应用数学和力学

1992 Vol. 13, No. 6

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The Numerical Solution of a Singularly Perturbed Problem for Quasilinear Parabolic Differential Equation

Su Yu-cheng, Shen Quan

1992, 13(6): 479-488.

Abstract(2053) PDF(507)

Abstract:
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation,we construct a linear three-level finite difference scheme on a nonuniform grid.The uniform convergence in the sense of discrete L² norm is proved and numerical examples are presented.

Pansystems Clustering Analysis of Complex Systems

Zan Ting-quan, Wu Xue-mou

1992, 13(6): 489-495.

Abstract(2004) PDF(465)

Abstract:
In this paper,by use of equivalence operators δ_i and semi-equivalence operators δ_i we study the clustering problems of complex systems,present δ(1,3)disconnection principle,dual transformation principle and large-scale systems decomposition principle for analizing and operating complex systems,discuss inter connectivity and disconnectivity of complex systems in detail and present some related theorems.Finally,we discuss the levels of systems according to pansystems clustering approach proposed in this paper.

A General Solution of Axisymmetric Problem of Arbitrary Thick Spherical Shell and Solid Sphere

Bu Xiao-ming, Yan Zong-da

1992, 13(6): 497-503.

Abstract(2000) PDF(601)

Abstract:
In this paper,the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem,and the general solutions in forms of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.

The Vibration and Stability Analysis of Moderate Thick Plates by the Method of Lines

Tang Shou-gao, Yuan Si

1992, 13(6): 505-513.

Abstract(2617) PDF(648)

Abstract:
The method of lines based on Hu Hai-chang's theory for the vibration and stability of moderate thick plates is developed.The standard nonlinear ordinary differential equation(ODE) system for natural frequencies and critical load is given by use of ODE techniques,and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition.Numerical examples show that the present method is very effective and reliable.

The Expression of Soliton Solution for Sine-Gordon Equation

Xu Bao-zhi, Fang Xiao-wei

1992, 13(6): 515-518.

Abstract(2515) PDF(545)

Abstract:
In this paper,we study the inverse scattering solution for Sine-Grodon equation
u_xt=sinu(A)
A particularly concise expression of the soliton solution is obtained,and the single soliton and double soliton solutions are discussed.

Calculation of the Fundamental Solution for the Theory of Shallow Shells Considering Shear Deformation

Lü Pin, Huang Mao-guang

1992, 13(6): 519-527.

Abstract(2193) PDF(465)

Abstract:
In this paper,some formulas are derived for the numerical computation of the fundamental solution obtained in ref.[1] and relevant computer methods are also discussed in detail.As an application of the fundamental solution,problems of a concentrated normal force acting on infinite shallow shells having positive,zero and negative Gaussian curvatures are calculated according to the numerical methods given in the paper.

An Exact Solution for the Bending of Point-Supported Orthotropic Rectangular Thin Plates

Jiang Zhi-qing, Liu Jin-xi

1992, 13(6): 529-538.

Abstract(1934) PDF(474)

Abstract:
A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates.The positions of support points and the distribution of transverse loadare arbitrary.If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution.For the square plate simply supported on the middle of each edge and free at each corner,the results are very close to the numerical solutions in the past.

On the Inefficiency of the Quasi-Gradient Screening Algorithm

Sun Xing-ming, Luo Zhi-hui, Wei Ling-de

1992, 13(6): 539-542.

Abstract(2004) PDF(565)

Abstract:
In this paper,the well-knwon quasi-gradient screening algorithm on optimal sequencing cascaded development of water energy resources will be introduced.Then we will given a contraexample in practice and prove the inefficiency of the algorithm in theory.

Variational Principles for Hydrodynamic Impact Problems

Jin Fu-sheng

1992, 13(6): 543-552.

Abstract(2015) PDF(709)

Abstract:
We first establish the rigorous field equations of the two continuous stages before and after entering water.Then correspondently,we obtain the specific variational principles,bounded theorems,and boundary integral equations of the second stage problems.The existence of solutions are proved and the scheme of solving the solutions are provided.Finally,as a numerical example,the ship's wave resistence problem is used to demonstrate the specific application of the second stage problems and its accuracy.Then we provide a rigorous and sound theoretical basis of variational finite element method and boundary element method for calculating the accurately fundamental equations.

Large Range Analysis for Nonlinear Dynamic Systems——Element Mapping Method

Liu Tie-niu, Xu Dao-lin

1992, 13(6): 553-561.

Abstract(1943) PDF(599)

Abstract:
This paper presents a new method for global analysis of nonlinear system.By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous,the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition.Hence,the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations.Still further,the exact position of the fixed points can be found by the iterative technique.It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping.In this paper,the attractive kernel far the stationary fixed points is defined,which makes great advantage for describing the attractive domains of the fixed points.The new method is more convenient and effective than the cell mapping method[1].And an example for two-dimensional mapping is given.

Criteria for Finite Element Algorithm of Generalized Heat Conduction Equation

Ouyang Hua-jiang

1992, 13(6): 563-571.

Abstract(1898) PDF(676)

Abstract:
To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation,the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria.This idea is borrowed here to deal with generalized heat conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented.Some new and useful conclusions are drawn.