应用数学和力学

2008 Vol. 29, No. 4

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Nonlinear Active Control and Damage Detection of Piezoelectric Smart Laminated Plates With Damage

FU Yi-ming, RUAN Jian-li

2008, 29(4): 379-392.

Abstract(3034) PDF(623)

Abstract:
Based on Hamilton's principle,the higher-order shear deformation plate theory,von Kàrmàn type geometrically nonlinear strain-displacement relations and the strain energy equivalence theory,considering the mass and stiffness of the piezoelectric layers and the damage effect of the composite layers,the nonlinear dynamic equations of the piezoelectric smart laminated plates with damage are derived.A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects was used to realize the active control and damage detection of the piezoelectric smart laminated plates through a closed control loop.Numerical examples for simply supported rectangular laminated plates with immovable edges were presented.And the influences of locations of the piezoelectric layers on the vibration control were investigated.Also,the effects of the degree and location of the damage on the sensor output voltage were discussed.And a way of damage detection is introduced.

Exact Traveling Wave Solutions for an Integrable Nonlinear Evolution Equation Given by M. Wadati

LI Ji-bin

2008, 29(4): 393-397.

Abstract(2720) PDF(613)

Abstract:
By using the method of dynamical systems,the travelling wave solutions of for an integrable nonlinear evolution equation was studied.Exact explicit parametric representations of kink and anti-kink wave solutions,periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given.

Differential-Algebraic Approach to Large Deformation Analysis of Frame Structures Subjected to Dynamic Loads

HU Yu-jia, ZHU Yuan-yuan, CHENG Chang-jun

2008, 29(4): 398-408.

Abstract(2687) PDF(619)

Abstract:
A nonlinear mathematical model for the large deformation analysis of frame structures with discontinuity conditions as well as initial displacements subjected to the dynamic loads was first formulized by the arc-coordinate.Secondly,the differential quadrature element method (DQEM) was applied to discretize the nonlinear mathematical model in the spatial domain,and an effective method was presented to deal with discontinuity conditions of multi-variables in application of DQEM.A set of DQEM discretization equations were obtained,which are a set of nonlinear differential-algebraic equations with singularity in the temporal domain.A method to solve the nonlinear differential-algebraic equations was presented also.As application,the static and dynamical analyses of large deformation of frames and combined frame structures,subjected to the concentrated and distributed forces,were presented.The obtained results were compared with the results in existing literatures.The numerical results show that the methods of dealing with the discontinuity conditions of multi-variables and solving the differential-algebraic equations presented are effective and general,which have the advantages of little amount of nodes and computation,high precision and good convergence and so on.

Fully Discrete Jacobi-Spherical Harmonic Spectral Method for Navier-Stokes Equations

HUANG Wei, GUO Ben-yu

2008, 29(4): 409-431.

Abstract(3261) PDF(678)

Abstract:
A fully discrete Jacobi-spherical harmonic spectral method was provided for the Navier-Stokes equations in a ball.Its stability and convergence were proved.Numerical results show the efficiency of this approach.The proposed method is also applicable to other problems in spherical geometry.

Iterative Algorithm of Solutions for Multivalued General Mixed Implicit Equilibrium-Like Problems

ZANG Xiao-yan, DENG lei

2008, 29(4): 432-438.

Abstract(2464) PDF(694)

Abstract:
The multivalued general mixed implicit equilibrium-like problems are introduced and studied.For solving these problems,a new predictor-corrector iterative algorithm was suggested and analyzed by using the auxiliary principle technique.The convergence of the suggested algorithm in weaker conditions was also proved.

Analytic Solutions of Problem About an Elliptic Hole With Two Straight Cracks in One-Dimensional Hexagonal Quasicrystals

GUO Jun-hong, LIU Guan-ting

2008, 29(4): 439-446.

Abstract(3051) PDF(802)

Abstract:
By means of the complex variable function method and using the technique of conformal mapping,the anti-plane shear problem about an elliptic hole with two straight cracks in one-dimen-sional hexagonal quasicrystals was investigated and the solution of the stress intensity factor(SIFs) of mode ó was found out.Under the condition of limitation,not only the known result can be obtained but also the solutions of the SIFs at the crack tip to a circular hole with two straight cracks and a cross crack in one-dimensional hexagonal quasicrystals are found out.

Global Stability Analysis of a Ratio-Dependent Predator-Prey System

LU Tie-jun, WANG Mei-juan, LIU Yan

2008, 29(4): 447-452.

