应用数学和力学

2009 Vol. 30, No. 1

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System of Set-Valued Mixed Quasi-Variational-Like Inclusions Involving H-eta-Monotone Operators in Banach Spaces

DING Xie-ping, WANG Zhong-bao

2009, 30(1): 1-14.

Abstract(2575) PDF(810)

Abstract:
A new system of set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H-eta-monotone operators is introduced and studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-eta-monotone operators, a new iterative algorithm for finding the approximation solutions of the SSMQVLI was suggested and analyzed. It was also proved that the iterative sequences generated by the algorithm converge strongly to the exact solution of the SSMQVLI under suitable assumptions. These results are new, and extend and improve the corresponding results in this field.

3D Analysis of the Functionally Graded Material Plates With Complex Shapes and Various Holes

CAO Zhi-yuan, TANG Shou-gao, CHENG Guo-hua

2009, 30(1): 15-20.

Abstract(2987) PDF(564)

Abstract:
Basic formulas for Semi-analytical Graded FEM on FGM members were derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with parameters of a given FGM plate, the FGM plate problems under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, and proves to be an effective numerical method for mechanical analyses of FGM structures. Last, several FGM plate examples with complex shapes and various holes were provided.

Open-Plus-Closed-Loop Control for Chaotic Mathieu-Duffing Oscillator

SHEN Jian-he, CHEN Shu-hui

2009, 30(1): 21-29.

Abstract(2906) PDF(618)

Abstract:
Utilizing the idea of the open-plus-closed-loop (OPCL) control, a controller which is composed of an external excitation and linear feedback was designed to entrain the chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of the open-plus-closed-loop control was proved by combining Liapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations were performed to demonstrate the theoretical results.

Optimal Error Estimates for Fourier Spectral Approxiation of the Generalized KdV Equation

DENG Zhen-guo, MA He-ping

2009, 30(1): 30-39.

Abstract(3097) PDF(725)

Abstract:
A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed and corresponding optimal error estimate in L2-norm is obtained, which improves the one by Maday and Quarteroni. Also a modified Fourier pseudospectral method is presented and it is proven that it enjoys the same convergence properties as the Fourier spectral method.

Elastodynamics of Axi-Symmetric Deformation in Magneto-Micropolar Generalized Thermoelastic Medium

Rajneesh Kumar, Rupender

2009, 30(1): 40-50.

Abstract(2954) PDF(573)

Abstract:
An axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to mechanical or thermal source in a transverse magnetic field is concerned with. Laplace and Hankel transform techniques were used to solve the problem. To illustrate the application of approach, two different type of sources i. e., concentrated force and thermal source over the circular region were considered. The integral transforms were inverted by using a numerical technique to obtain the components of stresses, temperature distribution and induced electric and magnetic fields. The expressions of these quantities were illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i. e., Lord and Shulman (L-S theory) and Green and Lindsay (G-L theory). A particular interesting case was also deduced.

Efficient FEM Approach for Pressure Analysis of Oil Film in a Piston Pump

Tadeusz Zloto, Arkadiusz Nagorka

2009, 30(1): 51-63.

Abstract(2613) PDF(514)

Abstract:
Numerical analysis of pressure distribution of oil film on the valve plate in variable height gap of an axial piston pump is concerned. The analysis employs the finite element method. For determination of oil pressure variations in the gap the Reynolds equation, commonly applied in the theory of lubrication by Pasynkov, was applied. The equation was solved numerically with the use of self-developed program based on finite element method. In order to obtain high accuracy of the results an adaptive mesh refinement based on residual estimations of solution errors was applied. The calculation results were represented as dependent on the geometric and working parameters of the pump.

Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing

LI Fang-fang, LIU Jing, YUE Kai

2009, 30(1): 64-74.

