Applied Mathematics and Mechanics (English Edition)

Thermoelastic analysis of functionally graded annulus with arbitrary gradient

彭旭龙李显方

2009, 30(10): 1211-1220. doi:10.1007/s10483-009-1001-7

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A thermoelastic problem of a circular annulus made of functionally graded materials with an arbitrary gradient is investigated. Different from previous works, our analysis neither requires a special form of the gradient of material properties nor demands partitioning the entire structure into a multilayered homogeneous structure. Instead, we propose a new method for solving the thermoelastic problem of a functionally graded circular annulus by transforming it to a Fredholm integral equation. The distribution of thermal stresses and radial displacement can be obtained by solving the resulting equation. Illustrative examples are given to show the effects of varying gradients on the thermal stresses and radial displacement for given temperature changes at the inner and outer surfaces. The results indicate that the thermal stresses can be relaxed for specified gradients, which is beneficial to design an inhomogeneous annulus to maintain structural integrity.

Interaction between heat dipole and circular interfacial crack

肖万伸谢超刘又文

2009, 30(10): 1221-1232. doi:10.1007/s10483-009-1002-x

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The heat dipole consists of a heat source and a heat sink. The problem of an interfacial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theorem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interfacial fracture are analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different positions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.

A novel virtual node method for polygonal elements

唐旭海吴圣川郑超张建海

2009, 30(10): 1233-1246. doi:10.1007/s10483-009-1003-3

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A novel polygonal finite element method (PFEM) based on partition of unity is proposed, termed the virtual node method (VNM). To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

Numerical simulation of solid tumor angiogenesis with Endostatin treatment: a combined analysis of inhibiting effect of anti-angiogenic factor and micro mechanical environment of extracellular matrix

蔡彦吴洁古娜张洪一曹金凤许世雄龙泉柯林斯

2009, 30(10): 1247-1254. doi:10.1007/s10483-009-1004-z

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To investigate the influence of anti-angiogenesis drug Endostatin on solid tumor angiogenesis, a mathematical model of tumor angiogenesis was developed with combined influences of local extra-cellular matrix mechanical environment, and the inhibiting effects of Angiostatin and Endostatin. Simulation results show that Angiostatin and Endostatin can effectively inhibit the process of tumor angiogenesis, and decrease the number of blood vessels in the tumor. The present model could be used as a valid theoretical method in the investigation of anti-angiogenic therapy of tumors.

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

S.Nadeem Anwar Hussain M.Y.Malik T.Hayat

2009, 30(10): 1255-1262. doi:10.1007/s10483-009-1005-6

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This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method (HAM). Two-dimensional and axisymmetric shrinking flow cases are discussed.

Space-time objective decomposition of vortex equations and mechanism analysis of subtropical high abnormal activities

洪梅张韧薛峰刘科峰

2009, 30(10): 1263-1270. doi:10.1007/s10483-009-1006-z

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To analyze the dynamic mechanism of unusual activities of the subtropical high, the space-time varible separation of the partial differential vortex equations is carried out with Galerkin methods based on the heat force and the whirl movement dissipation effect. Aiming at the subjective and man-made conventional method of choice in the space basis functions, we propose to combine the empirical orthogonal function (EOF) analysis with the genetic algorithm to inverse the space basis functions from the actual sequence of fields. A group of trigonometric functions are chosen as a generalized space basis function. With the least-squares error of the basis function and EOF typical fields, and with the complete orthogonality of basis functions, we can get the dual-bound function. A genetic algorithm is then introduced to carry out surface fitting and coefficient optimization of the basis function. As a result, the objective and reasonable constant differential equation of the subtropical high is obtained by inversion. Finally, based on the obtained nonlinear dynamics model, the dynamic behavior and mechanism of the subtropical high is analyzed and discussed under the influence of heat force. We find that solar radiation and zonal differences in land and sea are important factors impacting the potential field and flow field changes of the subtropical areas. These factors lead to strength changes of the subtropical high and medium-term advance/retreat activities. The former is a gradual change, while the latter shows more break characteristics. Meaningful results are obtained in the analysis.

