应用数学和力学

2007 Vol. 28, No. 1

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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): 1-8.

Abstract(3133) PDF(634)

Abstract:
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 was used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings was 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 was 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-Eta-Monotone Mapping and Resolvent Operator Technique for Solving Generalized Implicit Variational-Like Inclusions

ZHANG Qing-bang, DING Xie-ping

2007, 28(1): 9-16.

Abstract(2513) PDF(661)

Abstract:
A new class of g-Eta-monotone mappings and a class of generalized implicit variational-like inclusions involving g-Eta-monotone mappings are introduced. The resolvent operator of g-Eta-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 sequence generated by the algorithm is also proved.

Advanced Response Surface Method for Mechanical Reliability Analysis

LÜ Zhen-zhou, ZHAO Jie, YUE Zhu-feng

2007, 28(1): 17-24.

Abstract(2560) PDF(611)

Abstract:
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 converging 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): 25-33.

Abstract(3103) PDF(653)

Abstract:
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 it drops the coarse solution of the region near the boundary. At last, by overlapping domain decomposition, the parallel algorithms are obtained. The error of these algorithms are analyzed and some error estimates are got which are better than that 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 highly 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): 34-44.

Abstract(2599) PDF(660)

Abstract:
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 di-f ferential 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): 45-52.

Abstract(2948) PDF(537)

Abstract:
Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material was established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch was presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate were considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure was 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. The present method has a wide application a.

Thermal Post-buckling Analyses of Functionally Graded Material Rod

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

2007, 28(1): 53-60.

Abstract(2825) PDF(638)

Abstract:
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 changing while the bottom temperature parameter remains constant, and when the bottom temperature parameter is changing 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): 61-69.

Abstract(2590) PDF(489)

Abstract:
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 was applied and the viscosity-temperature relation was 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, was 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 was 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 were presented in terms of the Brinkman number, the P clet 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 RCCD

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

2007, 28(1): 70-76.

Abstract(2334) PDF(527)

Abstract:
The construction interfaces of RCCD have a distinct influence on the deformation of dams. The characters and rules on deformation of construction interfaces were studied. The methods simulating the interfaces. deformation at different stages were proposed. A thickness analytic model and a no-thickness analytic model of construction interfaces were 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 that 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, YE Jian-shu, ZHAO Xin-ming

2007, 28(1): 77-84.

Abstract(2273) PDF(505)

Abstract:
The finite strip controlling equation of pinned curve box was deduced on the basis of Novozhilov theory and with flexibility method, the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was founded for the first time. 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 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): 85-91.

Abstract(2613) PDF(578)

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

Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces

DENG Lei, YANG Ming-ge

2007, 28(1): 92-98.

Abstract(2633) PDF(639)

Abstract:
The concepts of weakly R-KKM mappings, R-convex and R-β-quasiconvex in general topological spaces without any convex structure are introduced. Relating to these, an extension to general topological spaces of Fan's matching theorem is obtained, namely Lemma 1.2. 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. The results generalize and improve the corresponding results in the literature.

SHI Pei-hu, WANG Ming-xin

2007, 28(1): 99-106.

Abstract(2670) PDF(667)

Abstract:
The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms had been studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ODE. Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE had been investigated, 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 the investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.

Superconvergence Analysis of Wilson’s Element on Anisotropic Meshes

SHI Dong-yang, LIANG Hui

2007, 28(1): 107-113.

Abstract(2398) PDF(578)

Abstract:
The Wilson finite element method is considered to solve a class of two-dimensional second order elliptic boundary value problems. By using the particular structure of the element and some new techniques, the superclose and global superconvergence on anisotropic meshes are obtained. 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): 114-126.

Abstract(2680) PDF(568)

Abstract:
Mobile ad hoc networks (MANETs) have become a hot issue in the area of wireless networks for their non-infrastructure and mobile features. 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 n times in the flooding process, which is named as an n-SRBDM model. The performance of the network is analyzed 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 limit0, the probability that a request packet finds a S-time-valid route or a symmetrical-valid route, and the average time needed t o 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. Two models with spatial reuse and without spatial reuse are compared by evaluating these parameters. It is shown that the spatial reuse model is much more effective in routing.