应用数学和力学

1996 Vol. 17, No. 5

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Green’s Functions of Two-Dimensional Anisotropic Body with a Parabolic Boundary

Hu Yuantai, Zhao Xinghua

1996, 17(5): 377-385.

Abstract(1926) PDF(678)

Abstract:
For two-dimensional anisotropic body with a parabolic boundary, the simple explicit expressions of Green's functions are presented when a concentraled force is applied at a point in material for two kind boundary conditions, which are of free surfoce and rigid surface. When parabolic curve degenerales into a half-infinite crack or a half-infinite rigid defect the stress singular fields near the crack tip are obtained by using the results obtained. Specially, when the concentrated force is applied at a point on the parabolic boundary, its Green's functions are studied, too. By them and their integral, the arbitrary parabolic boundary value problems can be solved. The limit case that the boundary degenerates into a crack is studied and the corresponding stress intensity factors are obtained.

ALE Finite Element Analysis of the Opening and Closing Process of the Artificial Mechanical Valve

Zhang Jianhai, Chen Dapeng, Zou Shengquan

1996, 17(5): 387-396.

Abstract(2028) PDF(539)

Abstract:
Employing arbitrary Lagrangian-Eulerian (ALE) finite element method, this poper studies the opening and closing process of a St. Jude medical valve through a two-dimensional model of the mechanical valve-blood interaction in which the valve is regarded as a rigid body rotating around a fixed point, and the blood is simplified as viscous incompressible Newtonian fluid. The numerical analysis of the opening and closing behaviour of as St. Jude valve suggested that: 1. The whole opening and closing process of an artificial mechanical valve is consisted of four phases: Ⅰ Opening phase; Ⅱ Opening maintenance phase; Ⅲ Closing phase; Ⅳ Closing maintenance phase. 2. The St. Jude medical valve closes with prominent regurgitat which results in waterhammer effect. 3. During the opening and closing process of the St. Jude valve,high shear stresses occur in the middle region of the two leaflets and on the valve ring. The present model has made a breakthrough on the coupling computational analysis considering the interactive movement of the valve and blood.

A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation

Liu Guoqing, Su Yucheng

1996, 17(5): 397-404.

Abstract(2016) PDF(552)

Abstract:
In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.

On General Type of Digital optimal Preview Servo System

Liao Fucheng, Egami Tadashi, Tsuchiya Takeshi

1996, 17(5): 405-417.

Abstract(1720) PDF(510)

Abstract:
Usually, only siep future desired singals are utilized in the field of preview servo systems design. In this paper, we discuss the design problem of optimal preview servo system while the future desired signal and future disturbance signal are polynomials or outputs of linear free systems. (1) Conditions of controllability and observability for enlarged system, (2) A design method of optimal preview servo controllers,(3) A simple and convenient algorithm of control law are obtained.

Flat-Plate Boundary-Layer Flows Induced by Dusty Shock Wave

Wang Boyi, Tao Feng

1996, 17(5): 419-425.

Abstract(2086) PDF(424)

Abstract:
When a dusty shock wave propagates along a flat plate, laminar boundary-layer flows are formed over the solid wall. The induced boundary layer problem is numerically investigated in the present paper. Using a two-continuum medium and two way coupling model, the governing equations for this two-phase flow system are given and then solved by the finite difference method. The calculation results indicate that the post-shock flow field is characterized by relaxation phenomenon. The effects of the relaxation structure of the dusty shock wave on the boundary layer are discussed in detail.

Characteristics of Subdifferentials of Functions

Guo Xingming

1996, 17(5): 427-432.

Abstract(2770) PDF(792)

Abstract:
In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially convexity of functions, are described by subdifferentials.

An Approximate Solution of Eigen-Frequencies of Transverse Vibration of Rectangular Plates with Elastical Restraints

Zhou Ding

1996, 17(5): 433-438.

Abstract(2175) PDF(694)

Abstract:
This poper presents an approximate solution for calculating eigen-frequencies of transverse vibration of rectangular plates elastically restrained against rotation along edges. The formulae are not only very simple and easily programmed but also have high accuracy. Finally, some numerical results are given and compared with other results obtained.

On the Unification of the Hamilton Principles in Non-Holonomic System and in Holonomic System

Liang Lifu, Wei Yang

1996, 17(5): 439-444.

Abstract(2127) PDF(583)

Abstract:
In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.

Existence of Positive Solutions for a Class of Singular Two Point Boundary Value Problems of Second Order Nonliear Equation

Yang Zuodong

1996, 17(5): 445-454.

Abstract(2159) PDF(560)

Abstract:
In this paper, we establish the existence of positive solutions of (|y'|^p-2y')'+f(t,y)= 0 (p>1). y(0)=y(1)=0. The function f is allowed to be singular when y=0.

Large Deflection Problem of Thin Orthotropic Circular Plate on Elastic Foundation with Variable Thickness under Uniform Pressure

Wang Jiaxin, Liu Jie

1996, 17(5): 455-463.

Abstract(2675) PDF(546)

Abstract:
Basic equations for large deflection theory of thin orthotropic circular plate on elastic foundation with variable thickness under uniform pressure are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate on elastic foundation with variable thickness under uniform pressure, If ε=0, R=100 and R=200, μ=0,3, λ=1 then the result derived from the solution in this paper agrees statisfactorily with the result given by Galerkin's method^[1] for solving large deflection problem of thin circular, plate with constant thickness on elastic foundation under uniform pressure.

An Analytical Solution of Heat Conduction on a Locally Nonvniformly Heated Surface of a Plale with Finite Thickness

Wang Mingrui, Jin Hui

1996, 17(5): 465-470.

Abstract(1698) PDF(588)

Abstract:
In engineering and technology, the following problem is often touched upon A certain portion of a plate with finite thickness is heated on its surface, so that the heat flux along the surface is distributed nonuniformly and varying with time. For this kind of heal conduction, there is no available analytical solution given in existing treatises concerning heat conduction. This paper presents an analytical solution of this problem, its calculation results are in good agreement with the experimental data.