应用数学和力学

1984 Vol. 5, No. 4

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Time-Independent Anisotropic Plastic Behavior by Mechanical Subelement Models

Theodore H. H. Pian

1984, 5(4): 461-470.

Abstract(1623) PDF(483)

Abstract:
The paper describes a procedure for modelling the aniso-tropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the viscoplasticity theory.

Wave and Earthquake Effects on Axisymmetric Offshore Structures

Professor Michael Isaacson, Wu Song-ren

1984, 5(4): 471-480.

Abstract(1727) PDF(532)

Abstract:
Vertical axisymmetric structures have found a variety of applications in offshore engineering, including oil storage tanks, production platforms and so on. The present paper describes an efficient calculation procedure for determining the interaction of such structures with the surrounding ocean. In particular, numerical calculations are explicated for:-wave forces and runup for a fixed structure,-added-mass and damping coefficients for an oscillating structure,-earthquake loading in terms of base shear and overturning moment,-motions of a floating structure.The approach used is based on a boundary element method involving an axisymmetric Green's function, and exploits the structure's ax.i symmetry to provide a highly efficient computational procedure suitable for carrying out on a desk-top computer. Results are presented for surface-piercing conical structures under various loading conditions.

Some Applications of the Singular Perturbation Method to the Bending Problems of Thin Plates and Shells

Chou Huan-wen

1984, 5(4): 481-488.

Abstract(1532) PDF(663)

Abstract:
This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.

Load Supporting Prefabricated Wall Reinforced by a Frame

Chang Fo-van, Yan Kun-fu

1984, 5(4): 489-498.

Abstract(1679) PDF(520)

Abstract:
This load supporting prefabricated wall consists of a thin plate reinforced along its boundaries by a frame. With the loads acting on the frame, the plate has its boundary conditions defined neither by forces nor by displacements. On the basis of satisfying the biharmonic equation of the stress function for the plate, we make the total strain energy to be minimum to ensure the compatibility of displacements for the two elastic bodies. Thus we get a set of infinite simultaneous equations. The results obtained indicate the method of solution is effective.

The Generalized Boussinesq Equations and Obliquely Interacting Solitary Waves in a Stratified Fluid

Dai Shi-qiang

1984, 5(4): 499-509.

Abstract(1659) PDF(771)

Abstract:
In this paper, on the basis of Boussinesq's shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.

On the Heat Conduction Problems and a Design Principle for Plasma Arc Furnace

Rong Sheng

1984, 5(4): 511-517.

Abstract(1753) PDF(627)

Abstract:
In this paper a plane heat conduction problem with variable coefficients of heat conductivity K(T) is analysed with given electric power supplied to the plasma arc. The governing equation for unknown temperature distribution is a nonlinear one with a δ function as its nonhomogeneous term. To make the problem attractable by the method of separation of variables, a set of transformation of governing equation is introduced. An explicit simple formula is found for the efficiency of the furnace η, η depends linearly on r₀, the nondimensional distance between the arc and surface of melted material, as well as on another nondimensional quantity Q, we describe the above in detail in this paper. This relationship holds for r₀<0.4 and gives a good guidance for the design of furnace.

Pulsatile Flow in Arteries with External Restraint of Visco-Elastic Tissue

Liu Zhao-rong

1984, 5(4): 519-526.

Abstract(1891) PDF(429)

Abstract:
The presence of a longitudinal constraint must be conceived physiologically as due largely to the connective tissue attachments on the outside of the artery. Living tissues are yisco-elastic bodies. In order to analyse the effect of external visco-elastic tissue to pulsatile flow in arteries, in this paper the external connective tissue of artery will be considered as a Voigt visco-elastic body, and the expressions of pulse wave velocity and the velocity of pulsatile flow will be found by the velocity of pulsatile flow will be found by the blood motion equations (Navier-Stokes equation) as well as wall motion equations (Lamb equation). The results of free elastic tube^[4] and those of external elastic restraint^[6] by Womersley can be considered as a particular case and can be covered in this paper.

On Singular Perturbation Method of Perturbed Bifurcation Problems

Chu Zheng-you, Cheng Chang-jun

1984, 5(4): 527-534.

