应用数学和力学

2004 Vol. 25, No. 10

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An Improved Level-Set Re-Initialization Solver

WANG Zhi-liang, ZHOU Zhe-wei

2004, 25(10): 991-996.

Abstract(2303) PDF(539)

Abstract:
Re-initialization procedure in level-set interface capturing method were investigated.The algorithm accomplishes the re-initialization step through locking the interface positions.Better accuracy was obtained both on the interface positions and the total fluid volume keeping.Though one more step of the interpolations is added in the procedure,there is no significant increase in total machine time spent.

Mechanical Behavior of Amorphous Polymers in Shear

ZHANG Yun, HUANG Zhu-ping

2004, 25(10): 997-1006.

Abstract(2769) PDF(533)

Abstract:
Based on the non-equilibrium thermodynamic theory,a new thermo-viscoelastic constitutive model for an incompressible material is proposed.This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects.A set of second rank tensorial internal variables was introduced,and in order to adequately describe the evolution of these internal variables,a new expression of the Helmholtz free energy was suggested.The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied,and the/viscous dissipation induced0 anisotropy due to the change of orientation distribution of molecular chains was examined.Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed.Finally,the model predictions were compared with the experimental results performed by G.Sell et al,thus the validity of the proposed model is verified.

Free Fisher Information and Amalgamated Freeness

MENG Bin, GUO Mao-zheng, CAO Xiao-hong

2004, 25(10): 1007-1013.

Abstract(2313) PDF(1171)

Abstract:
The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Raoinequality in operator-valued settings is also obtained.

Analytical Solution for Bending Beam Subject to Lateral Force With Different Modulus

YAO Wen-juan, YE Zhi-ming

2004, 25(10): 1014-1022.

Abstract(2588) PDF(667)

Abstract:
A bending beam,subjected to two state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that,for the elastic bending beam with different tension-compression modulus in the condition of complex stress,the position of the neutral axis is not related with the shear stress,and the analytical solution can be derived by normal stress used as a criterion,improving the multiple cyclic method which determines the position of neutral point by the principal stress.Meanwhile,a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory,assuming the tension modulus is equal to the compression modulus,and those from the finite element method (FEM) numerical solution.The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus.Finally,a calculation correction of the structure with different modulus is proposed to optimize the structure.

Modeling the Interaction of Solitary Waves and Semi-Circular Breakwaters by Using Unsteady Reynolds Equations

LIU Chang-gen, TAO Jian-hua

2004, 25(10): 1023-1032.

Abstract(2982) PDF(614)

Abstract:
A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations.In this model,the k-epsilon models were used to close the Reynolds equations,and volume of fluid (VOF) method was used to reconstruct the free surface.The model was verified by experimental data.Then the model was used to simulate solitary wave interaction with submerged,alternative submerged and emerged semi-circular breakwaters.The process of velocity field,pressure field and the wave surface near the breakwaters was obtained.It is found that when the semi-circular breakwater is submerged,a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater,a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting,but the velocity near the bott om of the lee side wall of the breakwater is always relatively small.When the semi-circular breakwater is emerged,and solitary wave cannot overtop it,the solitary wave surface will run up and down secondarily during reflecting from the breakwater.It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.

Upwind Local Differential Quadrature Method for Solving Coupled Viscous Flow and Heat Transfer Equations

A. S. J. Al-Saif, ZHU Zheng-you

2004, 25(10): 1033-1041.

Abstract(2431) PDF(443)

Abstract:
The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics.But it is only limited to the flow problems in regular regions.At the same time,here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method.A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region.For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction,the satisfactory numerical solutions were obtained by using ULDQM with a few grid points.The numerical results show that the ULDQM possesses advantages including well convergence,less computational workload and storage as compared with the low-order finite difference method.

Nonlinear Dynamics of a Cracked Rotor in a Maneuvering Aircraft

LIN Fu-sheng, MENG Guang, Eric Hahn

2004, 25(10): 1042-1052.

Abstract(2307) PDF(518)

Abstract:
The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated.The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation,for quasi-periodic response and for chaotic response as well as for system stability.Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system,illustrating the possibility for on-line rotor crack fault diagnosis.

Decay of Vortex Velocity and Diffusion of Temperature in a Generalized Second Grade Fluid

SHEN Fang, TAN Wen-chang, ZHAO Yao-hua, T. Masuoka

2004, 25(10): 1053-1060.

Abstract(2733) PDF(578)

Abstract:
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced.The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations.Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function.The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.

Generalized Variational Data Assimilation Method and Numerical Experiment for Non-Differential System

HUANG Si-xun, DU Hua-dong, HAN Wei

2004, 25(10): 1061-1066.

Abstract(2142) PDF(539)

Abstract:
The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced,and then the generalized adjoint model was derived.The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations.Furthermore,ideas in inverse problems are introduced to 4DVAR of non-differential partial differential system with local observations.

Solution of Generalized Coordinate for Warping for Naturally Curved and Twisted Beams

YU Ai-min, YI Ming

2004, 25(10): 1067-1075.

Abstract(2491) PDF(551)

Abstract:
A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented,with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations.These governing equations,in special cases,can be readily solved and yield the solutions to the problem.The solutions can be used for the analysis of the beams,including the calculation of various internal forces,stresses,strains and displacements.The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads.The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results.Besides,the present theory is not limited to the beams with a double symmetric cross section,it can also be extended to those with arbitrary crosssectional shape.

Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions

JIN Yin-lai, ZHU De-ming

2004, 25(10): 1076-1082.

Abstract(2305) PDF(611)

Abstract:
By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincar map,the bifurcations of twisted homoclinic loop for higher dimensional systems are studied.Under the nonresonant and resonant conditions,the existence,number and existence regions of the 1-homoclinic loop,1-periodic orbit,2-homoclinic loop,2-periodic orbit and 2-fold 2-periodic orbit were obtained.Particularly,the asymptotic repressions of related bifurcation surfaces were also given.Moreover,the stability of homoclinic loop for higher dimensional systems and nontwisted homoclinic loop for planar systems were studied.

Spectral Galerkin Approximation of Couette-Taylor Flow

WANG He-yuan, LI Kai-tai

2004, 25(10): 1083-1092.

Abstract(2386) PDF(601)

Abstract:
Axisymmetric Couette-Taylor flow between two concentric rotating cylinders was simulated numerically by the spectral method.First,stream function form of the Navier-Stokes equations which homogeneous boundary condition was given by introducing Couette flow.Second,the analytical expressions of the eigenfunction of the Stokes operator in the cylindrical gap region were given and its orthogonality was proved.The estimates of growth rate of the eigenvalue were presented.Finally, spectral Galerkin approximation of Couette-Taylor flow was discussed by introducing eigenfunctions of Stokes operator as basis of finite dimensional approximate subspaces.The existence,uniquence and convergence of spectral Galerkin approximation of nonsingular solution for the steady-state NavierStokes equations are proved.Moreover,the error estimates are given.Numerical result is presented.

Dynamic Crack Models on Problem of Bridging Fiber Pull-Out of Composite Materials

Lü Nian-chun, CHENG Yun-hong, XU Hong-min, CHENG Jin, TANG Li-qiang

2004, 25(10): 1093-1100.

Abstract(2262) PDF(551)

Abstract:
An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed.A dynamic model of bridging fiber pull-out of composite materials was presented.Resultingly the fiber failure is governed by maximum tensile stress,the fiber breaks and hence the crack extension should occur in self-similar fashion.By the methods of complex functions,the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem,and a straightforward and easy analytical solution is presented.Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body.By utilizing the solution,the concrete solutions of this model are attained by ways of superposition.