Abstract(2867) PDF(792)

Abstract:
A ratio dependent predator-prey system with Holling type ó functional response was considered.The sufficient condition of the global asymptotic stability for the positive equilibrium and the existence of the limit cycle were given by studying the locally asymptotic stability of the positive equilibrium.At last,the condition when the positive equilibrium is no hyperbolic equilibrium was discussed by Hopf bifurcation.

Effect of Anisotropy on Thermoelastic Contact Problem

Sakti Pada Barik, M. Kanoria, P. K. Chaudhuri

2008, 29(4): 453-462.

Abstract(3677) PDF(541)

Abstract:
The stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting are concerned with.The frictional heat generation inside the contact region due to the sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account.With the help of Fourier integral transform the problem was reduced to a system of two singular integral equations.The equations were solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures.The effects of anisotropy and thermal effects were shown graphically.

Analysis of Particulate Behavior in Porous Media

Hani I. Siyyam, M. H. Hamdan

2008, 29(4): 463-468.

Abstract(2272) PDF(715)

Abstract:
The behavior of the particle phase in the flow of a particle-laden mixture through a porous medium was analyzed.An attempt was made to model the diffusion and dispersion processes,and to quantify the deviation terms that arise when intrinsic volume averaging is used to derive the flow equations.

Maximal Speed of the Particles of Super-Lévy Process

LIN Zheng-yan, CHENG Zong-mao

2008, 29(4): 469-476.

Abstract(2289) PDF(660)

Abstract:
Super-Lvy process was intr oduced.Maximal speed of all particles in ther ange and the support of a supper-Lvy process was studied.The state of historical super-Lvy process is a measure on the set of paths.The maximal speed of all particles was studied,during a given time period E, which turns out to be function of the packing dimension of E.The Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lvy process were calculated.

Two-Grid Partition of Unity Method for Second Order Elliptic Problems

WANG Cheng, HUANG Zi-ping, LI Li-kang

2008, 29(4): 477-482.

Abstract(2315) PDF(508)

Abstract:
A two-grid partition of unity method for second order elliptic problems was proposed and analyzed.The standard two-grid method is a local and parallel method which usually leads to a discontinuous solution in the whole computational domain.Partition of unity method was employed to glue all the local solutions together to get global continuous one,which is optimal in H1-norm.Furthermore,it is shown that the L2 error can be improved by using the coarse grid correction.Numerical experiments are reported to support the theory.

A UV-Decomposed Method for Solving an MPEC Problem

SHAN Feng, PANG Li-ping, ZHU Li-mei, XIA Zun-quan

2008, 29(4): 483-488.

Abstract(3068) PDF(861)

Abstract:
A UV-decomposition method for solving an MPEC problem with linear complementarity constraints is presented.First of all the problem was converted into a nonlinear programming one,and the structure of subdifferential of a corresponding penalty function and results of its UV-decomposition were given.Then a conceptual algorithm for solving this problem with a superlinear convergence rate was constructed in terms of the results obtained.

Research on the Prediction of Leaching Rate in Heap Leaching Process by the Grey Dynamic Model GDM(1,1)

LIU Jin-zhi, WU Ai-xiang

2008, 29(4): 489-490.

Abstract(2457) PDF(577)

Abstract:
The method of developing GM(1,1) model is extended on the basis of grey system theory.Some conditions of the transfer function,which not only improve the smooth degree of original data sequence but also decrease the revert error,were given.The grey dynamic model was first combined with the transfer function to predict the leaching rate in heap leaching process.The results show that high accuracy of prediction can be expected by the method used.This provides a new approach to realize the prediction and control of the future behavior of leaching kinetics.

Parameter Optimization of Pharmacokinetics Based on Artificial Immune Network

LIU Li, ZHOU Shao-dan, LU Hong-wen, XIE Fen, XU Wen-bo

2008, 29(4): 496-504.

Abstract(2714) PDF(664)

Abstract:
A new method for parameter optimization of pharmacokinetics based on artificial immune network named PKAIN is proposed.To improve local searching ability of the artificial immune network,a partition-based concurrent simplex mutation is developed.By means of evolution of network cells in the PKAIN artificial immune network,an optimal set of parameters of a given pharmacokinetic model was obtained.The Laplace transform was applied to the pharmacokinetic differential equations of remifentanil and its major metabolite,remifentanil acid.The PKAIN method was used to optimize parameters of the derived compartment models.Experimental results show that two-compartment model is sufficient for the pharmacokinetic study of remifentail acid for patients with mild degree of renal impairment.