应用数学和力学

2007 Vol. 28, No. 6

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Binary Discrete Method of Topology Optimization

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

2007, 28(6): 631-642.

Abstract(2620) PDF(657)

Abstract:
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 sign are also estimated wrongly.In order to overcome the problem,a new incremental sensitivity analysis formula was constructed based on the perturbation analysis of the elastic equilibrium increment equation,which can provide us with 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 was 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 simplicity,no need of much mathematics,and particularly 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): 643-650.

Abstract(2822) PDF(876)

Abstract:
The 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 was proved.A novel and innovative three-step iterative algorithm to compute approximate solution was constructed.And the existence of the solution of the generalized set-valued strongly nonlinear mixed variationa-llike inequality was showed by using the auxiliary principle technique.The convergence of three-step iterative sequences generated by the algorithm was also proved.

Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials

BIAN Wen-feng, WANG Biao

2007, 28(6): 651-658.

Abstract(2551) PDF(703)

Abstract:
Firstly,basic differential equations of piezoelectric materials expressed in terms of the potential functions,which are introduced in the very beginning,were worked out.Then these equations were primarily solved through Laplace transformation,seiminfinite Fourier sine transformation and cosine transformation.After that,the dual equations of dynamic cracks problem in the 2D piezoelectric materials were founded 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 ful use of Abel integral equation and its reverse transform,the dual equations were 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): 659-667.

Abstract(2825) PDF(731)

Abstract:
As vibration-based structural damage detection methods are easily affected by the environmental noise,a newly statistic-based noise analysis method was proposed together with 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, NODA Nao-Aki

2007, 28(6): 668-674.

Abstract(2796) PDF(557)

Abstract:
Stress intensity factors for a three dimensional rectangular interfacial crack are considered on the idea of 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 were chosen to express singular stress fields due to an interface crack exactly.The calculation shows that the present method gives rapidly converging numerical solutions and highly satisfied boundary conditions.The stress intensity factors for a rectangular interface crack are indicated accurately with varying the aspect ratio and bimaterial parameter.

Formation Around Planetary Displaced Orbit

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

2007, 28(6): 675-683.

Abstract(2564) PDF(598)

Abstract:
The relative motion around the planetary displaced orbit is investigated.Several kinds of displaced orbits for geocentric and Martian cases were discussed.First,the relative motion is 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 semiOnatural control law was designed based on the requirement of the Martian mission.The results show that large stable regions exist for the control law.

Dynamic Model of the Vertical Vehicle-Subgrade Coupled System Under Secondary Suspension

LIANG Bo, LUO Hong, MA Xue-ning

2007, 28(6): 684-692.

Abstract(2589) PDF(843)

Abstract:
As 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.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 was researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension was 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 the work is benefitial 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): 693-398.

Abstract(2273) PDF(810)

Abstract:
Torsional vibration of a circular piezoelectric shell of polarized ceramics mounted on a rotationally vibrating base was 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 BackwardOLooking Expectations

LEUNG Andrew Y T, XU Jia-na, TSUI Wing-shum

2007, 28(6): 699-712.

Abstract(2403) PDF(731)

Abstract:
This paper aims to analyze the housing price dynamics after an unanticipated economic shock,which was believed to have similar properties with the backward-looking expectation models. The analysis of the housing price dynamics was based on the cobweb model with a simple user cost affected demand and a stockOflow supply assumption.Several n thOorder delay rational difference equations were set up to illustrate the properties of housing dynamics phenomena,such as the equilibrium or oscillations,overshoot or undershoot and convergent or divergent,for a kind of heterogeneous backward-looking expectation models.The results show that demand elasticity is less than supply elasticity is not a necessary condition for the occurrence of oscillation.The housing price dynamics will vary substantially with the heterogeneous backward-looking expectation assumption and some other endogenous factors.

Generalized Contraction Mapping Principle in Intuitionistic Menger Spaces and an Application to Differential Equations

Servet Kutukcu, Adnan Tuna, Atakan T. Yakut

2007, 28(6): 713-723.

Abstract(2391) PDF(757)

Abstract:
Using the idea of Atanassov,the notion of intuitionistic Menger spaces was defined as a natural generalizations of Menger spaces due to Menger.A new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces were obtained.

Displacements and Stresses in a Composite Mult-Layered Media Due to Varying Temperature and Concentrated Load

M. K. Ghosh, M. Kanoria

2007, 28(6): 724-734.

Abstract(2624) PDF(567)

Abstract:
The determination of the thermo-elastic displacements and stresses in a mult-ilayered 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 is studied.Each layer is assumed to be made of homogeneous and isotropic elastic material.The relevant displacement components for each layer were 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 force.The equation was then solved by integral transform technique.Analytical expressions for thermo-elastic displacements and stresses in the underlying mass and the corresponding numerical codes have been constructed for any number of layers.However,the numerical comparison was made for three and four layers.

Note on the Barenblatt Power Series Solution to the Boussinesq Equation

SONG Zhi-yao, LI Ling, David Lockington

2007, 28(6): 735-740.

Abstract(2995) PDF(748)

Abstract:
A self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium when the hydraulic head at the boundary behaves like a power of time was presented(Barenblatt (1952) obtained a power series solution,but 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).The recurrent formula for the coefficients was obtained using the method of power series expansion,and the convergence of the series was proven.The results can be easily understood and used by engineers in catchment hydrology and baseflow studies as well as agricultural drainage problems.

Robust Stability of Uncertain Neutral Linear Stochastic Differential Delay Systems

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

2007, 28(6): 741-748.

Abstract(2581) PDF(742)

Abstract:
The La Salle-type theorem for the neutral stochastic differential equations with delay was established 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 was also given to verify the effectiveness of the obtained results.

Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Damped Systems

XIE Hui-qing, DAI Hua

2007, 28(6): 749-756.

Abstract(2868) PDF(659)

Abstract:
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.