应用数学和力学

1986 Vol. 7, No. 7

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The Propagation of Solitary Waves in a Nonlinear Elastic Rod

Zhuang Wei, Yang Gui-tong

1986, 7(7): 571-581.

Abstract(1786) PDF(792)

Abstract:
In this paper, the inverse scattering method is used to analyse strain solitary waves in a nonlinear elastic rod^[1]. Properties of solitary waves and their influence on solid structures are discussed in detail. Some quantitative results are given.

Some Lemmas on Doubly Quasi-Periodic Analytic Functions in Multiplication

Lu Jian-ke

1986, 7(7): 583-587.

Abstract(1842) PDF(598)

Abstract:
In this paper, some lemmas on doubly quasi-periodic analytic functions in multiplication are proved. Suchfunctions may not be identical to zero even if their real parts vanish on the boundary. Conditions for in which this case appears is also obtained. A concrete example is given to show that this case actually exists. Finally, the general solution of the considered Dirichlet problem of doubly quasi-periodic analytic functions with zero real parts on the boundary is obtained, provided the multipliers are not prescribed.

Determination of the Perturbation Parameter in Larger Deflection of Plates and Shallow Shells by Means of the Least Squares Method

Chen Shan-lin

1986, 7(7): 589-596.

Abstract(2011) PDF(496)

Abstract:
In this paper, the least square method of determination of the perturbation parameter is presented when the perturbation technique is used in the solution of large deflection of axisymmetrical plates and shallow shells. The examples of circular plates are calculated and compared with the exact solution and other perturbation solutions. The results show the best agreement with the exact solution among those perturbation solutions.

Existence and Comparison Results for Solutions’ of Random Integral and Differential Equations

Ding Xie-ping

1986, 7(7): 597-604.

Abstract(1718) PDF(632)

Abstract:
This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan^[2,3] and Lakshmikantham^[4,5].

Axisymmetrical Elements of Thin Shell of Revolution Corresponding to Different Types of Variational Principles

Zhang She-guang, Chen Wan-ji

1986, 7(7): 605-616.

Abstract(1856) PDF(570)

Abstract:
The purpose of this paper is to investigate, to some extent, the influnce of variational constraints on the finite element properties, which are based on different types of variational principles. Taking axisymmetrical elements of thin shell of revolution(abbreviated as TSR element) as comparative elements, and with the same geometrical description, we derive seven kinds of TSR hybrid elements and two kinds of TSR conforming elements corresponding to three types of hybrid variational principles and potential energy principle respectively. By analysing the element stiffness formulations and comparing the numerical calculations, such as corrugated shell, we discuss the differences in properties of different models, and the adaptability, limitation as well as relationship between two types of models. We also point out a divergence case of TSR hybrid displacement element, and suggest two kinds of more acceptable TSR elements.

Fixed Stream-Tube Method for Solving Two-Phase Plane Flow Problems and Its Theoretical Analysis

Chen Zhong-xiang, Yuan Yi-rang, Jiang Li-shang

1986, 7(7): 617-628.

Abstract(1738) PDF(521)

Abstract:
The fixed stream-tube method widely adopted in engineering field for giving an approximate solution to the two-dimensional problems of two-phase flow through porous media is summarized and an improvement has been made in thispaper. It scorepart, i.e., the fluid displacement within a one-dimensional stream tube with variable cross-sectional area under a given pressure difference across the tube is thoroughly studied. The existence and uniqueness of solution are proved, the exact solution, numerical solution and its convergence, stability analyses are given in this paper.

A Generalized Variationai Principle of Composite Shallow Shells and Its Application to the Folded Shell

Ni Hai-ying, Tong Jing-yu

1986, 7(7): 629-636.

Abstract(1564) PDF(504)

Abstract:
In this paper, a generalized variational principle of elastodynamics in composite shallow shells with edge beams is presented, and its equivalence to corresponding basic equations, ridge conditions and boundary conditions is proved. Then this variational principle is applied to the folded shell structure. By means of double series, the approximate analytical solutions for statics and dynamics under common boundary conditions are obtained. The comparison of our results with FEM computations and experiments shows the analytical solutions have good convergence and their accuracy is quite satisfactory.

The Ring Shells under Gravitative Loads

Wang Dai-yu, Chen Shan-lin, Wu Guo-ping

1986, 7(7): 637-646.

Abstract(1866) PDF(559)

Abstract:
This paper gives Novozlov's equation(ref. [1]) in a simple style of ring shells with equal thickness under the actions of gravitative loads. By means of Fourier series, the special solution of the equation is established. Using the results of the homogeneous solution in ref. [2], we find out the general solution of the problem, and derive the expressions of stress and displacement.Two examples are given as the application of the above results.

A New Quadrilateral Nonconforming Model and Its Convergence

Li Yong, Wu Chang-chun

1986, 7(7): 647-654.

Abstract(1957) PDF(649)

Abstract:
This paper presents a new quadrilateral nonconforming finite element. We deal with its convergence by using generalized patch teat. The error on stresses and displacements are obtained and numerical compulations for plane elastic problems are given.

Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness

Li Long-yuan

1986, 7(7): 655-662.

Abstract(1852) PDF(605)

Abstract:
In this paper, the flexural vibration analysis of moderate-thick rectangular plates with slowly varying thickness using perturbation method is described, and the explict expressions of free vibration frequencies for arbitrary thickness functions are derived. Finally, several numerical examples have been given and comparisons have been made with other proposed solution techniques. This comparison shows that the method yields very good results, so that this method may be regarded as an alternative effective method for the vibration and buckling analysis of plates and shells.

Uniformly Convergent Difference Schemes for First Boundary Value Problem for Elliptic Differential Equations with a Small Parameter at the Highest Derivative

Liu Bi-yue

1986, 7(7): 663-673.

Abstract(2236) PDF(520)

Abstract:
In this paper we consider the Dirichlet problem for elliptic differential equations. A special difference scheme is constructed from the necessary condition of uniform convergence. We also prove the uniform convergence and the asymptotic behavior of the solution of the difference problem, and give the error estimate.