应用数学和力学

2002 Vol. 23, No. 8

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Restudy of Theories for Elastic Solids With Microstructure

DAI Tian-min

2002, 23(8): 771-777.

Abstract(1995) PDF(626)

Abstract:
The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given.In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion,the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola.s theorem.These basic equations and the boundary conditions together with the initial conditions may be used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.

The Transient Elliptic Flow of Power-Law Fluid in Fractal Porous Media

SONG Fu-quan, LIU Ci-qun

2002, 23(8): 778-782.

Abstract(2518) PDF(603)

Abstract:
The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs.The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method:the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law.The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

Cavitated Bifurcation for Incompressible Hyperelastic Material

REN Jiu-sheng, CHENG Chang-jun

2002, 23(8): 783-789.

Abstract(2161) PDF(724)

Abstract:
The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined.The analytic solution for the bifurcation problem is obtained.The catastrophe and concentration of stresses are discussed.The stability of solutions is discussed through the energy comparison.And the growth of a pre-existing micro-void is also observed.

General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅰ)-Governing Equation and General Solution

ZHU Wei-ping, HUANG Qian

2002, 23(8): 790-797.

Abstract(2345) PDF(537)

Abstract:
The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed.The derivation of the equations was based upon the theory of flexible shells generalized by E.L.Axelrad and the assumption of the moderately slender ratio less than 1/3(i.e.ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution).The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems.It can be used to calculate the stresses and displacements of the related bellows.The whole work is arranged into four parts: (Ⅰ)Governing equation and general solution;(Ⅱ)Calculation for Omega-shaped bellows;(Ⅲ)Calculation for C-shaped bellows;(Ⅳ)Calculation for U-shaped bellows.This paper is the first part.

General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅱ)-Calculation for Omega-Shaped Bellows

ZHU Wei-ping, HUANG Qian

2002, 23(8): 798-804.

Abstract(2542) PDF(456)

Abstract:
(Ⅱ) is one of the applications of (Ⅰ),in which the angular stiffness,the lateral stiffness and the corresponding stress distributions of Omega-shaped bellows were calculated,and the present results were compared with those of the other theories and experiments.It is shown that the non-homogenous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself,and be more effective than by the theory of slender ring shells;but if a lateral slide of the bellows support exists the non-homogenous solution will no longer entirely satisfy the boundary conditions of the problem,in this case the homogenous solution of (Ⅰ)should be included,that is to say,the full solution of (Ⅰ) can meet all the requirements.

Numerical Simulation of Orientation Distribution Function of Cylindrical Particle Suspensions

LIN Jian-zhong, ZHANG Ling-xin

2002, 23(8): 805-810.

Abstract(2127) PDF(728)

Abstract:
The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated,and an application was taken in a wedge-shaped flow field.The relationship between the orientation distribution function and particle orientation angles was obtained.The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn.t vary much in range;the main difference is the anti-clockwise rotation in the right and upper field,that is,particles rotate more at the points where the velocity gradients are larger.The most probable orientations are close to the direction of local streamlines. In the direction of streamlines,with poleradius decreasing,the most probable angles increase,but the angles between their orientations and the local streamlines decrease.

Unilateral Contact Problems Using Quasi-Active Set Strategy

XUAN Zhao-cheng, LI Xing-si

2002, 23(8): 811-818.

Abstract(2316) PDF(522)

Abstract:
The unilateral contact problem can be formulated as a mathematical programming with inequality constraints.To resolve the difficulty in dealing with inequality constraints,a quasi-active set strategy algorithm was presented.At each iteration,it transforms the problem into one without contact in terms of the solution obtained in last iteration and initiates the current iteration using the solution of the transformed problem,and updates a group of contact pairs compared with Lemke algorithm that uqdates only one pair of contact points.The present algorithm greatly enhances the efficiency and numerical examples demonstrate the effectiveness and robustness of the proposed algorithm.

On Influence of Kinematics to Equivalent Linear Damping of Helicopter Blade Hydraulic Damper

HU Guo-cai, XIANG Jin-wu, ZHANG Xiao-gu

2002, 23(8): 819-826.

Abstract(2164) PDF(541)

Abstract:
An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve.The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain.Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity.Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.

