应用数学和力学

The Behavior of Two Parallel Symmetric Permeable Cracks in Piezoelectric Materials

ZHOU Zhen-gong, WANG Biao

2002, 23(12): 1211-1219.

Abstract(2411) PDF(721)

Abstract:
The behavior of two parallel symmetric cracks in piezoelectric materials under anti-plane shear loading was studied by the Schmidt method for the permeable crack face conditions. By using the Fourier transform, the problem can be solved with two pairs of dual integral equations in which the unknown variable is the jump of the diplacement across the crack surfaces. These equations were solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on the geometry of the crack. Contrary to the impermeable crack surface condition solution, it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.

On the Asymptotic Behavior of Hopfield Neural Network With Periodic Inputs

XIANG Lan, ZHOU Jin, LIU Zeng-rong, SUN Shu

2002, 23(12): 1220-1226.

Abstract(2469) PDF(755)

Abstract:
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application to Bellows(Ⅰ)

ZHU Wei-ping, HUANG Qian

2002, 23(12): 1227-1240.

Abstract(2442) PDF(609)

Abstract:
In order to analyze bellows effectively and practically, the finite-element-displacement-per- turbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturbation that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's non- linear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered..

Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application toBellows(Ⅱ)

ZHU Wei-ping, HUANG Qian

2002, 23(12): 1241-1254.

Abstract(2332) PDF(621)

Abstract:
The finite-element-displacement-perturbation method (FEDPM) for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order-perturbation solution (the linear solution) of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others. It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonliear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate, and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nomlinear solution they vary with respect to the convolutions of the bellows.Yet for most bellows, the linear solutions are valid in practice.

Ancient Chinese Algorithm:The Ying Buzu Shu(Method of Surplus and Deficiency)vs Newton Iteration Method

HE Ji-huan

2002, 23(12): 1255-1260.

Abstract(2417) PDF(1145)

Abstract:
An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Dynamic Analysis of a Spatial Coupled Timoshenko Rotating Shaft With Large Displacements

ZHU Huai-liang

2002, 23(12): 1261-1268.

Abstract(1847) PDF(718)

Abstract:
The dynamic simulation is presented for an axial moving flexible rotating shafts, which have large rigid motions and small elastic deformation. The effects of the axial inertia, shear deformation,rotating inertia, gyroscopic moment, and dynamic unbalance are considered based on the Timoshenko rotating shaft theory. The equations of motion and boundary conditions are derived by Hamilton principle, and the solution is obtained by using the perturbation approach and assuming mode method. This study confirms that the influence of the axial rigid motion, shear deformation, slenderness ratio and rotating speed on the dynamic behavior of Timoshenko rotating shaft is evident, especially to a high-angular velocity rotor.

Problem of Periodic Solutions for Neutral Functional Differential Equation

LU Shi-ping, GE Wei-gao

2002, 23(12): 1269-1275.

Abstract(2272) PDF(907)

Abstract:
The problem of periodic solutions for a kind of k-th order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder. s fixed point principle, a kind of k-th order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well.These results improve and extend some known results in recent literature.

Experimental Investigations on Diffusion Characteristics of High Concentration Jets in Environmental Currents

ZHANG Yan, WANG Dao-zeng, FAN Jing-yu

2002, 23(12): 1276-1282.

Abstract(2020) PDF(615)

Abstract:
By means of flow visualization and quantitative measurement, the diffusion pattern and concentration distribution characteristics of high concentration jets vertically discharged into shallow moving waterbody were experimentally investigated in water channel. The interactions between the high concentration jets and environmental flow conditions were analysed, and the formulae of impinging point coordinate and transverse spread angle are gained from data analysis. Experimental results indicate that the jets show complicated flow patterns and diffusion characteristics in near region, which are different from common submerged jets, and spread downstream in the manner of density currents.

Object-Oriented Finite Element Analysis and Programming in VC++

MA Yong-qi, FENG Wei

2002, 23(12): 1283-1288.

Abstract(2214) PDF(835)

Abstract:
The design of finite element analysis program using object-oriented programming (OOP) techniques is presented. The objects, classes and the subclasses used in the programming are explained. The system of classes library of finite element analysis program and Windows-type Graphical User Interfaces by VC++ and its MFC are developed. The reliability, reusability and extensibility of program are enhanced. It is a reference to develop the large-scale, versatile and powerful systems of object-oriented finite element software.

On the Generalized Fritz John Optimality Conditions of Vector Optimization With Set-Valued Maps Under Benson Proper Efficiency

SHENG Bao-huai, LIU San-yang

2002, 23(12): 1289-1295.

Abstract(2529) PDF(847)

Abstract:
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established,its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus

YAO Qing-liu, MA Qin-sheng

2002, 23(12): 1296-1300.

Abstract(2098) PDF(668)

Abstract:
Applying Krasnoselc skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains,subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.

The Positive Solution of Classical Gelfand Model With Coefficient That Changes Sign

YAO Qing-liu

2002, 23(12): 1301-1306.

Abstract(2350) PDF(657)

Abstract:
The existence and iteration of positive solution for classical Gelfand models are considered,where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.

An Algebraic Multigrid Method for Coupled Thermo-Hydro-Mechanical Problems

WANG Xi-cheng, GE Zeng-jie, WU Hong-yu

2002, 23(12): 1307-1313.

Abstract(2556) PDF(578)

Abstract:
An algebraic multigrid method is developed to solve fully coupled multiphase problem involving heat and mass transfer in deforming porous media. The mathematical model consists of balance equations of mass, linear momentum and energy and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressure, gas pressure and displacement. The gas phase is considered to bean ideal gas composed of dry air and vapour, which are regarded as two miscible species. The model makes further use of a modified effective stress concept together with the capillary pressure relatio nship. Phase change is taken into account as well as heat transfer though conduction and convection and latent heat transfer (evaporation-condensation). Numerical examples are given to demonstrate the computing efficiency of this method.

Remark on Stability of Ishikawa Iterative Procedures

XUE Zhi-qun, TIAN Hong

2002, 23(12): 1314-1318.

Abstract(2348) PDF(697)

Abstract:
The stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space. Under parameters satisfying certain conditions, the convergence of iterative sequences was proved. The results improve and extend the recent corresponding results, and supply the basis of theory for further discussing convergence of iteration procedures with errors.

2002 Vol. 23, No. 12