应用数学和力学

2006 Vol. 27, No. 9

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Predictor-Corrector Algorithms for Solving Generalized Mixed Implicit Quasi-Equilibrium Problems

DING Xie-ping, LIN Yen-cherng, YAO Jen-chih

2006, 27(9): 1009-1016.

Abstract(2694) PDF(730)

Abstract:
A new class of generalized mixed implicit quasi-equilibrium problems (GMIQEP) with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP were suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings.

Novel Regularized Boundary Integral Equations for Potential Plane Problems

ZHANG Yao-ming, LÜ He-xiang, WANG Li-min

2006, 27(9): 1017-1022.

Abstract(2712) PDF(709)

Abstract:
The universal practices have been centralizing on the research of regularization to the DBIE. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation was mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea was presented herein, in which the regularized boundary integral equations with indirect unknowns excluding the CPV and HFP integrals were established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.

A 1/3 Pure Sub-Harmonic Solution and Fractal Characteristic of Transient Process for Duffing’s Equation

XU Yu-xiu, HU Hai-yan, WEN Bang-chun

2006, 27(9): 1023-1028.

Abstract(2597) PDF(600)

Abstract:
The 1/3 sub-harmonic solution for the Duffing's with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution was introduced, and the domain of sub-harmonic frequencies was found. The asympt otical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Optical Diagnostic and Modeling the Solution Growth Process of NaClO₃ Crystals

WANG Tao, DUAN Li

2006, 27(9): 1029-1035.

Abstract(2677) PDF(659)

Abstract:
Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous NaClO₃ crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity

WANG Lin-xiang, Roderick V. N. Melnik

2006, 27(9): 1036-1046.

Abstract(2980) PDF(620)

Abstract:
An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of the numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs were then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail. And its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.

Numerical Prediction of Process-Induced Residual Stresses in Glass Bulb Panel

ZHOU Hua-min, SUN Qiang, XI Guo-dong, LI De-qun

2006, 27(9): 1047-1055.

Abstract(2140) PDF(632)

Abstract:
A numerical simulation model for predicting residual stresses which arise during the solidification process of pressed glass bulb panel was developed. The solidification of a molten layer of glass between cooled parallel plates was used to model the mechanics of the buildup of residual stresses in the forming process. A thermorheologically simple thermoviscoelastic model was assumed for the material. The finite element method employed was based on the theory of shells as an assembly of flat elements. This approach calculates residual stresses layer by layer like a truly three-dimensional calculation, which is well suited for thin pressed products of complex shape. An experimental comparison is employed to verify the proposed models and methods.

Adaptive H-infinity Control of a Class of Uncertain Nonlinear Systems

MU Xiao-wu, GUO Xiao-li, CHENG Gui-fang

2006, 27(9): 1056-1064.

Abstract(2852) PDF(805)

Abstract:
It is concerned with the problem of disturbance attenuation with stability for uncertain nonlinear systems by adaptive output feedback. By a partial-state observer and Backstepping technique, an adaptive output feedback controller is constructed, which can solve the standard gain disturbance attenuation problem with internal stability.

Fixed Point Theorems for Mappings Satisfying an Implicit Relation on Two Complete and Compact Metric Spaces

Abdlkrim Aliouche, Brian Fisher

2006, 27(9): 1065-1070.

Abstract(2774) PDF(718)

Abstract:
First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.

Blood Flow and Macromolecular Transport in Curved Blood Vessels

WEI Lan, WEN Gong-bi, TAN Wen-chang

2006, 27(9): 1071-1078.

Abstract(2571) PDF(692)

Abstract:
A numerical analysis of the steady/pulsatile flow and macromolecular (such as LDL and Albumin) transport in curved blood vessels was carried out. The computational results predict that the vortex of the secondary flow is time-dependent in the aortic arch. The concentration of macromolecule concentrates at the region of sharp curve, and the wall concentration at the outer part is higher than that at the inner part. Atherosclerosis is prone to develop in such regions with sharp flow.

Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod

LÜ Ke-pu, GUO Peng, ZHANG Lei, YI Jin-qiao, DUAN Wen-shan

2006, 27(9): 1079-1083.

Abstract(2443) PDF(810)

Abstract:
The longitudinal oscillation of a nonlinear elastic rod with lateral inertia were studied. Based on the far field and simple wave theory, a nonlinear Schr^L dinger (NLS) equation was established under the assumption of small amplitude and long wavelength. It is found that there are NLS envelope solitons in this system. Finally the soliton solution of the NLS equation is presented.

Elastic Interaction Between a Wedge Disclination Dipole and an Internal Crack

FANG Qi-hong, LIU You-wen

2006, 27(9): 1084-1092.

