应用数学和力学

2002 Vol. 23, No. 11

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New Collectively Fixed Point Theorems and Applications in G-Convex Spaces

DING Xie-ping, Park Jong-yeoul

2002, 23(11): 1101-1112.

Abstract(2650) PDF(649)

Abstract:
By applying the technique of continuous partition of unity and Tychonoff.s fixed point theorem,some new collectively fixed point the orems for a family of set-valued mappings defined on the product space of noncompact G-convexs paces are proved.Asapplications,some nonempty intersection the orems of Ky Fantype for a family of subsets of the products pace of G-convex spaces are proved;An existence the orem of solutions for a system of nonlinear inequlities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces.Our theorems improve,unify and generalizd many important known results in the recent literature.

A Micromechanics Method to Study the Effect of Domain Switching on Fracture Behavior of Polycrystalline Ferroelectric Ceramics

CHENG Jin-quan, WANG Biao, DU Shan-yi

2002, 23(11): 1113-1123.

Abstract(2076) PDF(571)

Abstract:
The effect of domain switching on anisotropic fracture behavior of polycrystalline ferroelectric ceramics was revealed on the basis of the micromechanics method.Firstly,the electroelastic field inside and outside an inclusion in an infinite ferroelectric ceramics is carried out by the way of Eshelby-Mori-Tanaka.s theory and a statistical model,which accounts for the influence of domain switching. Further,the crack extension force(energy-release rate)G_ext for a penny-shape crack inside an effective polycrystalline ferroelectric ceramics is derived to estimate the averaged effect of domain switching on the fracture behavior of polycrystalline ferroelectric ceramics.The simulations of the crack extension force for a crack in a BaTiO₃ ceramics are shown that the effect of domain switching must be taken into consideration while analyzing the fracture behavior of polycrystalline ferroelectric ceramics.These results also demonstrate that the influence of the applied electric field on the crack propagation is more profound at smaller mechanical loading and the applied electric field may enhance the crack extension in a sense,which are consistent with the experimental results.

The Stress Subspace of Hybrid Stress Element and the Diagonalization Method for Flexibility Matrix H

ZHANG Can-hui, FENG Wei, HUANG Qian

2002, 23(11): 1124-1132.

Abstract(2188) PDF(650)

Abstract:
The following is proved:1)The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix.2)The equivalent assumed stress modes lead to the identical hybrid element.The Hilbert stress subspace of the assumed stress modes is established.So,it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method.Because of the resulting diagonal flexibility matrix,the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly.The numerical examples show that the method is effective.

Stability Margin of Systems With Mixed Uncertainties Under the IQC Descriptions

DONG Hai-rong, GENG Zhi-yong, WANG Jin-zhi, HUANG Lin

2002, 23(11): 1133-1140.

Abstract(2062) PDF(600)

Abstract:
Stability perturbation bounds problem for systems with mixed uncertainties is discussed.It is supposed that the linear part in the forwark loop is of parametric unceratinties described by interval perturbation mode,and that the non-linear part in the feedback loop is characterized by an integral quadratic constraint(IQC).The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional.The infinite stability checking problem of the mixed uncertain system can be coverted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave functions and their properties.The result is illustrated to be efficient through an example.

Nonlinear Galerkin Method for the Exterior Nonstationary Navier-Stokes Equations

HE Yin-nian, LI Kai-tai

2002, 23(11): 1141-1149.

Abstract(2548) PDF(781)

Abstract:
A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved.If the fine meshh is choosed as coarse mesh H-sgure, the nonlinear Galerkin method,nonlineatity is only treated on the coarse grid and linearity is treated on the fine grid.Hence,the new algorithm can save a large amount of computational time.

An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix

YAN Qing-you, XIONG Xi-wen

2002, 23(11): 1150-1168.

Abstract(2819) PDF(1481)

Abstract:
An efficient and stable structure preserving algorithm,which is a variant of the QR like (SR)algorithm due to Bunse-Gerstner and Mehrmann,is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix.In the algorithm two strategies are employed,one of which is called dis-unstabilization technique and the other is preprocessing technique.Together with them,a socalled ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm.It is shown that the new algorithm can overcome the instability and breakdown at low cost.Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.

Motion of Level Sets by a Generalized Mean Curvature

ZHENG Yong-ai, LIU Zu-han

2002, 23(11): 1169-1176.

Abstract(2322) PDF(677)

Abstract:
Short time existence and uniqueness for the classical motion are studied by the function of the principal curvatures of a smooth,surface and the Evans and Spruck's results are generalized.

Study on Catastrophic Mechanism for Rotor Drop Transient Vibration Following Magnetic Bearing Failure

FANG Zhi-chu

2002, 23(11): 1177-1182.

Abstract(2572) PDF(682)

Abstract:
The nonlinear and transient vibration of a rotor,which dropped onto back-up bearings when its active magnetic bearings were out of order,was investigated.After strictly deriving its equations of motion and performing numerical simulations,the time-histories of rotating speed of the dropping rotor,and normal force at the rubbing contact point as well as the frequency spectrum of the vibration displacement of back-up bearings are fully analyzed.It is found that the strong and unsteady forced bending vibration of the unbalancced and damped rotor decelerating through its first bending vibtation of the unbalaned and damped rotor decelerating through its first critical speed as well as chattering at high frequencies caused by the non-linearity at the rubbing contact point between the journal and back-up bearings may lead to the catastrophic damage of the system.

Convergence Theorems for the AOR Method

HUANG Ting-zhu, WANG Guang-bin

2002, 23(11): 1183-1187.

Abstract(2908) PDF(579)

Abstract:
Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition for H-matrices are studied.The obtained convergence conditions suited to matrices which need not to be diagonally dominant.

Boundedness and Persistence and Global Asymptotic Stability for a Class of Delay Difference Equations With Higher Order

LI Xian-yi

2002, 23(11): 1188-1194.

Abstract(2544) PDF(633)

Abstract:
Some sufficient conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained,which partly solve G. Ladas.two open problems and extend some known results.

Nonlinear Saturation of Baroclinic Instability in the Generalized Phillips Model(Ⅱ)-The Lower Bound on the Disturbance Energy and Potential Enstrophy to the Nonlinearly Unstable Basic Flow

ZHANG Gui, XIANG Jie

2002, 23(11): 1195-1202.

Abstract(2047) PDF(723)

Abstract:
On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated.The lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance.

Higher Order Multivariable N^Lrlund Euler-Bernoulli Polynomials

LIU Guo-dong

2002, 23(11): 1203-1210.

Abstract(2055) PDF(629)

Abstract:
The definitions of higher order multivariable N^Lrlund Euler polynomials and N^Lrlund Bernoulli polynomials are presented and some of their important properties are expounded.Somei-dentities involving recurrence sequences and higher order multivariable N^Lrlund Euler-Bernoulli polynomials are established.