Table of Content

18 January 2007, Volume 28 Issue 1

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Articles

Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string

ZHANG Neng-hui;WANG Jian-jun;CHENG Chang-jun

2007, 28(1):  1-9 .  doi:10.1007/s10483-007-0101-x

Abstract ( 1380 )   PDF (306KB) ( 739 )  

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Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

ZHANG Qing-bang;DING Xie-ping

2007, 28(1):  11-18 .  doi:10.1007/s10483-007-0102-y

Abstract ( 1496 )   PDF (155KB) ( 499 )  

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A new class of g-η-Monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-Monotone mappings are introduced. The resolvent operator of g-η-Monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.

Advanced response surface method for mechanical reliability analysis

LU Zhen-zhou;ZHAO Jie;YUE Zhu-feng

2007, 28(1):  19-26 .  doi:10.1007/s10483-007-0103-x

Abstract ( 1315 )   PDF (279KB) ( 906 )  

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Based on the classical response surface method (RSM), a novel RSM using improved experimental points (EPs) is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance between the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point (MPP). Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.

Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations

MA Fei-yao;MA Yi-chen;WO Wei-feng

2007, 28(1):  27-35 .  doi:10.1007/s10483-007-0104-x

Abstract ( 1549 )   PDF (230KB) ( 597 )  

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Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.

Governing equations and numerical solutions of tension leg platform with finite amplitude motion

ZENG Xiao-hui;SHEN Xiao-peng;WU Ying-xiang

2007, 28(1):  37-49 .  doi:10.1007/s10483-007-0105-1

Abstract ( 1499 )   PDF (712KB) ( 884 )  

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It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Hamiltonian parametric element and semi-analytical solution for smart laminated plates

QING Guang-hui;QIU Jia-jun;LIU Yan-hong

2007, 28(1):  51-58 .  doi:10.1007/s10483-007-0106-z

Abstract ( 1317 )   PDF (376KB) ( 746 )  

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Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient esponse of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.

Thermal post-bunkling analyses of functionally graded material rod

ZHAO Feng-qun;WANG Zhong-min;LIU Hong-zhao

2007, 28(1):  59-67 .  doi:10.1007/s10483-007-0107-z

Abstract ( 1385 )   PDF (279KB) ( 621 )  

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The non-linear governing differential equations of immovably simply supported functionally graded material (FGM) rod subjected to thermal loads were derived. The thermal post-buckling behaviors of FGM rod made of ZrO₂ and Ti-6A1-4V were analyzed by shooting method. Firstly, the thermal post-buckling equilibrium paths of the FGM rod with different gradient index in the uniform temperature field were plotted, and compared with the behaviors of the homogeneous rods made of ZrO₂ and Ti-6A1-4V materials, respectively. For given value of end rotation angles, the influence of gradient index on the thermal post-buckling behaviors of FGM rod was discussed. Secondly, the thermal post-buckling characteristics of the FGM rod were analyzed when the temperature difference parameter is changed while the bottom temperature parameter remains constant, and when the bottom temperature parameter is changed while the temperature difference parameter remains constant, and compared with the characteristics of the two homogeneous material rods.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

K. Hooman;H. Gurgenci

2007, 28(1):  69-78 .  doi:10.1007/s10483-007-0108-z

Abstract ( 1464 )   PDF (498KB) ( 770 )  

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Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut.

Analytic model of deformation of construction interfaces of rolled control concrete dam

GU Chong-shi;HUANG Guang-ming;LAI Dao-ping

2007, 28(1):  79-86 .  doi:10.1007/s10483-007-0109-z

Abstract ( 1456 )   PDF (377KB) ( 675 )  

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The construction interfaces of RCCD have a distinct influence on the deformation of dams. The characters and rules on deformation of construction interfaces are studied. The methods simulating the deformation of the interfaces at different stages are proposed. A thickness analytic model and a no-thickness analytic model of construction interfaces are built. These models can reflect the elastic deformation, the attenuation creep deformation, the irreversible creep deformation and the accelerating creep deformation of interfaces. The example shows that these proposed models can simulate the deformation of the dam structure objectively. Especially, the results of the thickness analytic model which simulates the gradual changing regularities of interfaces can tally with those of monitoring in situ preferably. The methods proposed and the analytic models can be generalized and applied to general concrete dams, especially to the analysis on deformation rules of fault and interlayer in dam base.

Dynamic Bayesian estimation of displacement parameters of continuous curve box based on Novozhilov theory

ZHANG Jian;Jian-shu;ZHAO Xin-ming

2007, 28(1):  87-95 .  doi:10.1007/s,10483-007-0110-z

Abstract ( 1322 )   PDF (358KB) ( 745 )  

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The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was found. The corresponding formulas of dynamic Bayesian expectation and variance were derived. After the method of solving the automatic search of step length was put forward, the optimization estimation computing formulas were also obtained by adapting conjugate gradient method. Then the steps of dynamic Bayesian estimation were given in detail. Through analysis of a classic example, the criterion of judging the precision of the known information is gained as well as some other important conclusions about dynamic Bayesian stochastic estimation of displacement parameters of continuous curve box.

Sensitivity analysis of generalized set-valued quasi-variational
inclusion in Banach spaces

ZENG Lu-chuan;YAO Jen-chih

2007, 28(1):  97-102 .  doi:10.1007/s10483-007-0111-1

Abstract ( 1414 )   PDF (146KB) ( 525 )  

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The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.

Weakly R-KKM mappings---intersection theorems and minimax inequalities in topological spaces

DENG Lei;YANG Ming-ge

2007, 28(1):  103-109 .  doi:10.1007/s10483-007-0112-1

Abstract ( 1378 )   PDF (161KB) ( 661 )  

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In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and R-beta-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.

Self-similar singular solution of fast diffusion equation with gradient absorption terms

SHI Pei-hu;WANG Ming-xin

2007, 28(1):  111-118 .  doi:10.1007/s10483-007-0113-1

Abstract ( 1287 )   PDF (181KB) ( 483 )  

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The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.

Superconvergence analysis of Wilson element on anisotropic meshes

SHI Dong-yang;LIANG Hui

2007, 28(1):  119-125 .  doi:10.1007/s10483-007-0114-1

Abstract ( 1461 )   PDF (237KB) ( 651 )  

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The Wilson finite element method is considered to solve a class of two-dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.

Analysis of reactive routing protocols for mobile ad hoc networks in Markov models

WANG Han-xing;HU Xi;FANG Jian-chao;JIA Wei-jia

2007, 28(1):  127-139 .  doi:10.1007/s10483-007-0115-1

Abstract ( 1290 )   PDF (248KB) ( 673 )  

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Mobile ad hoc networks (MANETs) have become a hot issue in the area of wireless networks for their non-infrastructure and mobile features. In this paper, a MANET is modeled so that the length of each link in the network is considered as a birth-death process and the space is reused for n times in the flooding process, which is named as an n-spatial reuse birth-death model (n-SRBDM). We analyze the performance of the network under the dynamic source routing protocol (DSR) which is a famous reactive routing protocol. Some performance parameters of the route discovery are studied such as the probability distribution and the expectation of the flooding distance, the probability that a route is discovered by a query packet with a hop limit, the probability that a request packet finds a t-time-valid route or
a symmetric-valid route, and the average time needed to discover a valid route. For the route maintenance, some parameters are introduced and studied such as the average frequency of route recovery and the average time of a route to be valid. We compare the two models with spatial reuse and without spatial reuse by evaluating these parameters. It is shown that the spatial reuse model is much more effective in routing.