Abstract(2943) PDF(618)

Abstract:
The system of a wedge disclination dipole interacting with an internal crack is investigated. By using the complex variable method, the closed from solutions of complex potentials to this problem were presented. The analytic formulae of the physics variables, such as stress intensity factors at the tips of the crack produced by the wedge disclination dipole and the image force acting on disclination dipole center were obtained. The influence of the orientation, the dipole arm and the location of the disclination dipole on the stress intensity factors was discussed in detail. Furthermore, the equilibrium position of the wedge disclination dipole was also examined. It is shown that the shielding or antishielding effect of the wedge disclination to the stress intensity factors is significant when the disclination dipole moves to the crack tips.

Stochastic Discrete Model of a Two-Stage Isolation System With Rigid Limiters

HE Hua, FENG Qi, SHEN Rong-ying, WANG Yu

2006, 27(9): 1093-1100.

Abstract(2496) PDF(693)

Abstract:
The possible intermittent impacts of a two-stage isolation system with rigid limiters have been investigated. The isolation system is under periodic external excitation disturbed by small stationary Gaussian white noise after shock. The maximal impact Poincar map is proposed based on the multi-body dynamics with unilateral constraints. Then in the period after shock, the zero order approximate stochastic discrete model and the first order approximate stochastic model were developed. The real isolation system of an MTU diesel engine was used to evaluate the established model. After calculating numerical example, the effects of noise excitation on the isolation system were discussed. The results show that the property of the system is complicated due to intermittent impact. The difference between zero order model and the first order model may be great. The effect of small noise is obvious. The results may be expected useful to the naval designers.

Comparison of Stability Between Navier-Stokes and Euler Equations

SHI Wei-hui, WANG Yue-peng, SHEN Chun

2006, 27(9): 1101-1107.

Abstract(2621) PDF(693)

Abstract:
The stabilities about Navier-Stokes equation and Euler equation were brought into comparison; and by taking their typical initial value problem for example, the reason of leading to the difference in stability between Navier-Stokes and Euler equations was also analyzed.

A Regular Value of a Compact Deformation

J. M. Soriano

2006, 27(9): 1108-1116.

Abstract(2499) PDF(704)

Abstract:
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one value in a specific open ball. The proof of the result is constructive and is based upon continuation methods.

Preconditioned Gauss-Seidel Type Iterative Methods for Solving Linear Systems

CHENG Guang-hui, HUANG Ting-zhu, CHENG Xiao-yu

2006, 27(9): 1117-1121.

Abstract(2917) PDF(770)

Abstract:
The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, was presented. Convergence of the preconditioned method applied to Z-matrices was discussed. Also the optimal parmeter was presented. Numerical results show that the proper choice of the preconditioner can lead to effective the preconditioned Gauss-Seidel type iterative methods for solving linear systems.

Dynamic Load Analysis of Underground Structure Under the Effect of Blast Wave

REN Yun-yan, ZHANG Li, HAN Feng

2006, 27(9): 1122-1128.

Abstract(3038) PDF(676)

Abstract:
A semi-analytical method of solving the problem of dynamic stress concentration of arbitrary underground structure under the effect of blast waves was introduced. Using the Fourier Transform theory, the shock waves (in the forms of SH-waves) can be converted into frequency bands. After employing complex functions and conformal mapping, the admittance functions of various underground structures were obtained. Then, the problem of the time domain dynamic stress response of underground structure can be easily solved through the Fourier inverse transform. At last, the results and curves of the dynamic stress for the square, triangle and horseshoe cavity are presented.

Squeeze Film Flow With Nonlinear Boundary Slip

ZHOU Ping, WU Cheng-wei, MA Guo-jun

2006, 27(9): 1129-1134.

Abstract(2137) PDF(624)

Abstract:
A nonlinear boundary slip model consisting of an initial slip length and a critical shear rate was used to study the nonlinear boundary slip of squeeze fluid film confined between two approaching spheres. It is found that the initial slip length controls the slip behavior at small shear rate, but the critical shear rate controls the boundary slip at high shear rate. The boundary slip at the squeeze fluid film of spherical surfaces is a strongly nonlinear function of the radius coordinate. At the center or far from the center of the squeeze film, the slip length equals the initial slip length due to the small shear rate. However, in the high shear rate regime the slip length increases very much. The hydrodynamic force of the spherical squeeze film decreases with increasing the initial slip length and decreasing the critical shear rate. The effect of initial slip length on the hydrodynamic force seems less than that of the critical shear rate. When the critical shear rate is very small the hydrodynamic force increases very slowly with a decrease in the minimum film thickness. The theoretical predictions agree well with the experiment measurements.