应用数学和力学

1982 Vol. 3, No. 1

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The Velocity of Sand Particles Relative to Water and the Variation of Fluctuation Velocity due to the Concentration of Suspended Sand Particles

Cai Shu-tang

1982, 3(1): 1-10.

Abstract(1941) PDF(596)

Abstract:
In this paper, we discuss three fundamental problems of the theory of suspended sand particles based on the theory of fluid dynamics. They are:(l) the relative velocity of sand particles to the surrounding fluid in the turbulent flow,(2) the variation of the velocity fluctuation of the fluid when the suspended sand particles exist,(3) the profile of the vertical distribution of the concentration of the suspended sand particles in two-dimensional uniform steady channel flow and the modification of usual diffusion theory. The results of our theoretical analysis are somewhat different from the corresponding expressions-in the textbooks of hydraulics and river mechanics.

Exact Solution for Circular Sandwich Plate with Large Deflection

Liu Ren-huai, Shi Yun-fang

1982, 3(1): 11-23.

Abstract(1790) PDF(609)

Abstract:
This paper gives the exact solution of large deflection of circular sandwich plate under the action of uniform lateral load by the method of power series. Making use of this solution, we can judge the accuracy of Liu Ren-huai's⁽⁴⁾ analytic solution obtained by means of the modified iteration method. This indicates that the previous solution has very satisfactory accuracy.

An Application of the Method of Multiple Scales to Magnetohydrodynamic Flow

Jiang Fu-ru

1982, 3(1): 25-32.

Abstract(1590) PDF(509)

Abstract:
In this paper we study the flow of an incompressible conducting fluid along an elliptic duct imposed in an uniform magnetic field. In case Hartmann number of the flow is sufficiently large, the method of multiple scales is adopted for constructing the asymptotic approximation of solution up to any order. Our method can also be applied to study the magnetohydro-dynamic flow along any duct whose cross section has smooth boundary.

Asymptotic Expression of the Solution of General Boundary Value Problem for Higher Order Elliptic Equation with Perturbation Both in Boundary and in Operator

Lin Zong-chi

1982, 3(1): 33-48.

Abstract(1761) PDF(754)

Abstract:
In this paper basing on [1] and [2], we study the singular perturbation of general boundary value problem for higher order elliptic equation with perturbation both in the boundary and in the operator, so as to establish the asymptotic expression involving two parameters. Thus, the iterative process of finding the asymptotic solution is derived and the estimation of the remainder term is given out, we extend and improve the previously published papers.

The Finite Deflection Equations of Anisotropic Laminated Shallow Shells

Wang Zhen-ming, Liu Guo-xi, Lü Ming-shen

1982, 3(1): 49-65.

Abstract(1791) PDF(875)

Abstract:
In this paper, basing on ref. [1] we improved and extended that which is concerned with a view of investigating the finite deflection equations of anisotro-pic laminated shallow shells subjected to static loads, dynamic loads and thermal loads. We have considered the most general bending-stretching couplings and the shear deformations in the thickness direction, and derived the equilibrium equations, boundary conditions and initial conditions. The differential equations expressed in terms of generalized displacements u₀ v₀ φ_x φ_y and w are obtained. From them, we could solve the problems of stress analysis,deformation,stability and vibration. For some commonly encountered cases, we derived the simplified equations and methods.

Seismic Response Analysis for Multi-storeyed Buildings Composed of Nonorthogonal Members under Bi-Directional Horizontal Earthquake Ground Motions

Wei Lian, Dai Gou-ying, Zhu Jing-xin, Jiang Zhi-li

1982, 3(1): 67-82.

Abstract(1691) PDF(558)

Abstract:
This paper presents a method for analyzing both linear and nonlinear seismic responses of multi-storeyed buildings composed of nonorthogonal structural members under the action of bi-directional horizontal earthquake waves. Different kinds of restoring force model are used. An efficient computer programme for the computation of nonlinear seismic response of the structure was worked out. In order to illustrate the application of this method, an example of a ten-storeyed building of such sort is given.

Generalized Reynolds Equation and Variational Inequality in Lubrication Theory

LI Kai-tai, Huang Ai-xiang

1982, 3(1): 83-99.

Abstract(1818) PDF(689)

Abstract:
This paper has derived generalized Reynolds equation in lubrication theory in terms of tensor analysis and S-coordinate system, and has provided corresponding varia-tional inequality. The curved effect of flow of lubricant fluid is considered, and the influence of intrinsic properties of surfaces of axis and axle sleeve on flow are counted.

Calculation of Stresses and Deformations of Bellows by Initial parameter Method of Numerical Integration

Hwang Chien

1982, 3(1): 101-112.

Abstract(1918) PDF(619)

Abstract:
By reducing the boundary value problem in stress analysis of bellows into initial value problem, this paper presents a numerical solution of stress distribution in semi-circular arc type bellows based upon the toroidal shell equation of V. V. Novozelov^[8]. Throughout the computation, S. Gill's method^[10] of extrapolation is used. The stresses and deformations of bellows under axial load and internal pressure are c-alculated, the results of which agree completely with those derived from the general solution of Prof. Chien Wei-zang^[1-4]. The extrapolation formula presented in this paper greatly promotes the accuracy of discrete calculation.The computer program in BASIC language of Wang 2200 VS computer is included in the appendix.

On the Torsional Rigidity for Bars with L-and +-Cross-Section

Chen Yi-zhou, Chen Yi-heng

1982, 3(1): 113-118.

Abstract(1928) PDF(614)

Abstract:
This paper is a continuation of the senior author's previous papers^[1-3]. using the harmonic continuation technique, the torsional rigidity for bars with L- and +-cross-section can be easily found.Numerical results are shown in Tables 1-3 respectively.

A Note on the Expression for the Rotation Tensor in Terms of Euier Angles

Cheng Yuan-sheng

1982, 3(1): 119-123.

Abstract(2011) PDF(497)

Abstract:
It is pointed out in this paper that the derivation of the expression for the rotation tensor in terms of Euler angles by N. E, Kochin^[1] is erroneous. To point out Kochin's deficit on this problem is advantageous for perfecting the concept of the rotation tensor and its method of expression.

A Conservative Integral Independent of the Constitutive Relation

Zhang Pei-yuan

1982, 3(1): 125-130.

Abstract(1774) PDF(391)

Abstract:
The J-integral defined by Rice depends on the constitutive relation of mediums. In the present paper, a conservative integral independent of the constitutive relation of mediums is defined in order to extend Rice's definition of the J-integral which depends on the constitutive relation. Its main properties which are similar to those of the prevailing J-integral are proved. In the case of the elastic mediums, the extensive conservative integral is the same with Rice's J-integral.