012

Abstract(1722) PDF(834)

Abstract:
A new hybrid projection iterative scheme was introduced for approximating a common elementof the solution set of a generalized mixed equilibrium problem,the solution set of a variational inequalityproblem and the set of fixed points of a relatively weak nonexpansive mapping in Banach spaces. The results obtained generalize and improve the recent ones announced by many others.