应用数学和力学

2000 Vol. 21, No. 6

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Krylov Subspace Projection Method and ItsApplication on Oil Reservoir Simulation

Liu Xiaoming, Lu Zhiming, Liu Yulu

2000, 21(6): 551-560.

Abstract(2525) PDF(723)

Abstract:
Krylov subspace projection methods are known to be highly efficient for solving large linear systems.Many different versions arise from different choices to the left and right subspaces.These methods were classified into two groups in terms of the different forms of matrix H_m,the main properties in applications and the new versions of these two types of methods were briefly reviewed,then one of the most efficient versions,GMRES method was applied to oil reservoir simulation.The block Pseudo-Elinimation method was used to generate the preconditioned matrix.Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method,which is now in use in oil reservoir simulation.Finally,some limitations of Krylov subspace methods and some potential improvements to this type of methods are furtherly presented.

A New NND Difference Scheme of Second Order in Time and Space

Wu Wangyi, Cai Qingdong

2000, 21(6): 561-572.

Abstract(2917) PDF(856)

Abstract:
The study by Zhang Hanxin shows that in order to suppress the spurious oscillation at both upstream and downstream of the shock,the coefficient of the third order derivative on the right hand side of the modified equation of the difference scheme must be positive upstream and negative downstream of the shock.According to this principle,a new non-oscillatory,containing no free parameters and dissipative difference scheme of second order both in time and space is proposed.It is proved that this scheme possesses TVD property and is generalized Gudunov scheme of second order.In the presence of the shock wave in the flow field,this scheme is the generalization and improvement of the Lax-Wendroff scheme'several numerical examples are given which demonstrate that the proposed scheme is nonoscillatory of high order accuracy and high resolution.It also has the advantages of compact form,greater maximum allowable Courant number and convenient to use.

General Solutions of Coupled Thermoelastic Problem

Ding Haojiang, Guo Fenglin, Hou Pengfei

2000, 21(6): 573-577.

Abstract(2061) PDF(921)

Abstract:
A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem.In the case of quasi-static problem,the present general solution is simpler since it involves one less potential function than Biot's solution.

Quasi-Equilibrium Problems in Noncompact Generalized Convex Spaces

Ding Xieping

2000, 21(6): 578-584.

Abstract(2120) PDF(742)

Abstract:
By applying a new fixed point theorem due to the author,some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces.These theorems improve and generalize a number of important known results in recent literature.

Yan Zhenya, Zhang Hongqing

2000, 21(6): 585-589.

Abstract(2126) PDF(884)

Abstract:
With the aid of MATHEMATICA,the direct reduction method was extended and applied in 2+1-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation(VCGKPE).As a result,several kinds of similarity reductions for VCGKPE are obtained which contain PainleveⅠ,Painleve Ⅱ and PainleveⅣ reductions.

Dynamic Stress Field Around the Mode Ⅲ Crack Tip in an Orthotropic Functionally Graded Material

Li Chunyu, Zhou Zhenzhu, Duan Zhuping

2000, 21(6): 590-596.

Abstract(2649) PDF(951)

Abstract:
The problem of a Griffith crack in an unbounded orthotr opic functionally graded material subjected to antiplane shear impact was studied.The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient.By using integral transforms and dualimtegral equations,the local dynamic stress field was obtained.The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.

On Solutions of Backward Stochastic Differential Equations With Jumps,With Unbounded Stopping Times as Terminal and With Non-Lipschitz Coefficients,and Probabilistic Interpretationof Quasi-Linear Elliptic TypeIntegro-Differential Equations

Situ Rong, Wang Yueping

2000, 21(6): 597-609.

Abstract(2624) PDF(693)

Abstract:
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non-Lipschitz condition are obtained.The convergence of solutions and the continuous dependence of solutions on parameters are also derived.Then the probabilistic interpretation of solutions to some kinds of quasi-linear elliptic type integrodifferential equations is obtained.

Nonlinear Deformation Theory of Thin Shell

Huang Yan, Tang Guojin

2000, 21(6): 610-616.