Abstract(1816) PDF(425)

Abstract:
In this paper, the general mathematical principle is over-all explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, λ=0,δ=0, by means of singular perturbation method. Simultaneously, Newton's polygon^[4] is generalized. Finally, the calculating results of two examples are given.

Hopf Bifurcation Phenomenon in Catalytic Reaction

Liu Zheng-rong, Lin Chang

1984, 5(4): 535-540.

Abstract(1749) PDF(469)

Abstract:
In this paper, we intend to discuss Hopf bifurcation phenomenon under the effect of the periddic small perturbation on local temperature fluctuations (flikeringiy) phenomenon of catalytic reaction. With the obtained results, we expect to provide basis for selecting reaction parameters.

The Fission of Spectrum Line of Monochoromatic Elastic Wave

Shen Hui-chuan

1984, 5(4): 541-551.

Abstract(1724) PDF(666)

Abstract:
On the basis of the anology with quantum electrodynamics, Dirac equation of elastic wave-phonon is developed and the fission of spectrum line of monochoromatic elastic wave under the action of an external field is studied in this paper.

Solution of Non-Linear Heat Conduction Equation and image Method

Zhang Guan-ren

1984, 5(4): 553-559.

Abstract(1774) PDF(475)

Abstract:
In this paper, the author proves that, for a nonlinear heat conduction equation, there is no discontinuous solution. Some methods of solution for a nonlinear conduction equation are depicted. For a plane interface, the reflection and transmission of a heat wave are given by the method of images. The 1st order of approximation of this method is proved. Lastly, the prevention of superheated electrons is laser implosion of deuterium tritium gas spnere with a shell made of high Z material is interpreted.

Fixed Point Theorems of Random Set-Valued Mappings and Their Applications

Ding Xie-ping

1984, 5(4): 561-575.

Abstract(1782) PDF(721)

Abstract:
In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4-7, 9, 11-17].

On the General Equations of Axisymmetric Problems of Ideal Plasticity

Shen Hui-shen

1984, 5(4): 577-582.

Abstract(1644) PDF(584)

Abstract:
In this paper, introducing a velocity potential, we reduce the fundamental equations of axisymmetric problems of ideal plasticity to two nonlinear partical differential equations. Front these equations we discuss compatibility of Harr-Kármán hypothesis with von Mises yield criterion and the associated flow law.

The Strain Energy Criterion of Mixed-Mode Brittle Fracture

Lin Bai-song

1984, 5(4): 583-588.

Abstract(1760) PDF(538)

Abstract:
In this paper, we proposed a new cr tenon or mixea-moae brittle fracture, i.e., the strain energy criterion, which can be stated as (K_Ⅰ/K_Ⅰc)² +(K_Ⅱ/K_Ⅱc)²+(K_Ⅲ/K_Ⅲc)²=1. This criterion is shown to be in good agreement with known experimental data.In this paper, an experimental criterion:(K_Ⅰ/K_Ⅰc)^m+(K_Ⅱ/K_Ⅱc)ⁿ=1, 1≤≤2.is also proposed.

On the Finite Displacement Problem of a Hollow Cylinder under Internal and External Pressures

Huang Ze-yan

1984, 5(4): 589-602.

Abstract(1662) PDF(747)

Abstract:
Using the method of successive approximations we find of this boundary-value problem the first-and second-order solutions. And then we obtain the formulae in the second approximation for the displacement, strain, and stress fields. Also, our results show that after deformation (i) a cross-section of the cylinder must be displaced into a plane section perpendicular to the central axis of the cylinder; and (ii) neither the sum of the strain components E_RR⁽²⁾ and E_φφ⁽²⁾ nor the sum of the stress components ∑_RR⁽²⁾ and ∑_φφ⁽²⁾ maintains contant throughout the cylinder. The latter effect, which is absent from classical elasticity, bears responsibility for the presence of the ∑_zz⁽²⁾ Moreover, there exhibits a linear relation between ∑_zz⁽²⁾ and (∑_RR⁽²⁾+∑_φφ⁽²⁾), with the proportionality coefficients depending only on the material of the cylinder.