应用数学和力学

1996 Vol. 17, No. 4

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A Comparative Study of the Opening and Closing Process of Two Types of Mechanical Heart Valves Using ALE Finite Element Method

Chen Dapeng, Zhang Jianhai

1996, 17(4): 287-296.

Abstract(2071) PDF(580)

Abstract:
Using arbitrary Lagrangian-Eulerian(ALE) finite element method,this paper made a comparative study of the opening and closing behaviour of a downstream directional valve(DDM) and a St.Jude medical valve(SJM) through a two dimensional model of mechanical valve-blood interaction in which the valve is considered as a rigid body rotating around a fixed point,and the blood is simplified as viscous incompressible fluid It's concluded that:(1) Compared with SJM valve,DDM valve opens faster and closes the more gently.(2) The peak badk-flow-flow of DDM is smaller than that of SJM.The present investigation shows that being a better analogue of natural valve,DDM has a brighter potential on its durability than SJM.

Point Force Solution for a Transversely Isotropic Elastic Layer

Ding Haojiang, Liang Jian, Wang Yun

1996, 17(4): 297-305.

Abstract(1806) PDF(588)

Abstract:
By introduction of transmitting matrices' technique for layered structure,mixed equations with stresses and displacements are derived from the basic equations of transversely isotropic elasticity.Then,using Fourier transformation and the general solutions in Zhou et al.^[7],the point force solution for transversely isotropic elastic layer is obtained and it can be degenerated to the corresponding solution of isotropic medium.In this paper,all equations are derived by the use of computer algebra software.

A General Frequency Dependent Digital optimal Preview Servo System

Liao Fucheng, Egami Tadashi, Tsuchiya Takeshi

1996, 17(4): 307-318.

Abstract(1819) PDF(421)

Abstract:
In this paper,we present a design method for a kind of general frequency dependent digital optimal preview servo svstem which is effective to improve frequency characteristics of closed loo Psystem.By the method,for any rational expression frequency dependent weight which loads on error vector,we can design an optimal preview servo system.The result is applied to an air slide linear motor in simulation and its effectivity is proved.

Construction of Modified Taylor-Galerkin Finite Elements and its Application in Compressible Flow Computation

Zhu Gang, Shen Mengyu, Liu Qiusheng, Wang Baoguo

1996, 17(4): 319-325.

Abstract(1808) PDF(509)

Abstract:
In this paper we begin with Taylor-Galerkin Finite Elements,then improve it completely and finally construct Modified Taylor-Galerkin Finite Elements.Computation is done by two methods to study two kinds of subsonic and supersonic flow field.The results show that the new one is much better than the old one.

Approximate Inertial Manifolds for the System of the J-J Equations

Cat Rizeng, Xu Zhenyuan

1996, 17(4): 327-334.

Abstract(1765) PDF(504)

Abstract:
In this paper foe Liapunov functionals has been constructed.the decay property of the high dimensional modes of the J-J equations in the Josephson junctions is obtained,and thus the approxtmate inertial manifolds are given.

Exact Solutions of Near Crack Line Fields for Mode I Crack under Plane Stress Condition in an Elastic Perfectly Plastic Solid

Yi Zhijian, Wang Shine

1996, 17(4): 335-342.

Abstract(2508) PDF(1216)

Abstract:
The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσ_y,and σ_xy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σ_x is different.

Analysis of Interphase Mechanical Behavior with Interface Element in the Composite Materials

Ye Biquan, Yi Xuming, Jing Shengyong, Liang Zhiru

1996, 17(4): 343-348.

Abstract(1818) PDF(818)

Abstract:
In this paper,stress distribution is obtained by employing the interface element to simulate the interphase feature between fiber-matrix in single-ply laminar which consists of fiber arranged periodically in the x-axis direction and matrix,and which is subjected to far-field transverse load the contour of stress σ_sz and radial stress σ_r in the vicinity of interphase are plotted for three different interphase cases.It is made known that the effect of interphase properties in stress distribution is obvious.

Numerical Simulation of Three Dimensional Turbulent Flow in Suddenly Expanded Rectangular Duct

Guo Jiahong, Xu Hongyi

1996, 17(4): 349-356.

Abstract(1925) PDF(594)

Abstract:
In this paper,to simulate the three dimensional turbulent flow in suddenly expanded rectangular duct numerically,the SIMPLEC algorithm is employed to solve the incompressible Navier-Stckes equation with k-εturbulence model.The numerical resulis show well the three dimensional turbulent flow field in the rectangular duct behind the sudden expansion cross-section.and agree.fairly well with the experimental result of the length of the main circumfluence.The numerical method of this paper can be applied to numerical analysis of this kind of turbulent flow.

Spectral Method in Time for KdV Equations

Wu Shengchang, Liu Xiaoqing

1996, 17(4): 357-362.

Abstract(2282) PDF(602)

Abstract:
This paper presents a fully spectral discretization method for solving KdV equations with periodic boundary conditions.Chebyshev pseudospectral approximation in the time direction and Fourier Galerkin approximation in the spatial direction.The expansion coefficients are determined by minimizing an object funictional.Rapid convergence of the method is proved.

The Equation of Motion for the System of the Variable Mass in the Non-Linear Non-Holonomic Space

Qiu Rong

1996, 17(4): 363-367.

Abstract(2042) PDF(493)

Abstract:
The dot product of bases vectors on the super-surface of constraints of the nonlinear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable mass.These are very simple and convenient for computation.From these known equations,the equations of Chaplygin,Nielson,Appell,Mac-Millan et al.are derivd,it is unnecessary to introduce the definition if Appell-Chetaev or Niu Qinping for the virtual displacement.These are compatible with the D'Alembert-Lagrange's principle.

Research of the Periodic Solution for a Class of Nonlinear Differential Equations

Jin Jun

1996, 17(4): 369-375.

Abstract(2345) PDF(486)

Abstract:
In this paper,we study the existence,uniqueness and asymptotic stabgility of the periodic solution for a class of the most,universal fourth-order nonlinear nonautonomous periodic systems.We give the relevant Liapunov function by using the method of analogical slowly changing coefficients.We also give a considerably accurate estimation of the slowly changing coefficients and obtain the sufficient conditions which guarantee the existence,uniqueness and asymptotic Stability of the periodci solutions.