Abstract(2678) PDF(806)

Abstract:
The exact relation between strain and displacement is given for nonlinear deformation of thin shell.The fundamental formula of large deformation when the deflection is on the same class with the thickness of the shell is derived after simplified rationally.The fundamental formula of large deformation when the deflection is on the same class with the length of the shell is derived exactly for cylinder shell deformed cylindrical shaped.

A Close-Form Solution to Simply Supported Piezoelectric Beams Under Uniform Exterior Pressure

Lin Qirong, Liu Zhengxing, Jin Zhanli

2000, 21(6): 617-624.

Abstract(2303) PDF(621)

Abstract:
On the basis of two-dimensional constitutive relationships of piezoelectric materials,the analytic solution for simply supported piezoelectric beams under uniform exterior pressure was derived.Furthermore the results were also compared with the ones of FEM for piezoelectric materials.Thus the foundation for further research of piezoelectric materials' distribution sensing mechanism and the validation of numerical methods such as FEM is provided.

Dynamic Response of Elastic RectangularPlates by Spline State Variable Method

Chen Rongyi, Shen Xiaopu, Shen Pengcheng

2000, 21(6): 625-632.

Abstract(2334) PDF(712)

Abstract:
Application of spline element and state space method for analysis of dynamic response of elastic rectangular plates is presented.The spline element method is used for space domain and the state space method in control theory of system is used for time domain.A state variable recursive scheme is developed,then the dynamic response of structure can be calculated directly'several numerical examples are given.The results which are presented to demonstrate the accuracy and efficiency of the present method are quite satisfactory.

Numerical Analysis of theLarge Deflection of an Elastic-Plastic Beam

Gan Hong

2000, 21(6): 633-639.

Abstract(3007) PDF(1403)

Abstract:
The layered approach was adopted to study the numerical procedure of the large deflection of an elastic-plastic Timoshenko's beam,and the nonlinear equilibrium equation was derived by TL Formula.The solution was conducted by means of mNR method.The tangential stiffness matrix of the beam was introduced,and the solving procedures were presented in detail.The solution of the problem is satisfactory.

Dynamic Modeling and Simulation of Flexible Cable With Large Sag

Li Bin, Li Yinghui, Ying Xuegang

2000, 21(6): 640-646.

Abstract(2866) PDF(961)

Abstract:
Discrete model of flexible cable with large sag is established by using multiple rigid body- spherical hinge model,and dynamic equation of that discrete model is derived according to dynamics theory of multiple rigid body system.Displacement and velocity of system are revised to eliminate violation phenomenon of the differential-algebra equation in numerical simulation based on the theory of generalized inverse of matrices.Numerical simulation proves the validity of our method.

Thermoelastic Free Vibration of Clamped Circular Plate

Shu Xuefeng, Zhang Xiaoqing, Zhang Jinxiang

2000, 21(6): 647-654.

Abstract(2240) PDF(616)

Abstract:
An analysis was given for the free vibration of clamped circular plate when temperature and stress fields were coupled.A nonlinear differential equation about time was obtained by using Galerkin's method.The numerical results of vibration amplitude vs time were compared with the uncoupled case.It is found that if the given initial dispacement is small,the effect of thermoelastical coupling will make the natural frequency increase; if the given initial displacement is large,it will be the opposite case.Effects of some different vibration factors are also discussed.

Implicit TVD Schemes Applied to Gas-Droplet Detonation Calculation

Guo Yonghui, Tian Zhou, Hao Baotian

2000, 21(6): 655-660.

Abstract(2526) PDF(668)

Abstract:
In order to investigate parameters of FAE(fuelair explosive) explosion,the two-phase gas-droplet conservation equations with two-dimensional axial symmetry in the Euler coordinate were used.High-resolution implicit TVD(total variation diminishing) schemes were applied to gas phase equations and MacCormack schemes to liquid equations.The formation and propagation of gas-droplet detonation wave were simulated numerically.The simulation results and the others are compared with a good agreement.