Numerical Simulation of Oil Migration-Accumulation of Multilayer and Its Application

YUAN Yi-rang, ZHAO Wei-dong, CHENG Ai-jie, WANG Wen-qia, HAN Yu-ji

2002, 23(8): 827-836.

Abstract(2262) PDF(572)

Abstract:
From such actual conditions as the effects of fluid mechanics in porous media and three-dimensional geology characteristics,the mathematical model and a kind of modified method of second order splitting-up implicit interactive scheme were put forward.For the actual problem of Dongying hollow(single layer)and Huimin hollow(multilayer)of Shengli Petroleum Oil Field,this numerical simulation test and the actual conditions are basically coincident,thus the well-known problem has been solved.

Some Problems in the Z-C-X Space

ZHU Chuan-xi

2002, 23(8): 837-842.

Abstract(2287) PDF(657)

Abstract:
The new concepts of the Z-C-X space and excellent cone are introduced.Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space.At first,an important inequality is proved.Secondly,several new conclusions are proved by means of random fixed point index in the theory of random topological degree.A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained,famous Altman.s theorem is generalized in partially ordered Z-C-X space.Therefore,some new results are obtained.

Topology and Vortex Structures of a Curving Turbine Cascade With Tip Clearance (Ⅰ)-Experimental Model and Topological Flow Patterns on Both Endwalls and Blade Surfaces

YANG Qing-hai, HUANG Hong-yan, HAN Wan-jin

2002, 23(8): 843-850.

Abstract(1980) PDF(629)

Abstract:
By means of ink trace visualization of the flows in conventional straight,positively curved and negatively curved cascades with tip clearance,and measurement of the aerodynamic parameters in the transverse section,and by appling topology theory,the structures on both endwalls and blade surfaces were analyzed.Compared with conventional straight cascade,blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation,while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

Topology and Vortex Structures of a Curving Turbine Cascade With Tip Clearance (Ⅱ)-Topological Flow Pattern and Vortex Structure in the Transverse Section of a Blade Cascade

YANG Qing-hai, HUANG Hong-yan, HAN Wan-jin

2002, 23(8): 851-854.

Abstract(2169) PDF(527)

Abstract:
By means of ink trace visualization of the flows in conventional straight,positively curved and negatively curved cascades with tip clearance,and measurement of the aerodynamic parameters in transverse section,and by appling topology theory,the topological structures and vortex structure in the transverse section of a blade cascade were analyzed.Compared with conventional straight cascade,blade positive curving eliminates the separation line of the upper passage vortex,and leads the secondary vortex to change from close separation to open separation,while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

Series Perturbations Approximate Solutions to N-S Equations and Modification to Asymptotic Expansion Matched Method

LI Da-ming, ZHANG Hong-ping, GAO Yong-xiang

2002, 23(8): 855-863.

Abstract(2689) PDF(525)

Abstract:
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted.Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted.By the ameliorative asymptotic expansion matched method,the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.

Chaos-Regularization Hybrid Algorithm for Nonlinear Two-Dimensional Inverse Heat Conduction Problem

WANG Deng-gang, LIU Ying-xi, LI Shou-ju

2002, 23(8): 864-870.

Abstract(2860) PDF(677)

Abstract:
A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature.Combining the chaos optimization algorithm with the gradient regularization method,a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm.Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule,the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements.Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values,and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.

Bifurcations of Subharmonic Solutions in Periodic Perturbation of a Hyperbolic Limit Cycle

HAN Mao-an, GU Sheng-shi

2002, 23(8): 871-875.

Abstract(2512) PDF(633)

Abstract:
Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed.By using a Poincar map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained.An example is given in the end of the paper.

Perturbation Theory for Nonlinear Klein-Gordon Equation

LIU Tian-gui, YAN Jia-ren

2002, 23(8): 876-880.

Abstract(2027) PDF(582)

Abstract:
The effects of pertur bations on a nonline ar Klein-Gordon the soliton to the first-order approx imation are obtained,namely,the soliton parameters changing slowly with time,and the concrete expression of the first-order correction are got.

2002, 23(8): 881-881.

Abstract(1874) PDF(461)

Abstract:

2002, 23(8): 882-882.

Abstract(1631) PDF(352)

Abstract: