应用数学和力学

2004 Vol. 25, No. 3

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On the Stability Analysis of Plates and Shells Using a Quadrilateral,16-Degrees of Freedom Plat Shell Element DKQ16

ZHENG Chang-liang, LI Li-hua, ZHONG Wan-xie

2004, 25(3): 221-227.

Abstract(2621) PDF(736)

Abstract:
The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral, 16-degrees of freedom flat shell element (called DKQ16). The geometrical stiffnees matrix was established. Comparision of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.

Mathematical Problems in the Integral-Transformation Method of Dynamic Crack

BIAN Wen-feng, WANG Biao, JIA Bao-xian

2004, 25(3): 228-232.

Abstract(2582) PDF(660)

Abstract:
In the investigation on fracture mechanics, the potential function was introduced, and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied. After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility. A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.

Computing the Eigenvectors of a Matrix With Multiplex Eigenvalues by SVD Method

CHI Bin, YE Qing-kai

2004, 25(3): 233-238.

Abstract(2560) PDF(1263)

Abstract:
Every matrix is similar to a matrix in Jordan canonical form, which has very important sense in the theory of linear algebra and its engineering application. For a matrix with multiplex eigenvalues, an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed. Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues. It is superior to MATLAB and MATHEMATICA.

Robust Control of Periodic Bifurcation Solutions

LIANG Jian-shu, CHEN Yu-shu, Andrew Y. T. Leung

2004, 25(3): 239-246.

Abstract(2749) PDF(610)

Abstract:
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method.

Dynamic Analysis of Underground Composite Structures Under Explosion Loading

ZHAO Xiao-bing, XUE Da-wei, ZHAO Yu-xiang

2004, 25(3): 247-252.

Abstract(2873) PDF(502)

Abstract:
In selecting rational types of underground structures resisting explosion, in order to improve stress states of the structural section and make full use of material strength of each part of the section, the research method of composite structures is presented. Adopting the analysis method of micro-section free body, equilibrium equations, constraint equations and deformation coordination equations are given. Making use of the concept of generalized work and directly introducing Lagrange multiplier specific in physical meaning, the validity of the constructed generalized functional is proved by using variation method. The rational rigidity matching relationship of composite structure section is presented through example calculations.

Microcosmic Bound Theorem of Daycy’s Law and Its Application

XU You-sheng, LIU Ci-qun, LIN Ji

2004, 25(3): 253-261.

Abstract(3186) PDF(683)

Abstract:
By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of Darcy's law was obtained through taking variable average over Navier-Stokes equation on some representative space in porous media, and finally an example was taken to prove its reliability.

On the Well-Posedness of the Initial Value Problem of Non-Static Rotating Fluid

CHEN Da-duan, HE You-hua

2004, 25(3): 262-270.

Abstract(2771) PDF(717)

Abstract:
A systematic study was made on the topological nature of the system of non-static rotating fluid. Several initial (boundary) value problems and their well-posedness were discussed.

Analytic Expression of Magnetic Field Distribution of Rectangular Permanent Magnets

GOU Xiao-fan, YANG Yong, ZHENG Xiao-jing

2004, 25(3): 271-278.

Abstract(4399) PDF(2786)

Abstract:
From the molecular current viewpoint, an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk, but also for that of several rectangular permanent magnet bulks. By using this expression, the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets, in order to describe its distribution, two quantities, one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field, were defined. Furthermore, the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.

Tracking and Reconstruction Methods for Moving-Interfaces

LIU Ru-xun, LIU Xiao-ping, ZHANG Lei, WANG Zhi-feng

2004, 25(3): 279-290.

Abstract(2576) PDF(1261)

Abstract:
A simple, efficient and accurate high resolution method to tracking moving-interfaces (the characteristisc integral) averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation, their characters, advantages and shortcomings are compared, analyzed and commended in particular.

Impulsive Control for the Stabilization and Synchronization of Lur’e Systems

SUN Ji-tao, WU Qi-di

2004, 25(3): 291-296.

Abstract(2602) PDF(800)

Abstract:
An impulsive control scheme of the Lur'e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur'e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur'e system and impulsive control law are given, a theory of impulsive synchronization of two Lur'e system is also presented. A numerical example is used to verify the theoretical result.

Robust Adaptive Control of Nonholonomic Systems With Uncertainties

MU Xiao-wu, YU Ji-min, BI Wei-ping, CHENG Dai-zhan

2004, 25(3): 297-304.

Abstract(3275) PDF(742)

Abstract:
Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed. The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.

Dynamic Characteristic Analysis of a 3-D Semi-Submerged Body as a Fluid-Structure Interaction System

XU Gang, REN Wen-min

2004, 25(3): 305-312.

Abstract(2897) PDF(618)

Abstract:
An Arnoldi's method with new iteration pattern, which was designed for solving a large unsymmetric eigenvalue problem introduced by displacement-pressure FE pattern of a fluid-structure interaction system, was adopted here to get the dynamic characteristics of the semi-submerged body. The new iteration pattern could be used efficiently to obtain the Arnoldi's vectors in the shift-frequency technique, which was used for the zero-frequency problem. Numerical example showed that the fluid-structure interaction is one of the important factors to the dynamic characteristics of large semi- submerged thin-walled structures.

Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity

ZHANG Guo-qing, YU Jian-xing

2004, 25(3): 313-322.

Abstract(2601) PDF(652)

Abstract:
The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functionals and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.

Some Results on Continuous Type Conditional Input-Output Equation——Fixed Point and Surjectivity Methods

LIU Ying-fan, CHEN Xiao-hong

2004, 25(3): 323-330.

Abstract(2776) PDF(618)

Abstract:
Based on the classical(matrix type) input-output analysis, a type of nonlinear(continuous type) conditional Leontief model, input-output equation were introduced, as well as three corresponding questions, namely, solvability, continuity and surjectivity, and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result, the main theorems are obtained, which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprise s consuming operator.