Abstract(3353) PDF(675)

Abstract:
Analytically solving three dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult, however theoretically importantm. The moving heat source model and the Green function method were introduced for the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces were obtained. Further, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes was also analytically solved. A closed form analytical solution to the bioheat phase change process by taking account of contributions from blood perfusion heat transfer, metabolic heat generation and heat sink of cryoprobe was derived. The present method is expected to be of significant value for analytically solving complex bioheat transfer problems with phase change.

Parametric Type of KKM Theorem in FC-Spaces With Applications

DENG Lei, ZANG Xiao-yan

2009, 30(1): 75-82.

Abstract(2917) PDF(674)

Abstract:
First, the authors proved a characteristic property in FC-spaces, then using the connectedness of set, a parametric type of KKM theorem was established in noncompact FC-spaces by introducing a linear ordered space. As consequences, some recent known results such as the noncompact minimax inequalities, saddle point theorem and section theorem were improved. The results improve and generalize the corresponding results in the literature.

Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System

WANG Fang-lei, AN Yu-kun

2009, 30(1): 83-89.

Abstract(3304) PDF(695)

Abstract:
There exist at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, using the Green function and maximum principle, the existence of solutions of nonlinear telegraph system was equivalent to the existence of fixed points of an operator. Finally, imposing growth conditions on the nonlinearities, the existence of at least three fixed points in cone was obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces, namely, there exist at least three positive doubly periodic solutions of the nonlinear telegraph system.

CCH-Based Geometric Algorithms for SVM and the Applications

PENG Xin-jun, WANG Yi-fei

2009, 30(1): 90-100.

Abstract(2891) PDF(749)

Abstract:
The support vector machine (SVM) is a novel machine learning tool in data mining. The geometric approach based on the compressed convex hull (CCH) with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull (RCH), CCH preserves the shape of geometric solid for the data set; meanwhile, it is easy to give the necessary and sufficient condition of determining its extreme points. As the practical applications of CCH, spare and probabilistic speed-up geometric algorithms were developed. Results of some numerical experiments show that the proposed algorithms can reduce the kernel evaluation and display nice performances.

Free Vibration and Transverse Stresses of Viscoelastic Laminated Plates

HU Ming-yong, WANG An-wen

2009, 30(1): 101-108.

Abstract(2898) PDF(437)

Abstract:
Based on Reddy.s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate were derived by using the quadratic inter polation function for displacement in the direction of plate thickness. And the vibration frequencies and loss factors were calculated for free vibration of simply supported viscoelastic sandwich plate, which shows a good agreement with the data in the reference. And harmonio us transverse stresses can be obtained. The transverse shear stresses are the main factor that leads to the delamination of viscoelastic laminated plate in lower-frequency free vibration and the transverse normal stress in higher-frequency free vibration. The relationship of the modulus of viscoelastic materials to transverse stress was analyzed. The ratio of transverse stress max-value to in-plane stress max-value was obtained. The results show that the method, equations and programs are reliable.

Spectral Properties and Geometric Interpretation of R-Filters

LENG Tuo

2009, 30(1): 109-119.

Abstract(2353) PDF(684)

Abstract:
Applying the Fourier analysis, the spectral properties of the R-filters are studied. Further, it was proved that R-filters is a generalization of least squares polynomial adjustment. And the geometric interpretation of R-filters was given.

An Iterative Modified Kernel Based on Training Data

ZHOU Zhi-xiang, HAN Feng-qing

2009, 30(1): 120-126.

Abstract(2253) PDF(684)

Abstract:
In order to improve the performance of a support vector regression, a new method for modified kernel function is proposed. In this method the information of whole samples is included in kernel function by conformal mapping. So the kernel function is data-dependent. With random initial parameter of kernel function, the kernel function is modified repeatedly until a satisfactory effect is achieved. Compared with the conventional model, the improved approach needs not selecting parameters of kernel function. Simulation was finished for one-dimension continue function and strong earthquake event. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the iteration number increasing, the figure of merit will decrease and converge. The speed of convergence depends on the parameters in the algorithm.