应用数学和力学

2002 Vol. 23, No. 3

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Linearization and Correction Method for Nonlinear Problems

HE Ji-huan

2002, 23(3): 221-228.

Abstract(2483) PDF(754)

Abstract:
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques,the present theory does not assume that the solution is expressed in the form of a power series of small parameter.To obtain an asymptotic solution of nonline...

Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity

DAI Tian-min

2002, 23(3): 229-238.

Abstract(2535) PDF(750)

Abstract:
The theories of thermopiezoelectricity and magnetoelasticty for microplar continua have been systemetically developed by W.Nowacki.In this paper the theories are restudied.The reason why they were restricted to linear cases is analyzed.The more general conservation principle of energy,energy balance...

A New Quadrilateral Thin Plate Element Based on the Membrane-Plate Similarity Theory

HUANG Ruo-yu, ZHENG Chang-liang, ZHONG Wan-xie, YAO Wei-an

2002, 23(3): 239-248.

Abstract(2242) PDF(780)

Abstract:
A new effective path has been proposed to formulate thin plate element by using the similarity theory between plane elasticity and plate bending.Because of avoiding the difficulty of c¹ continuity,the construction of thin plate elements becomes easier.The similarity theory and its applications were ...

Micromechanics Analysis on Evolution of Crack in Viscoelastic Materials

ZHANG Shuang-yin

2002, 23(3): 249-253.

Abstract(2279) PDF(644)

Abstract:
A preliminary analysis on crack evolution in viscoelastic materials was presented.Based on the equivalent inclusion concept of micro-mechanics theory,the explicit expressions of crack opening displacement δ and energy release rate G were derived,indicating that both δ and G are increasing with time....

The Loss of Stability of Laminar Flow in Open Channel and the Mechanism of Sand Ripple Formation

BAI Yu-chuan, LUO Ji-shen

2002, 23(3): 254-268.

Abstract(2454) PDF(646)

Abstract:
In the flow on a mobile bed in an open channel,sand ripple often appears after the sediment begins to move.Different scholars have different views on the formation of sand ripples.This paper holds that as the ripple in general is very small,its formation is due to the instability of the laminar flow...

A Method of Adjusting Bar-Iength of Statically Indeterminate Truss for Increasing Its Load Capacity

SUI Yun-kang, SHAO Jian-yi

2002, 23(3): 269-272.

Abstract(2711) PDF(682)

Abstract:
Based on the character of the internal force distribution of the statically indeterminate truss,the elements stresses were changed by adjusting the length of bars to increase load capacity of structure.The efficiency of the method is illustrated by several examples.

Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation

RONG Hai-wu, XU Wei, WANG Xiang-dang, MENG Guang, FANG TONG

2002, 23(3): 273-282.

Abstract(2633) PDF(597)

Abstract:
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The behavior,stability and bifurcation of steady state response...

Stability Criteria in Terms of Two Measures for Delay Differential Equations

KOU Chun-hai, ZHANG Shu-nian

2002, 23(3): 283-291.

Abstract(2510) PDF(584)

Abstract:
By using the variational Liapunov method,stability properties in terms of two measures for delay differential equations are discussed.In the case that the unperturbed systems are ordinary differential systems,employing auxiliary measure h^*(t,x),criteria on nonuniform and uniform stability in terms o...

Numerical Simulation of Roll Forming for Channel Section With Outer Edge

HAN Zhi-wu, LIU Cai, LU Wei-ping

2002, 23(3): 292-298.

Abstract(2211) PDF(555)

Abstract:
The finite strip method in structural analysis has been extended,and elastic-plastic large deformation spline finite strip method based on the Updated-Lagrange method(U.L.method)was established to simulate roll forming process of channel section with outer edge.The deformation characteristics of str...

A Stress Vector-Based Constitutive Model for Cohesionless Soil(Ⅰ)-Theory

SHI Hong-yan, XIE Ding-yi

2002, 23(3): 299-308.

Abstract(2572) PDF(653)

Abstract:
On the basis of the sufficient consideration of vectorial characteristics of stress,a new nonlinear constitutive model for cohesionless soil under plane strain and 3-D conditions was presented in a way that the action effects of stress vector are decomposed into the action effect of mean effective s...

Fixed Ponts of Increasing Operators in Ordered Space With Applications

YANG Cuang-chong

2002, 23(3): 309-315.

Abstract(2080) PDF(677)

Abstract:
The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized.The obtained results are then applied to singular nonlinear boundary problem in ordinary differential ...

Theoretical Model of Vibrating Object Transmitting Noise Towards External Sound

YAO Zhi-yuan

2002, 23(3): 316-320.

Abstract(2442) PDF(556)

Abstract:
On the basic theory of modal method,the coupling relation between the vibration of objects and external sound was analyzed,the theoretical model solving the vibration and noise was provided,the corresponding calculation formula was given.The calculating results show out that this calculation formula...

Global Attractivity for a Class of Nonlinear Delay Difference Equations

LIU Yu-Ji

2002, 23(3): 321-330.

Abstract(2474) PDF(543)

Abstract:
The global attractivity of the delay difference equation $x_n+a_nx_n+f{}=0, which includes the discrete type of many mathematical ecologic equations,was dicussed.The sufficient conditions that guarantee every solution to converge to zero were obtained.Many known results are improved and generated.