Table of Content

18 April 2008, Volume 29 Issue 4

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Articles

Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection

FU Yi-ming;RUAN Jian-li

2008, 29(4):  421-436 .  doi:10.1007/s10483-008-0401-4

Abstract ( 1583 )   PDF (345KB) ( 883 )  

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Considering mass and stiffness of piezoelectric layers and damage effects of composite layers, nonlinear dynamic equations of damaged piezoelectric smart laminated plates are derived. The derivation is based on the Hamilton's principle, the higher-order shear deformation plate theory, von Karman type geometrically nonlinear strain-displacement relations, and the strain energy equivalence theory. A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection with a closed control loop. Simply supported rectangular laminated plates with immovable edges are used in numerical computation. Influence of the piezoelectric layers' location on the vibration control is investigated. In addition, effects of the degree and location of damage on the sensor output voltage are discussed. A method for damage detection is introduced.

Exact traveling wave solutions for an integrable nonlinear evolution equation given by M. Wadati

LI Ji-bin

2008, 29(4):  437-440 .  doi:10.1007/s10483-008-0402-y

Abstract ( 1442 )   PDF (167KB) ( 843 )  

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By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, 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):  441-452 .  doi:10.1007/s10483-008-0403-7

Abstract ( 1437 )   PDF (615KB) ( 776 )  

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A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method (DQEM) is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multi-variables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with discontinuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.

Fully discrete Jacobi-spherical harmonic spectral method for Navier-Stokes equations

HUANG Wei;GUO Ben-yu

2008, 29(4):  453-476 .  doi:10.1007/s10483-008-0404-1

Abstract ( 1448 )   PDF (357KB) ( 642 )  

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A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show 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):  477-484 . 

Abstract ( 1533 )   PDF (114KB) ( 737 )  

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The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.

Analytic solutions to problem of elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals

GUO Jun-hong;LIU Guan-ting

2008, 29(4):  485-493 .  doi:10.1007/s10483-008-0406-x

Abstract ( 1478 )   PDF (173KB) ( 875 )  

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By means of the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals is investigated. The solution of the stress intensity factor (SIF) for mode III problem has been found. Under the condition of limitation, both the known results and the SIF solution at the crack tip of a circular hole with two straight cracks and cross crack in one-dimensional hexagonal quasicrystals can be obtained.

Global stability analysis of a ratio-dependent predator-prey system

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

2008, 29(4):  495-500 .  doi:10.1007/s10483-008-0407-y

Abstract ( 1440 )   PDF (121KB) ( 675 )  

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A ratio dependent predator-prey system with Holling type III functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.

Effect of anisotropy on thermoelastic contact problem

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

2008, 29(4):  501-510 .  doi:10.1007/s10483-008-0408-z

Abstract ( 1355 )   PDF (266KB) ( 903 )  

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This paper is concerned with the stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting. 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 is reduced to a system of two singular integral equations. The equations are solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures. The effects of anisotropy and thermal effects are shown graphically.

Analysis of particulate behavior in porous media

Hani I. Siyyam;M. H. Hamdan

2008, 29(4):  511-516 .  doi:10.1007/s10483-008-0409-3

Abstract ( 1356 )   PDF (96KB) ( 790 )  

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In this work, we analyze the behavior of the particle phase in the flow of a particle-laden mixture through a porous medium. An attempt is 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 particles in super-Lévy process

LIN Zheng-yan;CHENG Zong-mao

2008, 29(4):  517-525 .  doi:10.1007/s10483-008-0410-x

Abstract ( 1314 )   PDF (136KB) ( 636 )  

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We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of paths. We study the maximal speed of all particles during a given time period, which turns out to be a function of the packing dimension of the time period. We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super- Lévy process.

Two-grid partition of unity method for second order elliptic problems

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

2008, 29(4):  527-533 .  doi:10.1007/s10483-008-0411-x

Abstract ( 1451 )   PDF (137KB) ( 718 )  

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A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the 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 theoretical results.

A UV-decomposed method for solving an MPEC problem

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

2008, 29(4):  535-540 .  doi:10.1007/s10483-008-0412-y

Abstract ( 1418 )   PDF (116KB) ( 618 )  

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A UV-decomposition method for solving a mathematical program with equilibrium constraints (MPEC) problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its UV-decomposition are given. A conceptual algorithm for solving this problem with a superlinear convergence rate is then constructed in terms of the obtained results.

Prediction of leaching rate in heap leaching process by grey dynamic model GDM(1,1)

LIU Jin-zhi;WU Ai-xiang

2008, 29(4):  541-548 .  doi:10.1007/s10483-008-0413-5

Abstract ( 1214 )   PDF (147KB) ( 719 )  

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The method of developing GM(1,1) model is extended on the basis of grey system theory. Conditions for the transfer function that improve smoothness of original data sequence and decrease the revert error are given. The grey dynamic model is first combined with the transfer function to predict the leaching rate in heap leaching process. The results show that high prediction accuracy can be expected by using the proposed method. This provides a new approach to realize 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):  549-558 .  doi:10.1007/s10483-008-0414-7

Abstract ( 1277 )   PDF (189KB) ( 940 )  

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A new method for parameter optimization of pharmacokinetics based on an 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 is obtained. The Laplace transform is applied to the pharmacokinetic differential equations of remifentanil and its major metabolite, remifentanil acid. The PKAIN method is used to optimize parameters of the derived compartment models. Experimental results show that the two-compartment model is sufficient for the pharmacokinetic study of remifentanil acid for patients with mild degree of renal impairment.