应用数学和力学

1981 Vol. 2, No. 2

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A Physical Model of the Structure and Attenuation of Shock Waves in Metals

Duan Zhou-ping

1981, 2(2): 145-165.

Abstract(1854) PDF(616)

Abstract:
In this paper, a physical model of the structure and attenuation of shock waves in metals is presented. In order to establish the constitutive equations of materials under high velocity deformation and to study the structure of transition zone of shock wave, two independent approaches are involved. Firstly, the specific internal energy is decomposed into the elastic compression energy and elastic deformation energy, and the later is represented by an expansion to third-order terms in elastic strain and entropy, including the coupling effect of heat and mechanical energy. Secondly, a plastic relaxation function describing the behaviour of plastic flow under high temperature and high pressure is suggested from the viewpoint of dislocation dynamics. In addition, a group of ordinary differential equations has been built to determine the thermo-mechanical state variables in the transition zone of a steady shock wave and the thickness of the high pressure shock wave, and an analytical solution of the equations can be found provided that the entropy change across the shock is assumed to be negligible and Hugo-niot compression modulus is used instead of the isentropic compression modulus. A quite approximate method for solving the attenuation of shock wave front has been proposed for the flat-plate symmetric impact problem.

On a Theory of Micropolar Protoelastic Material Bodies and Constitutive Equations for Nonlocal Micropolar Elastic Continua

Tai Tien-min

1981, 2(2): 167-172.

Abstract(1853) PDF(476)

Abstract:
In this paper the definition of micropolar protoelastic material bodies is given and with the help of the principle of virtual power, the variational principle of those bodies is derived. In terms of that same idea and the definition of micropolar protopotential presented here, the constitutive equations for nonlocal micropolar elastic continue are naturally derived.

Nonlinear Bending of Circular Sandwich Plates

Liu Ren-huai

1981, 2(2): 173-190.

Abstract(1931) PDF(1064)

Abstract:
In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to slip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.All results are presented in figures which are ready for direct application.

Application of Chien’s Theorem to the Establishing of General Variational Principle in Polar Elasticity of Finite Deformation

Chen Zhi-da

1981, 2(2): 191-196.

Abstract(2038) PDF(732)

Abstract:
Variational principles of minimum potential energy and complementary energy of linear polar elasticity has been formulated by No,packi[3].As it has been proved by Chien Wei-zang, that the tveo generalized variational principles are equivalent in functionals; we now apply this important statement Chien's theorem, and Lagrange's method of multiphers to the establishing of generalized variational principle in polar elasticity for finite deformation. The fundamental equations of mechanics of finite deformation used are of which has been established in the author's paper[7],[4].

Heat Conduction Problem for Tightly Compressed Adjacent Layers of Plane Plates with Gradually Varying Heat Conduction Coefficients

Liu Hsien-chih

1981, 2(2): 197-205.

Abstract(1779) PDF(632)

Abstract:
According to the conventional usage, in dealing mth the heat conduction problem for composite blocks with many tightly compressed plate layers of different heat conduction coefficients, we solve them laye, by layer but submetang to the intermediatc heat trans for reqmrement: As well-knmwn, this method is rather a tedious and annoying manipvlatron In the present paper,we have considered such heat conducts in coefficients instead of varying abruptly but gradually from layer to layer in order to make it possible to treat such problem as a whole even though in some cases it is inevitable to yield only approx:mate results This defect may be offsetted by the time saving gain, since the heat condor tion problem is anyhow m most cases unable to obta}r, very satisfactocy accuracy

The Network Node Relabeling Optimum Algorithms for Large Finite Element Program System

Hua Bo-hao

1981, 2(2): 207-218.

Abstract(1769) PDF(654)

Abstract:
This paper describes the optimization algorithms of network node relabeling relating to large finite elements program system mainly during the period from 1968 to 1976. Some computation techniques of the application of these algorithms are discussed and a more efficient executive program of RCM algorithm is given for application.

An Analysis and Calculation of Unsteady Flow through Exhaust System of Diesel Engines

Liu Zhao-rong, Chen Jin-e

1981, 2(2): 219-234.

Abstract(1597) PDF(537)

Abstract:
In this paper we make analysis and calculation for unsteady non-homoentropic flow through earhaust system of diesel engines by means of the characteristic method. With reference to certain rational reduction and treatment introduced into calculation, particularly for boundary conditions,the program of calculation is to have general applicability,while the convergence is quite fast.Finally, we take exhaust system of 6135 tvbocharged engines as an illustrative example, its numerical results are quite good.

Dynamic Response of Viscoelastic Beam

Sun Jia-ju, Jing Ke-hwa

1981, 2(2): 235-242.

Abstract(1608) PDF(696)

Abstract:
The ynamic analysis of the viscoelastic simple supported beam has been made in accordance with the relationship between stress and strain expressed by the simplest Voigt mechanical model, from which several analytic expressions have been obtained.It is shown that the reduction of the ratio of. natural frequencies progresses with the increase of the exciting frequency for high modes [Tab.1]. In the final part of this paper, the forced vibration of simple supported beam subjected to a random and harmonic excitation has also been dealt with, and the representations of the beam deflection have been derived.

On the Completeness of Hu Hai-chang’s Solution

Wang Min-zhong

1981, 2(2): 243-250.

Abstract(1668) PDF(567)

Abstract:
In this paper, the completeness of Hu Hai-chang's solution is proved in the case of convex regions in z-direction under a supplementary condition. On the other hand, for those non-convex regions in z-direction, Hu Hai-chang's solution is proved to be incomplete.

1981, 2(2): 251-253.

Abstract(1613) PDF(594)

Abstract: