应用数学和力学

1985 Vol. 6, No. 5

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The TSHB Technique for Material Testing at High Rates of Strain

Yang Gui-tong, Song Yu-zhao

1985, 6(5): 383-388.

Abstract(1711) PDF(484)

Abstract:
The material testing technique of Torsional Split Hopkinson Bar(TSHB) is investigated in this paper. It can solve nearly all the problems of Split Hopkinson Pressure Bar(SHPB). Furthermore, accurate experimental results can be obtained in large deformation condition. In this paper some dynamic stress-strain curves of some engineering materials are also given which are obtained from a TSHB apparatus made by ourselves.

Uniformly Convergent Difference Schemes for Singular Perturbation Problem

Wu Chi-kuang

1985, 6(5): 389-394.

Abstract(1546) PDF(504)

Abstract:
In this paper, a class of uniformly convergent difference schemes for singular perturbation problem are given.

Asymptotic Analysis of Strongly Nonlinear Oscillators

Dai Shi-qiang

1985, 6(5): 395-400.

Abstract(1632) PDF(667)

Abstract:
In this paper, an asymptotie method is presented for the analysis of a class of observed nonlincar autonomous oscillators. The equations governing the amplitude and phase faeter are obtained, and the amplitude and stabilitv of the corresponding limit cycles are determined.

New Solutions of Novozhilov’s Equation of Toroidal Shells

Dong Ming-de

1985, 6(5): 401-413.

Abstract(1799) PDF(475)

Abstract:
New solutions are obtained for Novozhilov's equation of toreidal shells having general slenderness ratio 0<a<1(a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.

Perfectly Plastic Stress Field at a Stationary Crack Tip

Lin Bai-song

1985, 6(5): 415-421.

Abstract(1757) PDF(536)

Abstract:
Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.

The Numerical Solution for Problems of Turning Point Without Resonance

Lin Peng-cheng, Yan Peng-xiang

1985, 6(5): 423-430.

Abstract(1966) PDF(558)

Abstract:
In this paper the uniform convergence of IL'in scheme to the turning point problems without resonance is provedby means of Kellogg's method The given estimation is shown to be optimal.

On the Structure of Solutions of Linear Partial Differential Equation i+j≤n a_ijpⁱq^jφ=0 With Two Independent Variables and Constant Coefficients

Gai Bing-zheng

1985, 6(5): 431-445.

Abstract(1765) PDF(488)

Abstract:
This paper is a continuation of [1]. In this paper, the solutions of the more general linear partial differential equation form with two independent variables and constant coefficients are discussed in detail. The general solution which can be used in the approximation to the conditions of the definite solution of the practical problems is presented. To illustrate the use of the results obtained in this paper, some practical examples in mechanics are given.

First Integral and Stability of Motion in the Critical Cases

Xu Ye-yi

1985, 6(5): 447-454.

Abstract(1588) PDF(562)

Abstract:
In this paper,we indicate that after the Liapunov function by using linear combination of mechanical first integral was suggested by Chetayev in 1946. He and his students solved stability of conservative system by means of this method. But he had trouble to solve the problems by means of cut and try. Moreover, the condition of stability is imperfect. Solution by this method is limitedfor problems of purely imaginary roots. The cases of zero roots have not been considered. Condition of stability secured is more strict.This paper suggests that the differential equation can be transformed into standard form by method of cancellation of cyclic coordinates(method of lowering degree of order), and condition of stability can be determined by energy integral. By this method not only the computation is clear and concise. But also zero roots can be considered. Therefore the problems of two cyclic coordinates can be transformed into second-order system, and we get new conclusion of the condition of stability simply. As for problems of single cyclic coordinate, in fact, Chetayev and his students did not solve the stability of the gyroscope of outer-gimbal with horizontal axis or arbitrary angle. In this paper, it shows that the method suggested here is useful for stability of these problems. The condition of conditional stability and instability were derived.

Composition of Composites

Liu Chang-tai

1985, 6(5): 455-463.

Abstract(1459) PDF(477)

Abstract:
For a special material needed is engineering, if it can be predicted on the basis of a certain theory and producing it to use the theory is successful, this is hoped to the of the engineering,For the aim,the author wants to investigate a proper theory and select a few materials to make a composite which is consistent with an object material given beforehand. In this paper, the theory is given in the preceding three parts,and the results are given in the fourth part. Theoretical calculations were made for the composites of the two object materials given in engineering. Composites are made according to the results of the calculations.The experiment is made yet to the composites. The results of them are satisfied.

Analysis of Two-Dimensional Cavity Flow by Finite Elements

Lin Bin-yao, Xu Xie-qing

1985, 6(5): 465-474.

Abstract(1846) PDF(552)

Abstract:
The variational principle in terms of stream function ψ for free surface gravity flow is discussed by the formulation of first-order variation in a variable domain. Because of different transversal conditions adopted, there are four forms of variational principle in terms of ψ.An air-gilled cavity flow with given discharge and total energy is then analysed by finite element method. At the end of the cavity, the free stream line is tangent to a short fictitious plate of given length, which joins the fixed boundary at on angle to be determined. The condition that the free stream line should be tangent to the fixed boundary at the point of separation makes the solution unique.Finally curves giving the cavity length as a function of the Fraude number, cavity pressure and channel bottom slope are presented.

The Weak Damped Oscillation in a Random Medium

Yang Xiao-xian, Chen Qun-biao, Xi Hong-sheng

1985, 6(5): 475-479.

Abstract(1918) PDF(614)

Abstract:
The paper gives a solution of the random differential equation with random coefficient, that is (t)+K²(t)x(t)=-ef(,t),where K(t) is a random process and e is a damp coefficient, it is a little parameter.

1985, 6(5): 480-480.

Abstract(1709) PDF(354)

Abstract: