应用数学和力学

2004 Vol. 25, No. 9

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Free-Parameter Perturbation-Method Solutions of the Nonlinear Stability of Shallow Spherical Shells

CHEN Shan-lin, LI Qi-zhong

2004, 25(9): 881-888.

Abstract(2836) PDF(548)

Abstract:
The free-parameter perturbation method is applied to solve the problems of nonlinear stability of spherical shallow shells under uniform load.As a modified perturbation method,the free-parameter perturbation method enables researchers to obtain all characteristic relations without choosing the certain perturbation parameter.Some examples were discussed to study the variety regulations of deflections and stress of shells in the process of buckling,and the results were compared with those of other researchers.

Impulsive Control of Chaotic Attractors in Nonlinear Chaotic Systems

MA Jun-hai, REN Biao, CHEN Yu-shu

2004, 25(9): 889-894.

Abstract(3067) PDF(625)

Abstract:
Based on the study both domestic and abroad,an impulsive control scheme on chaotic attractors in one chaotic system was presented.By applying impulsive control theory of the universal equation,the asymptotically stable condition of impulsive control on chaotic attractors in such nonlinear chaotic system was deduced,and with it,the upper bond of the impulse interval for asymptotically stable control was given.Numerical results are presented which are considered with important reference value for control of chaotic attractors.

Local Discontinuous Galerkin Method for Radial Porous Flow With Dispersion and Adsorption

WANG Ji-wen, LIU Ci-qun

2004, 25(9): 895-900.

Abstract(2453) PDF(549)

Abstract:
Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e.the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.

Analytical Solution of Bending-Compression Column Using Different Tension-Compression Modulus

YAO Wen-juan, YE Zhi-ming

2004, 25(9): 901-909.

Abstract(2637) PDF(1031)

Abstract:
Based on elastic theory of different tension-compression modulus,the analytical solution was presented for bending-compression column subject to combined loadings by the flowing coordinate system and phased integration method.The formulations for the neutral axis,stress,strain and displacement were developed,the finite element program was compiled for calculation,and the comparison between the result of finite element and analytical solution were given too.Finally,the results of different modulus and the same modulus are compared and analyzed,the difference of the two theories in result is obtained,and the reasonable suggestion for the calculation of this structure is proposed.

Analysis of Thermal-Elastic Coupling Vibration of Large Deflection Cylindrical Shell

SHU Xue-feng, LAN Jiao-xia, WU Yong-zhong

2004, 25(9): 910-916.

Abstract(2261) PDF(645)

Abstract:
The governing equation and energy equations for thermal-elastic coupling vibration of cylindrical shell were developed.The Garlerkin method was used in numerical process.Some useful result can be concluded from numerical result.With the increase of the amplitude of temperature and coupling coefficient,the speed of vibration decaying becomes slower and the coupling effect becomes weaker.The larger the ration of length to radius and length to thickness,the faster the decaying of the vibration amplitude and the vibration frequency increase.It means the coupling effect gets stronger.The larger the coupling coefficient,the smaller the axial stress,the axial force and the bendind moment are.

Steady-State Responses and Their Stability of Nonlinear Vibration of an Axially Accelerating String

WU Jun, CHEN Li-qun

2004, 25(9): 917-926.

Abstract(2901) PDF(777)

Abstract:
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated.The transport speed was assumed to be a constant mean speed with small harmonic variations.The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle.The method of multiple scales was applied directly to the equation.The solvability condition of eliminating the secular terms was established.Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained.Some numerical examples showing effects of the mean transport speed,the amplitude and the frequency of speed variation were presented.The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance.Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.

AINV and BILUM Preconditioning Techniques

GU Tong-xiang, CHI Xue-bin, LIU Xing-ping

2004, 25(9): 927-934.

Abstract(2668) PDF(1030)

Abstract:
It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations,in which the use of sparse approximate inverse(AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated.The resulting preconditioner re tains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner:the ability to control sparsity and increased parallelism.Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

Analysis of Dynamic Instability of Interfacial Slip Waves Based on the Surface Impedance Tensor

LI Nan, WANG Yue-sheng, YU Gui-lan

2004, 25(9): 935-942.

