应用数学和力学

1980 Vol. 1, No. 3

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On the Motion of Flying Plate under Explosive Attack

Chu Chao-hsiang, Jiang Da-ho

1980, 1(3): 275-285.

Abstract(1737) PDF(716)

Abstract:
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

Chien Wei-zang, Zheng Si-liang

1980, 1(3): 287-300.

Abstract(1912) PDF(633)

Abstract:
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.

A Comparison of Two Methods for Deriving the Differential Equation of Oscillation of an Ideal Liquid in Communica-tion Tube with Different End Cross Sections

Liu Hsien-chih

1980, 1(3): 301-310.

Abstract(1769) PDF(426)

Abstract:
Possibly not shorter than a half century, there has been ezisting a method for deriving the differential equation for the oscillation of an ideal liquid in communication tube with different end cross sections in the scientific literature, which,according to our opinion, is somewhat defective. With this paper we present another derivation in aiming to make possibly a convincing comparison. Our method leads to results from which the three different laws for vibration period setting up in the antiquity by Isaac Newton, Johann Bernoulli and Danielis Bernoulli can be degenerated outcomes.

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

Tsai Shu-tang

1980, 1(3): 311-318.

Abstract(1908) PDF(549)

Abstract:
In this article,we discuss the two problems of the semi-conductor physics with the point of View of the fluid dynamic. We get the conclusion that the methods of the usual treatment of these problems are mistaken.

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

Hsu Chin-yun, Yeh Kai-yuan

1980, 1(3): 319-334.

Abstract(1674) PDF(492)

Abstract:
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.

ЗАДАЧА ДИРИХЕ ЗЛЛИПТИЧЕСКОГО УРВНЕНИЯ ВЫСШЕГО ПОРЯДКА ДПЯ ДВОИХ ВОЗМУЩЕНИЙ ДИФФЕРЕНЛЬНОГО ОЛЕРАТОРА И ГРАНИЦЫ

Пинъ дзуя чи

1980, 1(3): 335-348.

Abstract(2021) PDF(467)

Abstract:

Bending of Uniformly Loaded Cantilever Rectangular Plates

Chang Fo-van

1980, 1(3): 349-362.

Abstract(2041) PDF(830)

Abstract:
In the theory of thin plates,the bending of cantilever rectangular plates has long remained one of the most difficult problems in this field of study. As a consequence the solution now available are all limited to the approximate ones.

Doubly Curved Shallow Shells with the Rectangular Bases Elastically Supported by Edge Arch Beams and Tie-Rods(Ⅰ)

Loo Wen-da

1980, 1(3): 363-390.

Abstract(1720) PDF(514)

Abstract:
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.

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

Jiang Wei

1980, 1(3): 391-406.

Abstract(1552) PDF(460)

Abstract:
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 Damping Dynamic Systems

Chang Wen

1980, 1(3): 407-416.

Abstract(1793) PDF(594)

Abstract:
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”

1980, 1(3): 417-417.

Abstract(1655) PDF(468)

Abstract:
Regarding the calculation of the rigidity matrix of the linear triangular elements, there is really the eristence of the nonconvergent terms.