应用数学和力学

1981 Vol. 2, No. 5

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Jiang Fu-ru

1981, 2(5): 461-473.

Abstract(2275) PDF(847)

Abstract:
In this paper, the defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Višik-Lyusternik) is noted, from those methods we can not construct the asymptotic expansion of boundary layer term substantially. So the method of multiple scales is proposed for constructing the asymptotic expansion of boundary layer term, the reasonable result is obtained. Furthermore, we compare this method with the method used by Levin-son, and find that both methods give the same asymptotic expansion of boundary layer term, but our method is simpler.Again, we apply this method to study some known works on singular perturbations. The limitations of those works have been noted, and the asymptotic expansion of solution is constructed in general condition.

A Perturbation Solution in the Nonlinear Theory of Circular Plates

Chou Huan-wen

1981, 2(5): 475-484.

Abstract(1817) PDF(572)

Abstract:
In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien's perturbation method, which uses the central deflection as the perturbation parameter.

Bending of Thick Plates with a Concentrated Load

Cheng Chang-jun

1981, 2(5): 485-494.

Abstract(2120) PDF(475)

Abstract:
In this paper, according to the simplified theory of [1], the bending of rectangular plates with two opposite edges simply supported and other two opposite edges being arbitrary under the action of a concentrated load is treated by means of properties of two-variable-function and the method of series, The effect of transverse shearing forces on the bending of plates is considered. When the thickness h of plates is small, and the term, whose orders are more than order of h² are neglected, then the results agree with the solutions corresponding to the problem of thin plates, At the end, the solutions of the bending problem of plates with arbitrary linear distributed load are also obtained.

Determination of Separated Region in a Curved Tube

Wu Wang-yi, Wen Gong-bi

1981, 2(5): 495-504.

Abstract(1793) PDF(462)

Abstract:
The formation of atherosclerosis in a curved a-orta is closely related to the existence of separated vortex region. This paper deals with the steady laminar motion of an incompressible Newtonian fluid through a curved tube with circular cross-section whose curvature is small and whose curvature gradient is not too large. Using the momentum integral method and the approximation of quasi-constant curvature, an equation which determines the location of separation and reattachment is derived. From this equation the earliest point of separation and the corresponding critical Reynolds number are obtained, and the relation between the position of separation and reattachment and Reynolds number R_e for different azimuthal angle are revealed. It is concluded that the separation first emerges at the position whose curvature gradient has the maximum absolute value. With increasing R_e, the separation region extends in the direction of mainstream, azimuthal angle and radius vector, and then forms a three-dimensional separated vortex, which gradually enlarges in all three directions with the increase of Reynolds number. The theoretical results also very clearly demonstrate the following striking experimental fact: if a symmetrical curved tube exhibits a separated vortex at the outside of the upstream, then it must have another one symmetrically placed at the inside of its downstream.

The Solid Variational Principles of the Discrete Form—The Variationai Principles of the Discrete Analysis by the Finite Element Method

Niu Xiang-jun

1981, 2(5): 505-520.

Abstract(2021) PDF(683)

Abstract:
This paper suggests a new solid variations, principle of discrete form. Basing on the true case of the discrete analysis by the finite element method and considering the variable boundaries of the elements and the unknown functions of piecewise approximation, the unknown functions have various discontinuities at the interfaces between successive elements.Thus, we have used mathematical technique of variable boundary with discontinuity of the unknown functions, based on the conditions that the first variation vanishes immediately, to establish the solid variation principles of discrete form. It generalizes the classical and non-classical variational principles.Successive equations that have to be satisfied by the unknown functions are the convergency necessary conditions for the finite elements method (including conforming and non-conforming). They expand that convergency necessary conditions of the compatibility conditions in the internal interfaces.

Perturbation Method for Thin Plate Bending Problems

Mo Jia-qi, Shi Bing-guo

1981, 2(5): 521-528.

Abstract(1842) PDF(468)

Abstract:
In this paper, problems of bending of a thin plate under the action of in-plane forces are studied by using the method of multiple scales.

A Series of Base Functions for Global Analytical Approach to Firing Table

Huang Wen-qi

1981, 2(5): 529-532.

Abstract(2012) PDF(518)

Abstract:
A series of base functions has been proposed for global analytical approach to the firing table on cannons and guns. Numerical tests on the firing table of a gun of specific model prove that it is satisfactory; showing that these functions should also be useful to approach to the firing table of firearms of other models.Methods of extension and invariability analysis developed for obtaining the base functions in question should be of value as a reference to global analytical approach to a great many other numerical functions.

Energy Element and Its Application in the Dynamic Calculation of Continuous Medium

Cao Zhi-yuan, Li Zi-cai

1981, 2(5): 533-539.

Abstract(1756) PDF(421)

Abstract:
The present paper which discusses the problem re-lated to the combination of the finite difference method and the finite element method, describes an en-ergry element calculating mode including the special features of the above two methods.

On Some Problems of Plastic Buckling of Plates and Shells

Cheng Xiang-sheng

1981, 2(5): 541-548.

Abstract(1762) PDF(461)

Abstract:
This paper gives the stress-strain relations of the variational types on the basis of an assumption concerning the small deformation in the theory of el-asto-plasticity.The compact form of fundamental equations of plastic buckling of the plates and shells is obtained in terms of secant modulus.

Some Solutions of Maxwell Equations

Xiong Xi-jin

1981, 2(5): 549-556.

Abstract(1936) PDF(511)

Abstract:
This article gives a class of solution of Maxwell equations which implies the solution of arbitrary ho-lomorphic hypercomplex functional with brief discussion of their physical meaning. It exhibites some wider nature than classical electromagnetic theory:(1) An electromagnetic field may spread non-periodically and may have the holographic nature and free shape.(2) The electromagnetic field may spread more slowly, equally or more quickly than light speed.(3) The electromagnetic field may spread in arbitrary curved direction.(4) There is a branch electromagnetic field in in-tergrowth space. An intergrrowth world may exist.This article also makes an inference and a description about the example of the above-mentioned strange electromagnetic field. It relates to some hard-to-explain phenomena through different physical models.

To Construct a Vector Field with Given Curl Function and Divergence Function

Li Chun-bao

1981, 2(5): 557-562.

Abstract(2022) PDF(816)

Abstract:
Two conclusions have been achieved in this paper.Firstly, a formal solution of the equations ∇×=, ∇·=P has been derived with different point of view from commonly known classical method developed by He-lmholtz(1),(2),(3).Secondly, a method to construct a vector field with given curl function and divergence function has been given in terms of the above solution.

Singular Perturbation of First Boundary Value Problem for Higher Order Elliptic Equations (Ⅱ)

Zheng Yong-shu

1981, 2(5): 563-574.

Abstract(1672) PDF(469)

Abstract:
In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter.

Discussion on Barenblatt’s Equations of Mean Movement of the Inhomogeneous Fluid

Wu De-yi

1981, 2(5): 575-578.

Abstract(1930) PDF(509)

Abstract:
In this paper, it is proved that Barenblatt's equation of mean movement of the inhomogeneous fluid is not correct, because his equations are based on the assumption that the characteristics of inhomogeneity of fluid are only affected with respect to gravitational terms. The correct form of the equation of mean movement of the inhomogeneous fluid is derived in this paper.

A Numerical Method for the Evaluation of Fourier Integrals

Tan Fu-qi

1981, 2(5): 581-584.

Abstract(1998) PDF(437)

Abstract:
This paper puts forward the use of spline function interpolation in the evaluation of Fourier integrals. At the same time, the numerical results of some common functions by various interpolation methods and a simplified method of construction of spline function for various boundary conditions are also presented.