Abstract(2401) PDF(614)

Abstract:
A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle.As an example,the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details.A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed.An explicit expression for the instabilility condition of the interfacial slip waves was presented.

Analysis of the Localization of Damage and the Complete Stress-Strain Relation for Mesoscopic Heterogeneous Rock Under Uniaxial Tensile Loading

ZHOU Xiao-ping, WANG Jian-hua, ZHANG Yong-xing, HA Qiu-ling

2004, 25(9): 943-950.

Abstract(2386) PDF(542)

Abstract:
The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads.A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth.The complete stress-strain relation including linear elasticity,nonlinear hardening,rapid stress drop and strain softening was obtained.The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes.The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched.Theoretical predictions have shown to be consistent with the experimental results.

Analysis of the Localization of Damage and the Complete Stress-Strain Relation for Mesoscopic Heterogeneous Brittle Rock Subjected to Compressive Loads

ZHOU Xiao-ping, WANG Jian-hua, ZHANG Yong-xing, HA Qiu-ling

2004, 25(9): 951-957.

Abstract(2478) PDF(581)

Abstract:
A micromechanics-based model is established.The model takes the interaction among sliding cracks into account,and it is able to quantify the effect of various parameters on the localization condition of damage and deformation for brittle rock subjected to compressive loads.The closed-form explicit expression for the complete stress-strain relation of rock containing microcracks subjected to compressive loads was obtained.It is showed that the complete stress-strain relation includes linear elasticity,nonlinear hardening,rapid stress drop and strain softening.The behavior of rapid stress drop and strain softening is due to localization of deformation and damage.Theoretical predictions have shown to be consistent with the experimental results.

Scattering of SH-Wave by Cracks Originating at an Elliptic Hole and Dynamic Stress Intensity Factor

LIU Dian-kui, CHEN Zhi-gang

2004, 25(9): 958-966.

Abstract(2768) PDF(699)

Abstract:
The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole,and the solution of dynamic stress intensity factor at the crack tip was given.A Green's function was constructed for the problem,which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary.With division of a crack technique,a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained.The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

Squeeze Flow of a Second-Order Fluid Between Two Parallel Disks or Two Spheres

XU Chun-hui, HUANG Wen-bin, XU Yong

2004, 25(9): 967-973.

Abstract(2679) PDF(657)

Abstract:
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method.Based on the Reynolds.lubrication theory,the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks.Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching,arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force.It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

Mathematical Models Arising From a Survey of Ferromagnetic Materials Under Magnetisation

GU Xiao-an, ZENG Jin, SHEN Rong-ying

2004, 25(9): 974-982.

Abstract(2576) PDF(763)

Abstract:
Sinusoidal alternating magnetic fields established inside the cores would cause vibrations of silicon steel sheets and make noises.The mechanical behavior of ferromagnetic materials must be modeled for such complicated problems.Mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization were focused on.Through combination of the electromagnetic field theory with the theory of elastic mechanics,several nonlinear systems of fourth-order partial differential equations were deduced.By making further assumptions,the first-order approximation of the above equations was established.Although the models were deduced based on assumption of linear,homogeneous,isotropic materials and simplified magnetization model,the results,which the formulations give,are proved to be good enough for engineering application.

Elastic-Viscoplastic Fieds Near The Tip of a Propagating Crack Under Anti-Plane Shear

LI Fan-chun, ZHAO Wen-sheng, TANG Long-sheng

2004, 25(9): 983-990.

Abstract(2231) PDF(598)

Abstract:
The elastic-viscoplastic model proposed by Bingham was used to alalyse the stress and strain surrounding the tip of a propagating crack under antiplane shear.The proper displacement pattern was given;the asymptotic equations were derived and solved numerically.The analysis and calculation show that for smaller viscosity the crack-tip possesses logarthmic singularity,and for larger viscosity it possesses power-law singularity.In critical case,the two kinds of singularity are consistent with each other.The result revealed the important role of viscosity for crack-tip field.