应用数学和力学

1998 Vol. 19, No. 6

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General Axisymmetry Problems for Shells of Revolution and Analyses of Intergral Equation

Chen Shanlin, Liu Dong

1998, 19(6): 471-479.

Abstract(2253) PDF(427)

Abstract:
In this paper, a simplified equation in complex form for axisymmetry elastic thin shells of revolution under arbitrary distributed loads is given. The equation is equivalent to the exact equations within the error range of the thin shell theory, with the singularities at the points of meridional extreme values eliminated. A Volterra integral equation of the problem and the numerical solutions are given.

Threshold Value for Diagnosis of Chaotic Nature of the Data Obtained in Nonlinear Dynamic Analysis

Ma Junhai, Chen Yushu, Liu Zengrong

1998, 19(6): 480-488.

Abstract(2445) PDF(734)

Abstract:
In this paper surrogate data method of phase-randomized is proposed to identify the random or chaotic nature of the date obtained in dynamic analysis. The calculating results validate the phase-randomized method to be useful as it can increase the extent of accuracy of the results. And the calculating results show that threshold values of the random timeseries and nonlinear chaotic timeseries have marked difference.

Algorithm of Solutions for Mixed Nonlinear Variational-Like Inequalities in Reflexive Banach Space

Ding Xieping

1998, 19(6): 489-496.

Abstract(2509) PDF(767)

Abstract:
In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequalit y obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, the author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

Singular Perturbation of General Boundary Value Problem for Nonlinear Differential Equation System

Zhou Yali, You Zhefeng, Lin Zongchi

1998, 19(6): 497-504.

Abstract(2759) PDF(706)

Abstract:
In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik^[1] and fixed point theory, the existence of the solution of the perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.

A Theoretical and Experimental Investigation of a Primary Resonance of a Three Circular Plates Torsion Vibration SystemGH

Yang Zhian, Qiu Jiajun, Li Li

1998, 19(6): 505-511.

Abstract(2789) PDF(630)

Abstract:
The method of averaging is applied in this paper to deal with a primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.

Near Crack Line Elastic-Plastic Analysis for a Finite Plate Loaded by Two Pairs of Antiplane Point Forces

Wang Cheng, Zhang Lukun

1998, 19(6): 512-519.

Abstract(2348) PDF(704)

Abstract:
In this paper, the improved near crack line analysis method proposed in Refs. [ 1] and [ 2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is, the elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.

Constitutive Relation and Stiffness Degradation of Cracked Anisotropic Composite Laminates(Ⅱ)——Determination of Resolved Stiffness and Investigation of Stiffness Degradation for Cracked Laminates

Wang Xingguo, Hua Yu, Li Zhengneng

1998, 19(6): 520-527.

Abstract(2074) PDF(582)

Abstract:
The study on property degradation of damaged composite laminates is extended to anisotropic laminates with matrix cracking. In(Ⅱ) of the paper, a solution for partitioned stiffness is given to complete the constitutive relations developed in(Ⅰ). The stiffness degradation in(θ_m/90_n)_s cracked laminates is calculated and the results are discussed.

On the Stability Estimation of Analytic Continuation for Potential Field

Xu Dinghua, Cheng Jin, Li Ming zhong

1998, 19(6): 528-537.

Abstract(2769) PDF(506)

Abstract:
This paper discusses the stability of solutions to a class of Cauchy pro blems for Laplace equatio ns under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamo to. smethods for solving ill-posed problems respectively, the stability estimations of weighted Hlder type and logarithmic type, have been obtained accor dingly.

The H^Lder Continuity of Generalized Solutions of a Class Quasilinear Parabolic Equations

Wang Xiangdong

1998, 19(6): 538-548.

Abstract(2420) PDF(607)

Abstract:
Let A and B satisfy the structural conditions(2), the local H^Lder continuity interior to Q=G×(0,T) is proved for the generalized solutions of quasilinear parabolic equations as follows:.

Torsion of Composite Laminated Bars with a Large Number of Layers

Zhang Jian, Li Sijian

1998, 19(6): 549-555.

Abstract(2447) PDF(564)

Abstract:
In view of the effective elastic moduli theory^[1]. analyzing the thick compositelaminated bars subjected to an externully applied torque are prasented by threedimensional finite element(3-D FEM) and global-local method in this paper.Numerical results involving,he distribution of shearing stresses on cross-section andthe torsional deformation and the interlaminar sirens near to free edges are given. tfnecessary elemeats discretization mad be densely carried ont only in the high stressgradient. region. Obviously, it requires less computer memory and computational time sothat it offers an effective way for evaluating strength of laminated bars torsion with agreat number of layers.

Application of Wavelet Transform to Bifurcation and Chaos Study

Zheng Jibing, Gao Hangshan, Guo Yinchao, Meng Guang

1998, 19(6): 556-563.

Abstract(2432) PDF(751)

Abstract:
The response of a nonlinear vibration system may be of three types, namely,periodic, quasiperiodic or chaotic. when foe parameters of foe system are changed. The periodic motions can be identified by Poincarb map, and harmonic wavelet transform(HAT) can distinguish quasiperiod from chaos, so the existing domains of differenttypes of motions of the system can be revealed in the parametric space with themethod of HWT joining with Poincare map.