Applied Mathematics and Mechanics (English Edition)

On the Motion of Flying Plate under Explosive Attack

朱兆祥;蒋大和

1980, 1(3): 293-304.

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The one-dimensional problem of the motion of a rigid flying plate under explosive attack has an analytic solution only when the polytropic index of detonation products equals to three. In general, a numerical analysis is required. In this paper, however, by utilizing the "weak" shock behavior of the reflection shock in the explosive products, and applying the small parameter pur-terbation method, an analytic, first-order approximate solution is obtained for the problem of flying plate driven by various high explosives with polytropic indices other than but nearly equal to three. Final velocities of flying plate obtained agree very well with numerical results by computers. Thus an analytic formula with two parameters of high explosive (i.e. detonation velocity and polytropic index) for estimation of the velocity of flying plate is established.

General Solutions of Axial Symmetrical Ring Shells

钱伟长;郑思梁

1980, 1(3): 305-318.

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This paper gives the general solutions of axial symmetrical ring shells for all values of slender-ness ratio. This solution is newly brought out, and can be used to solve various practical nroblems, including corrugated tubes, thermal expansion joints, Borden tubes, etc.

Comparison between Two Different Derivations of the Differential Equations for Free Vibration of the Ideal Fluid Column in a Communication Tube

刘先志

1980, 1(3): 319-332.

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How would the ideal fluid column in a communication tube moves, the present paper presents two different solutions, one of which has been existing in the literature not less than a half century, while the second is recommended by us with this article. We have deduced the differential equation anew and given the main motion features.According to our opinion, the hitherto, for a long time broadly used, derivation is not undis-putable. Noticeably, the results of our new derivation can duely degenerate into Newton, John Bernoulli- and Daniel Bernoulli-period laws of vibration.

Two Problems of the Semi-Conductor Physics Discussed with the Point of View of the Fluid Dynamics

蔡树棠

1980, 1(3): 333-339.

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In this article, we discuss two problems of the semi-conductor physics from the point of view of the fluid dynamics. Firstly, we discuss the problem of the p-n junction, and find that the previous treatment and the previous conclusion of the problem are somewhat erroneous. Secondly, we discuss the coefficient C of the block resistance, and find that the mathematical method of the previous treatment is erroneous.

The General Solution of Bending of a Spherical Thin Shallow Shell with a Circular Hole at the Center under Arbitrary Transverse Loads

许剑云;叶开沅

1980, 1(3): 341-356.

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Basing several suggestions appeared in [1], we find out the general solution of the bending of a spherical thin shallow shell with a circular hole at the center. As we know, very few papers had touched upon these problems.

Dirichlet Problem of Higher Order Elliptic Equation with Perturbation both in Differential Operator and in Boundary

林宗池

1980, 1(3): 357-370.

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This paper is the continuation of article [7]. It gives further results about the asymptotic expression for the solution of higher order elliptic equation in the case of boundary perturbation combined with operator perturbation. When unperturbed problem A0 is not on the spectrum, the asymptotic expression for the solution of perturbation problem A may be expanded with respect to the small parameter While A0 is on the spectrum, the asymptotic expression of the solution contains negative powers of the small parameter e . The approximation of arbitrary order to the solution is considered and the recursive formula for the general term and the estimation of remainder term are given.

Bending of Uniformly Cantilever Rectangular Plates

张福范

1980, 1(3): 371-383.

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An exact solution is given for the bending of uniformly loaded rectangular cantilever plates by using the idea of generalized simply supported edge together with the method of superposition. As illustrative examples, a square plate and a rectangular plate with the ratio of the clamped edge to the neighbouring free edge equal to two are solved numerically. The results are compared with those obtained from approximate methods to confirm the validity of the method presented.

Doubly Curved Shallow Shells with Rectangular Base Elastically Supported by Edge Arched Beams and Tie-rods (I)

卢文达

1980, 1(3): 385-411.

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The equations of equilibrium of shallow shells with rectangular base elastically supported with edge arched beams are obtained through the variational principle together with corresponding boundary conditions and corner conditions. It is assumed that edge arched beams are of narrow plate form, so that only the rigidities in their own planes are taken into consideration, torsional rigidities and bending rigidities out of their own planes are neglected. In this paper, two kinds of corner conditions are discussed. First of these is pinned corner conditions. Second of these is simply supported corner conditions, such that the corner can be moved freely in horizontal directions. The former corresponds to the conditions of those with heavy tension beams, in which the tension rigidities of the rods can be assumed infinite. The latter corresponds to the conditions of elastically supported edge arched beams without tension rods. In the former case, the edge tangential displacement of shallow shells is assumed to be zero everywhere, so that the vertical displacement of the edge arched beams gives the only elastic supported forces. This kind of supporting conditions is a good approximation for practical roof design.In this paper, the solutions of the problem of shallow spherical shell of square base supported elastically by edge arched beams and tie-rods under the conditions, such that the corners are restricted, are solved by the method of double trigonometric series. The edge conditions are integrated along their respective edge, and the conditions at corner are satisfied by proper choices of integral constants. The integrated edge conditions are then used to determine the unknown constants in the double trigonometric series. The result of this paper gives the tension in the tie-rods directly, which is an important quantity in the shell roof design practice.The method of integrated form of boundary conditions used in this paper in general is useful for the treatment of problem of plates and shells elastically supported by edge frames and tie-rods or by other means.This paper also gives the results of numerical calculation based upon the method of double trigonometric series on the problem of shallow spherical shell with square bases elastically supported by arched beams. The corner are pinned supported or simply supported. The calculated results for λ= 11.5936 show that the trigonometric series converges rapidly. The effect of elastic deformation in the arched beams to the components of membrane tensions, moments, and deflections of the shell are given.

The Finite-Element-Force Method for Solving Plane Problems of Elasticity

蒋炜

1980, 1(3): 413-429.

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Using elements in the form of arbitrary sectors, the author has devised a plan for solving plane problems of elasticity by the force method. The method is characterized by a smaller number of nodes, a more convenient computation and a perfect adaptability to the particular shape of the region in question.

The Forced Response of the L amped Dynamic Systems

张文

1980, 1(3): 431-440.

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This paper deals with the forced harmonie responses of the discrete or continuous damped systems to harmonic excitation, where the viscous damping matrix cannot be diagonalized. The explicit expressions of the response solutions are given. Hence, with these expressions, some general and analytical study of some phenomena in vibration is made. For example, the "fixed amplitude point" phenomena in the single damped systems have been demonstrated generally. The conditions, under which all forces that exert on the system and possess common phase, which will excite common phase responses, are also discussed.The solutions deduced here only involve the inverse matrices of lower order. Thus, in the numerical computation for digital computers, the method is more simple, economical, and accurate than others.The method described here can be used in the analysis of unbalance responses of the rotor systems.

On “Finite Element Analysis of Axisymmetric Elastic Body Problems”

Ding Hao-jiang;Chien Wei-zang

1980, 1(3): 441-441.

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