Topographic effects on polar low and tropical cyclone development in simple theoretical model

李子良傅刚郭敬天端义宏张美根

2009, 30(10): 1271-1282. doi:10.1007/s10483-009-1007-x

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The polar low and tropical cyclone type vortices over topography are assumed to be the axisymmetrical and thermal-wind balanced systems, which are solved as an initial value problem of a linearized vortex equation set in cylindrical coordinates. The roles of the sensible and latent heating, friction, and topography in the structure and intensification of the polar low and tropical cyclone type vortices are analyzed. The radial velocity, vertical velocity, azimuthal velocity, and the unstable growth rate including the topography effects are obtained. It is shown that the interaction between the flow and the topography plays a significant role in the structure and intensification of the polar low and tropical cyclone system. The analysis of the topography term indicates that, in the up-slope side of the mountain, the radial inflow and the vertical ascent forced by the mountain can intensify the polar low and tropical cyclone type vortex and increase the unstable growth rate. However, in the lee side of the mountain, the radial inflow and the vertical descent forced by the mountain can weaken the polar low and tropical cyclone type vortex and decrease the unstable growth rate of the polar low and tropical cyclone system. In addition, the evolutionary process and the spatial structure of the polar low observed over the Japan Sea on 19 December 2003 are investigated with the observational data to verify this theoretical result.

Recursive Lagrangian dynamic modeling and simulation of multi-link spatial flexible manipulator arms

章定国

2009, 30(10): 1283-1294. doi:10.1007/s10483-009-1008-2

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The dynamics for multi-link spatial flexible manipulator arms consisting of n links and n rotary joints is investigated. Kinematics of both rotary-joint motion and link deformation is described by 4 × 4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. In the modeling the recursive strategy for kinematics is adopted to improve the computational efficiency. Both the bending and torsional flexibility of the link are taken into account. Based on the present method a general-purpose software package for dynamic simulation is developed. Dynamic simulation of a spatial flexible manipulator arm is given as an example to validate the algorithm.

New modal identification method under the non-stationary Gaussian ambient excitation

杜秀丽汪凤泉

2009, 30(10): 1295-1304. doi:10.1007/s10483-009-1009-7

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Based on the multivariate continuous time autoregressive (CAR) model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model (CAR) of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a conditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.

A heterogeneous boundedly rational expectation model for housing market

梁以德徐佳娜崔詠芯

2009, 30(10): 1305-1316. doi:10.1007/s10483-009-1010-1

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This research aims to test the housing price dynamics when considering heterogeneous boundedly rational expectations such as naive expectation, adaptive expectation and biased belief. The housing market is investigated as an evolutionary system with heterogeneous and competing expectations. The results show that the dynamics of the expected housing price varies substantially when heterogeneous expectations are considered together with some other endogenous factors. Simulation results explain some stylized phenomena such as equilibrium or oscillation, convergence or divergence, and over-shooting or under-shooting. Furthermore, the results suggest that variation of the proportion of groups of agents is basically dependent on the selected strategies. It also indicates that control policies should be chosen carefully in consistence with a unique real estate market during a unique period since certain parameter portfolio may increase or suppress oscillation.

Asymptotic stability for impulsive functional differential equations

罗治国罗艳

2009, 30(10): 1317-1324. doi:10.1007/s10483-009-1011-z

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In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen’s inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

向家伟陈雪峰李锡夔

2009, 30(10): 1325-1334. doi:10.1007/s10483-009-1012-x

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A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

Eventually vanished solutions of a forced Li´enard system

张永新

2009, 30(10): 1335-1344. doi:10.1007/s10483-009-1013-6

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In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t→±∞, to a Li´enard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non-Hamiltonian form are overcome by applying the Schauder’s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Li´enard system.

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