应用数学和力学

2000 Vol. 21, No. 11

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Shear Beam Model for Interface Failure Under Antiplane Shear(Ⅰ)——Fundamental Behavior

SHEN Xin-pu, Zenon Mroz

2000, 21(11): 1101-1108.

Abstract(2185) PDF(769)

Abstract:
The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure.On the basis of the theory of elastoplasticity and fracture mechanics,the shear beam model for the solution of interface failure was presented.The concept of cohesive crack.was adopted to describe the constitutive behavior of the cohesive interfacial layer.Related fundamental equations such as equilibrium equation,constitutive equations were presented.The behavior of a double shear beam bonded through cohesive layer was analytically calculated.The stable propagation of interface crack and process zone was investigated.

Shear Beam Model for Interface Failure Under Antiplane Shear(Ⅱ)——Instability

SHEN Xin-pu, Zenon Mroz

2000, 21(11): 1109-1116.

Abstract(2249) PDF(632)

Abstract:
Based on the(Ⅱ) of the present work,the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied.The prime results include:1) discriminant equation which clarifies the mode of instability,snap-back or snap-through,was established; 2) analytical solution was given out for the double shear beam and the load-displacement diagram for monotonic loading was presented for a full process; and 3) the problem of the energy release induced by instability was discussed.

An Analytic and Application to State Space Reconstruction About Chaotic Time Series

MA Jun-hai, CHEN Yu-shu

2000, 21(11): 1117-1124.

Abstract(2379) PDF(1490)

Abstract:
The state space reconstruction is the major important quantitative index for describing nonlinear chaotic time series.Based on the work of many scholars,such as:N.H.Packard,F.Takens M.Casdagli J.F.Bibson,CHEN Yu-shu et al,the state space was reconstructed using the method of Legendre coordinate.Several different scaling regimes for lag time τ were identified.The influence for state space reconstruction of lag time τ was discussed.The result tells us that is a good practical method for state space reconstruction.

Equivalent Boundary Integral Equations With Indirect Unknowns for Thin Elastic Plate Bending Theory

ZHANG Yao-ming, SUN Huan-chun, YANG Jia-xin

2000, 21(11): 1125-1132.

Abstract(2301) PDF(768)

Abstract:
Equivalent Boundary Integral Equations(EBIE) with indirect unknowns for thin elastic plate bending theory,which is equivalent to the o riginal boundary value problem,is established rigoro usly by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle.The previous three kinds of boundary integral equations with indirect unknown sare discussed thoroughly and it is shown that all previousre sultsare not EBIE.

Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations

DING Xie-ping, ZHANG Hong-lin

2000, 21(11): 1133-1139.

Abstract(2291) PDF(827)

Abstract:
Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E.Let T:K→K be a uniformly continuous φ-hemicontractive operator with bounded range and {a_n},{b_n},{cn},{a'_n},{b'_n},{c'_n}be sequences in[0,1] satisfying:ⅰ)a_n+b_n+c_n=a'_n+b'_n+c'_n=1,∀n≥0; For any given x0,u0,v0∈K,define the Ishikawa type iterative sequence {x_n} as follows: where {u_n} and {v_n} are bounded sequences in K.Then {x_n} converges strongly to the unique fixed point of T.Related result deals with the convergence of Ishikawa type iterative sequence to the solution of φ-strongly accretive operator equations.

Technical Stability of Nonlinear Time-Varying Systems With Small Parameters

CHU Tian-guang, WANG Zhao-lin

2000, 21(11): 1140-1146.

Abstract(2451) PDF(766)

Abstract:
Technical stability allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered.Based on a differential comparison principle and a basic monotonicity condition,technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method.Explicit criteria of technical stability are established in terms of coefficients of the system under consideration.Conditions under which the technical stability of the system can be derived from its reduced linear time-varying(LTV) system were further examined,as well as a condition for linearization approach to technical stability of general nonlinear systems.Also,a simple algebraic condition of exponential asymptotic stability of LTV systems is presented.Two illustrative examples are given to demonstrate the availability of the presently proposed method.

A Method of Solving the Fuzzy Finite Element Equations in Monosource Fuzzy Numbers

LIU Chang-hong, CHEN Qiu

2000, 21(11): 1147-1150.

Abstract(1959) PDF(827)

Abstract:
For some cases the rules of monosource fuzzy numbers can be used into the solution of fuzzy stochastic finite element equations in engineering.This method can reduce the computing quantity of the solution.It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method(SFEM).In addition,a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modern engineering design.

A Form Function Method for Form Finding of Tension Structure

SUN Zong-guang, ZHAO Jian-bin

2000, 21(11): 1151-1155.

Abstract(2117) PDF(654)

Abstract:
A new form function involving parameters B i is presented.On the basis of the form function,an initial form of tension structure was found by interpolating through the control points on boundary of the structure.The form function can be controlled by changing Biaccording to the pretension and the boundary of the structure.The final form of a tension structure should be an equilibrium system under the pretension.To axamine the nature of the initial form,the FEM was used.Many examples show that the initial form gives a very ideal result for equal or unequal pretension in two directions of the structure.In general cases,there is little difference between the initial form and the final one.

The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance

MA Shi-wang, WANG Zhi-cheng, YU Jian-she

2000, 21(11): 1156-1164.

Abstract(2407) PDF(705)

Abstract:
The nonlinear system of first-order differential equations with a deviating argument x>(t)=Bx(t)+F(x(t-τ))+p(t),is considered,where x(t)∈R²,τ∈R,B∈R^2×2 F is bounded and p(t) is continuous and 2π-periodic.Some sufficient conditions for the existence of 2π-periodic solutions of the above equation,in a resonance case,by using the Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree are obtained.Some applications of the main results to Duffing's equations are also given.

Method of Equilibrium Differential Equation for Analysis of Strength of Large Deflection Drill String

LIU Yan-qiang

2000, 21(11): 1165-1171.

Abstract(2633) PDF(629)

Abstract:
To counter the strength problem of drill string in well of large curvature and small diameter,well axis was taken as datum axis.Based on description of deflection of well axis and on analysis of three dimensional forces of a small section of drill string,equilibrium differential equations of large deflection drill string were established.The internal forces were found by Longe-Kutta method.The stresses were found by using them and the strength prerequisite was established.Stresses of drill string in lateral horizontal well H767 were computed.The results are in agreement with those of finite element model and soft-rope rigidified model.But the method is simpler for computation than finite element model and is more perfect than soft-rope rigidified model.Curvature of the well is too large and there is stress concentration so that the fraction accident of drill string occurs.

A New Approach for the Computation of Hopf Bifurcation Points

YE Rui-song

2000, 21(11): 1172-1178.

Abstract(2120) PDF(807)

Abstract:
A new approach is proposed to compute Hopf bifurcation points.The method could produce small extended systems and therefore could reduce the computational effort and storage.One numerical example is presented to demonstrate that the method is efficient.

The Coupling Method for Torsion Problem of the Square Cross-Section Bar With Cracks

ZHAO Hui-ming, DONG Zheng-zhu, CAO Ying-luo

2000, 21(11): 1179-1184.

Abstract(2064) PDF(751)

Abstract:
By coupling natural boundary element method(NBEM) with FEM based on domain decomposition,the torsion problem of the square cross-sections bar with cracks have been studied,the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated,and some distribution pictures of the stresses have been drawn.During computing,the effect of the relaxed factors to the convergence speed of the iterative method has been discussed.The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM.

On the Electroelastic Interaction of a Piezoelectric Screw Dislocation With an Elliptical Inclusion in Piezoelectric Materials

LIU Jin-xi, JIANG Zhi-qing, FENG Wen-jie

2000, 21(11): 1185-1190.

Abstract(1878) PDF(709)

Abstract:
The electroelastic interaction of a piezoelectric screw dislocation with an elliptical inclusion in piezoelectric materials is considered.The electroelastic fields in both the matrix and the inclusion were given explicitly by using the perturbation concept and the method of Laurent series expansion.Furthermore,the expressions of the image force acting on a piezoelectric screw disolcation were obtained.Numerical examples are provided to reveal the effect of piezoelectricity and the relative stiff ness between the inclusion and the matrix on the image force.Consequently,the new interaction mechanism is found.

The Invariant Manifold Method and the Controllability of Nonlinear Control System

YANG Liu

2000, 21(11): 1191-1200.

Abstract(2802) PDF(619)

Abstract:
The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application.A.M.Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results.Based on Kovalev.s oriented manifold method,firstly,by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out.Then the realization of the necessary condition was discussed.At last,the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.

The Second Initial-Boundary Value Problem for a Quasilinear Prabolic Equations With Nonlinear Boundary Conditions

Pan Jia-qing

2000, 21(11): 1201-1207.

Abstract(2281) PDF(616)

Abstract:
With prior estimate method,the existence,uniqueness,stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated.The main results are:1) there exists only one global weak solution which continuously depends on initial value; 2) when t<T₀,the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.

Blow-up of the Solutions for the Initial-Boundary Problems of the Nonlinear Schr dinger Equations

WANG Fan-bin

2000, 21(11): 1208-1210.

Abstract(2180) PDF(697)

Abstract:
The conditions of blow-up of the solutions for one class of nonlinear Schr dinger equations by using the eigenvalue and eigenfunction of the Laplace operator are got,which complements and perfects the results of ZHANG Jian.