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(2334) 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 nonlinear system,the technique first searched for a solution for the linearized system,then a correction was added to the linearized solution.So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.

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

DAI Tian-min

2002, 23(3): 229-238.

Abstract(2366) 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 equation and Hamilton principle of thermopiezoelectricity and magnetoelasticity for micropolar continua are established.The corresponding complete equations of motion and boundary conditions as well as balance equations of energy rate for local and nonlocal micropolar thermopiezo-electricity and magnetothermoelasticity are naturally derived.By means of two new functionals and total variation the boundary conditions of displacement,microrotation,electric potential and temperature are also given.

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(2110) 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 discussed more deeply,and a new four nodes,sixteen D.O.F(degree of freedom)thin plate element was presented on the base of the similarity theory.Numerical results for typical problems show that this new element can pass the patch test and has a very good convergence and a high precision.

Micromechanics Analysis on Evolution of Crack in Viscoelastic Materials

ZHANG Shuang-yin

2002, 23(3): 249-253.

Abstract(2119) 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 equivalent modulus of the viscoelastic solid comprising cracks was evaluated.It is proved that the decrease of the modulus comes from two mechanisms:one is the visco-elasticity of the material,the other is the crack opening which is getting larger 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(2288) 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 or the evolution of the small-scale coherent structures in the sub-layer adjacent to the wall of the open channel.When the shear stresses caused by the disturbing waves or the coherent structure near the bed surface boundary and the water flow itself are greater than the shields stresses,responses on the bed surface appear and the sand ripple forms.If the frequency of the shear stress caused by the disturbance is close to the natural frequency of the sand grains that produced resonance,such a phenomenon is called the "detection property" of the sediment.It is at this point that the maximum resonance appears and the sand ripple develops rapidly.

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(2531) 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(2504) 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 were studied.Jumps were shown to occur under some conditions.The effects of damping,detuning,bandwidth,and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

Stability Criteria in Terms of Two Measures for Delay Differential Equations

KOU Chun-hai, ZHANG Shu-nian

2002, 23(3): 283-291.

Abstract(2321) 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 of two measures for delay differential equations are established.

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(2080) 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 strip was analyzed,and the three dimensional displacement field,strain field and stress field of deformed strip were got.The calculation example proves that the peak transverse pressing membrane strain is on the corner part of the deformed strip,and the peak longitudinal stretching strain is on the outer edge part of the deformed strip in front of rolls.In addition,the transverse deformation of the deformed strip is principal,and the longitudinal deformation is small.

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

SHI Hong-yan, XIE Ding-yi

2002, 23(3): 299-308.

Abstract(2365) 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 stress and that of the stress ratio vector(ratio of deviatoric stress vector to mean effective stress).The constitutive model can take account of the influence of both numerical and directional changes of stress vector on deformation of soil simultaneously,and is applicable of both static and dynamic loading.

Fixed Ponts of Increasing Operators in Ordered Space With Applications

YANG Cuang-chong

2002, 23(3): 309-315.

Abstract(1923) 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 equation without any assumption of continuity,compactness,convexity and concavity.

Theoretical Model of Vibrating Object Transmitting Noise Towards External Sound

YAO Zhi-yuan

2002, 23(3): 316-320.

Abstract(2251) 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 is correct.

Global Attractivity for a Class of Nonlinear Delay Difference Equations

LIU Yu-Ji

2002, 23(3): 321-330.

Abstract(2282) PDF(542)

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.