应用数学和力学

1999 Vol. 20, No. 2

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The Application of Nonlinear Gauge Method to the Analysis of Local Finite Deformation in the Necking of Cylindrical Bar

Cui Ximin, Chen Zhida

1999, 20(2): 111-118.

Abstract(2300) PDF(660)

Abstract:
Localized deformation and instability is the focal point of research in mechanics.The most typical problem is the plastic analysis of cylindrical bar necking and shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully.In this paper,on the basis of S(strain)-R(rotation)decomposition theorem,the authors obtain the local strain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modelling technique.

Weak Formulation of Mixed State Equation and Boundary Value Problem of Laminated Cylindrical Shell

Ding Kewei, Tang Limin

1999, 20(2): 119-125.

Abstract(2244) PDF(658)

Abstract:
Weak formulation of mixed state equations including boundary conditions are presented in a cylindrical coordinate system by introducing Hellinger-Reissner variational principle.Analytical solutions are obtained for laminated cylindrical shell by means of state space method.The present study extends and unifies the solution of laminated shells.

Theory and Method of Optimal Control Solution to Dynamic System Parameters Identification(Ⅰ) Fundamental Concept and Deterministic System Parameters Identification

Wu Zhigang, Wang Benli, Ma Xingrui

1999, 20(2): 127-133.

Abstract(2687) PDF(967)

Abstract:
Based on the concept of optimal control solution to dynamic system parameters identification and the optimal control theory of deterministic system,dynamics system parameters identification problem is brought into correspondence with optimal control problem.Then the theory and algorithm of optimal control are introduced into the study of dynamic system parameters identification. According to the theory of Hamilton-Jacobi-Bellman(HJB)equations.solution,the existence and uniqueness of optimal control solution to dynamic system parameters identification are resolved in this paper.At last,the parameters identification algorithm of deterministic dynamic system is presented also based on above mentioned theory and concept.

The Analysis of Crack Problems with Non-Local Elasticity

Zhao Minghao, Cheng Changjun, Liu Guoning, Shen Yapeng

1999, 20(2): 135-143.

Abstract(2788) PDF(722)

Abstract:
In this paper,the displacement discontinuity fundamental solutions(DDFS)corresponding to the unit concentrated displacement discontinuity for plane problems of nonlocal elasticity are obtained.Based on the displacement discontinuity boundary integral equation(DDBIE)and boundary element method(BEM),a method of analysis of crack problems in non-local elasticity with generalized purpose is proposed.By using this method,several important problems in fracture mechanics such as edge crack are studied.The study of edge crack shows that the stress concentration factor(SCF) near the crack tip is not a constant but varies with the crack length.With this result the effect of crack length on the fracture toughness K_Ⅰc is studied.The results obtained in this paper are in accordance with the published ones.

Basic Equations, Theory and Principle of Computational Stock Market (Ⅰ)——Basic Equations

Yun Tianquan

1999, 20(2): 145-152.

Abstract(2626) PDF(750)

Abstract:
This paper studies computational stock market by using network model and similar methodology used in solid mechanics.Four simultaneous basic equations,i.e.,equation of interest rate and amount of circulating fund,equations of purchasing and selling of share,equation of changing rate of share price,and equation of interest rate,share price and its changing rate,have been established.Discussions mainly on the solution and its simple applications of the equation of interest rate and amount of circulating fund are given.The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping,and the influence of amount of circulating fund with exponential attenuation due to the decreasing of banking interest rate.

On the Boundedness and Periodicity of the Solutions of a Certain Vector Differential Equation of Third-Order

Cemil Tun

1999, 20(2): 153-160.

Abstract(2206) PDF(725)

Abstract:
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third order.

Active Vibration Control and Suppression for Integrated Structures

Wang Zhongdong, Chen Suhuan, Yang Xiaodong

1999, 20(2): 161-168.

Abstract(2045) PDF(674)

Abstract:
The finite element dynamic model for integrated structures containing distributed piezoelectric sensors and actuators(S/As)is formulated with a new piezoelectric plate bending element in this paper.The problem of active vibration control and suppression of integrated structures is investigated under constant gain negative velocity feedback control law.A general method for active vibration control and suppression of integrated structures is presented.Finally,numerical example is given to illustrate the validity of the method proposed in this paper.

Parallel Interval Matrix Multisplitting AOR Methods and Their Convergence

Bai Zhongzhi

1999, 20(2): 169-174.

Abstract(2709) PDF(920)

Abstract:
This paper proposes a class of parallel interval matrix multisplitting AOR methods for solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H_matrices.

Meso Approaches for the Creep Damage Behavior of Nickel-Base Directionally Solidified Superalloys

Yue Zhufeng, Lü Zhenzhou, Zheng Changqing

1999, 20(2): 175-180.

Abstract(2256) PDF(829)

Abstract:
A self_consistent creep damage constitutive model and a finite element model have been developed for nickel_base directionally solidified superalloys.Grain degradation and grain boundary voiding are considered.The model parameters are determined from the creep test data of a single crystal and a directionally solidified superalloy with a special crystallographic orientation.The numerical analysis shows that the modeled creep damage behaviors of nickel_base directionally solidified superalloys with different crystallographic orientations are in good agreement with the experimental data.

Rational Finite Element Method for Elastic Bending of Reissner Plates

Sun Weiming, Yang Guangsong

1999, 20(2): 181-186.

Abstract(2270) PDF(800)

Abstract:
In this paper,some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements.And therefore the rational FEM,which is perfect combination of the analytic methods and numeric methods,has been presented.This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures.What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.

Output Regulation of the General Nonlinear Discrete-Time System

Li Tiecheng, Wang Zhaolin, Li Junfeng

1999, 20(2): 187-191.

Abstract(2281) PDF(566)

Abstract:
With the use of centre manifold and dynamic system theory,the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete-time system.This work generalizes and refines the corresponding results by Isidori and Byrnes on the affine nonlinear continuous-time system.

The Crack Tip Fields of Orthotropic Composite Plate under Bending

Yang Weiyang, Zhang Shaoqin

1999, 20(2): 193-199.

Abstract(2482) PDF(649)

Abstract:
In this paper,mechanics analysis for crack tip fields of linear elastic orthotropic composite plate under symmetric bending load was done.By using a complex variable method,the equations for bending moment,twisting moment,stress,strain and displacement fields near crack tip are derived.

Boundary Mixed Variational Inequality in Friction Problem

Ding Fangyun, Zhang Xin, Ding Rui

1999, 20(2): 201-210.

Abstract(2440) PDF(790)

Abstract:
In this paper,with the use of the friction problem in elasticity as the background,the existence and uniqueness for the solution of the nonlinear,indifferentiable mixed variational inequality are discussed.Its corresponding boundary variational inequality and the existence and uniqueness of solution are given.This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.

On Quasilinear Elliptic Hemivariational Inequalities

Liu Zhenhai

1999, 20(2): 211-216.

Abstract(2270) PDF(772)

Abstract:
In the present paper,quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied.This extension is strongly motivated by various problems in mechanics.By using the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators,the existence of solutions is proved.

A Priori Estimate for Lower Solutions of a Class Quasilinear Elliptic Equations

Wang Xiangdong, Han Puxian, Liang Ting

1999, 20(2): 217-219.

Abstract(2092) PDF(604)

Abstract:
A new priori estimate of lower solution is made for the following quasilinear elliptic equation: The result presented in this paper enriches and extends the corresponding result of Gilbarg-Trudinger.