Table of Content

18 June 2007, Volume 28 Issue 6

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Articles

Binary discrete method of topology optimization

MEI Yu-lin;WANG Xiao-ming;CHENG Geng-dong

2007, 28(6):  707-719 .  doi:10.1007/s10483-007-0601-z

Abstract ( 1227 )   PDF (756KB) ( 536 )  

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The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate, even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements, meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

XU Hai-li;GUO Xing-ming

2007, 28(6):  721-729 .  doi:10.1007/s10483-007-0602-x

Abstract ( 1310 )   PDF (169KB) ( 524 )  

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An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle technique. The convergence of three-step iterative sequences generated by the algorithm is also proved.

Dual equations and solutions of I-type crack of dynamic problems in piezoelectric materials

BIAN Wen-feng;WANG Biao

2007, 28(6):  731-739 .  doi:10.1007/s10483-007-0603-x

Abstract ( 1335 )   PDF (173KB) ( 526 )  

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This paper firstly works out basic differential equations of piezoelectric materials expressed in terms of potential functions, which are introduced in the very beginning. These equations are primarily solved through Laplace transformation, semi-infinite Fourier sine transformation and cosine transformation. Secondly, dual equations of dynamic cracks problem in 2D piezoelectric materials are established with the help of Fourier reverse transformation and the introduction of boundary conditions. Finally, according to the character of the Bessel function and by making full use of the Abel integral equation and its reverse transform, the dual equations are changed into the second type of Fredholm integral equations. The investigation indicates that the study approach taken is feasible and has potential to be an effective method to do research on issues of this kind.

Noise analysis for sensitivity-based structural damage detection

YIN Tao;ZHU Hong-ping;YU Ling

2007, 28(6):  741-750 .  doi:10.1007/s10483-007-0604-3

Abstract ( 1366 )   PDF (369KB) ( 796 )  

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As vibration-based structural damage detection methods are easily affected by environmental noise, a new statistic-based noise analysis method is proposed together with the Monte Carlo technique to investigate the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the commonly used random perturbation technique, the proposed technique is deduced directly by Moore-Penrose generalized inverse of the sensitivity matrix, which does not only make the analysis process more efficient but also can analyze the influence of noise on both frequencies and mode shapes for three commonly used sensitivity-based damage detection methods in a similar way. A one-story portal frame is adopted to evaluate the efficiency of the proposed noise analysis technique.

Numerical solutions of singular integral equations for planar rectangular interfacial crack in three dimensional bimaterials

XU Chun-hui;QIN Tai-yan;Nao-Aki Noda

2007, 28(6):  751-757 .  doi:10.1007/s10483-007-0605-y

Abstract ( 1508 )   PDF (285KB) ( 500 )  

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Stress intensity factors for a three dimensional rectangular interfacial crack were considered using the body force method. In the numerical calculations, unknown body force densities were approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack exactly. The calculation shows that the numerical results are satisfied. The stress intensity factors for a rectangular interface crack were indicated accurately with the varying aspect ratio, and bimaterial parameter.

Formation around planetary displaced orbit

GONG Sheng-ping;LI Jun-feng;BAOYIN He-xi

2007, 28(6):  759-767 .  doi:10.1007/s10483-007-0606-y

Abstract ( 1512 )   PDF (279KB) ( 607 )  

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The paper investigates the relative motion around the planetary displaced orbit. Several kinds of displaced orbits for geocentric and martian cases were discussed. First, the relative motion was linearized around the displaced orbits. Then, two semi-natural control laws were investigated for each kind of orbit and the stable regions were obtained for each case. One of the two control laws is the passive control law that is very attractive for engineering practice. However, the two control laws are not very suitable for the Martian mission. Another special semi-natural control law is designed based on the requirement of the Martian mission. The results show that large stable regions exist for the control law.

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

LIANG Bo;LUO Hong;MA Xue-ning

2007, 28(6):  769-778 .  doi:10.1007/s10483-007-0607-z

Abstract ( 1130 )   PDF (304KB) ( 856 )  

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As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the railway line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.

Piezoelectric generator based on torsional modes for power harvesting from angular vibrations

CHEN Zi-guang;HU Yuan-tai;YANG Jia-shi

2007, 28(6):  779-784 .  doi:10.1007/s10483-007-0608-y

Abstract ( 1216 )   PDF (321KB) ( 712 )  

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Torsional vibration of a circular piezoelectric shell of polarized ceramics mounted on a rotationally vibrating base is analyzed. The shell is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy from angular vibrations to electrical energy. Analytical expressions and numerical results for the output voltage, current, power, efficiency and power density are given.

Nonlinear delay difference equations for housing dynamics assuming heterogeneous backward-looking expectations

LEUNG Andrew Y.T.;XU Jia-na;TSUI Wing Shum

2007, 28(6):  785-798 .  doi:10.1007/s10483-007-0609-z

Abstract ( 1337 )   PDF (538KB) ( 607 )  

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Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Servet Kutukcu;Adnan Tuna;Atakan T. Yakut

2007, 28(6):  799-809 .  doi:10.1007/s10483-007-0610-z

Abstract ( 1309 )   PDF (227KB) ( 752 )  

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Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

Displacements and stresses in composite multi-layered media due to
varying temperature and concentrated load

M. K. Ghosh;M. Kanoria

2007, 28(6):  811-822 .  doi:10.1007/s10483-007-0611-5

Abstract ( 1315 )   PDF (285KB) ( 565 )  

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This paper deals with the determination of the thermo-elastic displacements and stresses in a multi-layered body set up in different layers of different thickness having different elastic properties due to the application of heat and a concentrated load in the uppermost surface of the medium. Each layer is assumed to be made of homogeneous and isotropic elastic material. The relevant displacement components for each layer are taken to be axisymmetric about a line, which is perpendicular to the plane surfaces of all layers. The stress function for each layer, therefore, satisfies a single equation in absence of any body forces. The equation is then solved by integral transform technique. Analytical expressions for thermo-elastic displacements and stresses in the underlying mass and the corresponding numerical codes are constructed for any number of layers. However, the numerical comparison is made for three and four layers.

Note on Barenblatt power series solution to Boussinesq equation

SONG Zhi-yao;LI Ling;David Lockington

2007, 28(6):  823-828 .  doi:10.1007/s10483-007-0612-x

Abstract ( 1334 )   PDF (160KB) ( 650 )  

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To the self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.

Robust stability of uncertain neutral linear stochastic differential
delay system

JIANG Ming-hui;SHEN Yi;LIAO Xiao-xin

2007, 28(6):  829-836 .  doi:10.1007/s10483-007-0613-x

Abstract ( 1332 )   PDF (226KB) ( 490 )  

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The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.

Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems

XIE Hui-qing;DAI Hua

2007, 28(6):  837-845 .  doi:10.1007/s10483-007-0614-4

Abstract ( 1282 )   PDF (224KB) ( 667 )  

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A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.