应用数学和力学

1982 Vol. 3, No. 6

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On the Equivalence of Non-Conforming Element and Hybrid Stress Element

Theodore Hsueh-huang Pianl

1982, 3(6): 715-719.

Abstract(1956) PDF(814)

Abstract:
This paper is intended to show that the non-conforming element by Wilson^[3] et al. and the hybrid stress element by Pian^[2] are equivalent.

Solitary Waves at the interface of a Two-Layer Fluid

Dai Shi-qiang

1982, 3(6): 721-731.

Abstract(2113) PDF(950)

Abstract:
In this paper, we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigid walls, taking the effect of surface tension into account.First of all, we establish the basic equations suitable for the model considered, and hence derive the ...

The Finite Element Scheme for Ordinary Differential Equation with Small Parameter

Wu Qi-guang

1982, 3(6): 733-736.

Abstract(1923) PDF(553)

Abstract:
In this short paper the author has constructed a speical finite element scheme and investigated the convergence of this scheme.

Recent Advances in the Method of Weighted Residuals on Solid Mechanics in China

Xu Ci-da

1982, 3(6): 737-742.

Abstract(2239) PDF(773)

Abstract:
This paper presents a review of research work in recent years on the method of weighted residuals (MWR) on solid mechanics in the People's Republic of China. MWR, as a kind of mathematical method by which approximate solutions of differential equations may be obtained, is being extensively used in t...

The Analytical Solution of G. I. Taylor’s Theory of Plastic Deformation in impact of Cylindrical Projectiles and its Improvement

Chien Wei-zhang

1982, 3(6): 743-756.

Abstract(2086) PDF(634)

Abstract:
The theory of plastic deformation in the impact of cylindrical projectiles on rigid targets was first introduced by G. I. Taylor(1948)^[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation...

Nonstationary Random Vibration Analysis of Linear Elastic Structures with Finite Element Method

Jin Wen-lu

1982, 3(6): 757-766.

Abstract(1919) PDF(661)

Abstract:
At present, the finite element method is an efficient method for analyzing structural dynamic problems. When the physical quantities such as displacements and stresses are resolved in the spectra and the dynamic matrices are obtained in spectral resolving form, the relative equations cannot be solve...

W. Shockley’s Equation and Its Limitation

Bai Zhe

1982, 3(6): 767-770.

Abstract(3736) PDF(1131)

Abstract:
The problem of P-n junction in Ref.[1] is discussed in this paper. We consider that Tsai Shu-tang's view that W.Shock-ley's equation cannot be applied to all circumstances is correct, but we cannot say, because of this, that W. Shockley's method of treatment and its conclusion for P-n junction are w...

Application of the Method of Split Rigidities to Anisotropic Laminated Shallow Shells

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

1982, 3(6): 771-780.

Abstract(2052) PDF(475)

Abstract:
In this paper, according to the method stated by Hu Hai-chang in [3], on the basis of [1], the method of split rigidities is generalized for the purpose of solving the problems of lateral deflection, stability and lateral vibration for anisotropic laminated shallow shells,and a simple and practical ...

The Relation between Markov Process Theory and Kolmogoroff’s Theory of Turbulence and the Extension of Kolmogoroff’s Laws——I. The Analysis of the Relation between the Two Theories

Yue Zeng-yuan, Zhang Bin

1982, 3(6): 781-789.

Abstract(1957) PDF(646)

Abstract:
The whole paper consists of two parts (Part Ⅰ and Part Ⅱ). In part X/we shall analyze the relation between the two theories of turbulence involving large Reynolds number:the Markov process theory from the La-grangian point of view and Kolmogoroff's theory from the Eulerian point of view. It will be ...

A Note on the Minimum Complementary Energy Theorem

Fu Bao-lian

1982, 3(6): 791-792.

Abstract(1717) PDF(897)

Abstract:
In this paper we propose a very simple and clear method which can prove that the minimum complementary energy theorem is equivalent to the condition of single-valued displacements and displacement boundary condition of the deformable body.

The Application of the Finite Element Method to Solving Biot’s Consolidation Equations

Zheng Jia-dong, Hu Hui-zhi, Xu Hong-jiang, Zhu Ze-min, Yin Zong-ze

1982, 3(6): 793-805.

Abstract(2294) PDF(809)

Abstract:
Biot's theory of consolidation of saturated soil.regards the consolidation process as a coupling problem between stress of elastic body and flow of fluid existing in pofes^[1]. It can more precisely reflect the mechanism of consolidation than Terzhigi's theory^[2]. In this article, we obtain the gener...

An Upper-Bound Solution for the Force of Combined Backward-Forward Extrusion

Wu Shi-chun, Tang Cai-rong, An Jiang-shui, Bin Feng

1982, 3(6): 807-816.

Abstract(1776) PDF(442)

Abstract:
A rigid-triangle velocity field for combined backward-forward extrusion based on the experiments and the slip-line field is proposed in this paper. The flow separation point in the rigid-triangle velocity field is defined in accordance with the slip-line theory. A formula of minimum upper bound solu...

Solution for Free Vibration Problem of the Membrane with Unequal Tension in Two Directions

Qian Guo-zhen

1982, 3(6): 817-824.

Abstract(1956) PDF(769)

Abstract:
In this paper, we obtain the analytic solution of free vibration frequency and mode shapes of rectangle, circle and elliptic membranes. The approximate solution of membrane with arbitrary boundary is also obtained. All of these membranes are acted on by unequal tension in two directions.For the rect...

Decompositions of Bäcklund Transformations for the Korteweg-de Vries Equation

Huang Xun-cheng

1982, 3(6): 825-828.

Abstract(1816) PDF(520)

Abstract:
In this paper, decomposition relations such B_a=S_a^-1B₁S_a, connecting scale transformations and Bäcklund transformations for the Korteweg-de Vries K-dV, modified K-dV, higher-order K-dV and cylindrical equations, are obtained.

Dynamical Stress Function Tensor

Shen Hui-chuan

1982, 3(6): 829-834.

Abstract(1625) PDF(768)

Abstract:
This paper generalizes the concept of stress function tensor in static elasticity into the more general case of continuum dynamics, and finds out the expressions for dynamical stress function tensor.

A Calculation Method of Blood Flow Velocity Distribution in Smaller Blood Vessels

Lin Xie-xian

1982, 3(6): 835-841.

Abstract(1930) PDF(834)

Abstract:
The calculative method presented in this paper is based on an improvement of boundary conditions for a micro-continuum fluid model with blood flow assuming that the blood cell velocity at blood vessel wall is unequal to zero.As for steady state flood flow equation (flow in vitre-a rigid circular tub...