应用数学和力学

1987 Vol. 8, No. 11

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Variational Methods for the Problems of Nonconservative Force Fields in the Micropolar Elastodynamics

Dai Tian-min, Fu Ming-fu, Lin Zhong-xiang, Yang De-pin

1987, 8(11): 943-952.

Abstract(1770) PDF(540)

Abstract:
Based on the properties of the convolution and the convolute commutation,some quasi-variational principles for the problems of nonconservative force field in the micropolar elastodynamics are given and verified in this paper.The theorem given in this paper can be applied to the theories of the nonlocal elastic mediums and the nonlocal micropolar elastic mediums.

The Effect of Local Geometric Imperfections of Rotational Shell on Its Natural Frequencies and Models

Loo Wen-da, Gao Shi-qiao

1987, 8(11): 953-958.

Abstract(1744) PDF(504)

Abstract:
In this paper,an additional stiff ness matrix of meridional geometric imperfections was formed by considering the geometric imperfections as initial displacements based on reference[7].Then,natural frequencies and models of rotational shell with symmetric geometric imperfections were analysed by perturbation method.From the computed example,it was known that the effect of geometric imperfections of frequencies is to increase them,and the larger the range of imperfection,the more the frequencies would be increased.

Photoviscoelasticity-an Experimental Method in Viscoelastic Stress Analysis

Karl-Hans Laermann

1987, 8(11): 959-966.

Abstract(2016) PDF(497)

Abstract:
In this paper,the photoviscoelasticity method of viscoelastic stress analysis has been discussed in detail.lt is shown that,in order to avoid the effects of shrinkage andaging in the test specimens,it is suggested that the specimens should be tempered for three days at a temperature of 60℃ before starting the experiments,and the temperature filtering arrangement is recommended in the experimental setups to keep the temperature absolutely constant.Besides the axi-symmetrical time-dependent stress state,the determination of the principle axes of the refraction tensor experimentally remains an unsufficiently solved problem.To avoid dynamic effect in the step wise loading,the time of measurement in every step should be limited in about one secend.

On Singularly Perturbed Quasilinear Systems

Liu Guang-xu

1987, 8(11): 967-976.

Abstract(1854) PDF(538)

Abstract:
In this paper,the objective is to give sufficient conditions for the existence of solution of the nonlinear two-point boundary value problem(1.1).And we employ these-results to consider the boundary layer phenomena of the quasilinear weakly coupled singularly perturbed system(DP)_q.

Instability of Hagen-Poiseuille Flow for Axisymmetric Mode

Wang F. M., J. T. Stuart(F. R. S.)

1987, 8(11): 977-984.

Abstract(2171) PDF(409)

Abstract:
An investigation is described for instability problem of flow through a pipe of circular cross section.As a disturbance motion,we consider an axisymmetric nonlinear mode.An associated amplitude or modulation equation has been derived for this perturbation.This equation belongs to the diffusion type.The coefficient of it can be negative with Reynolds number increasing,because of the complex interaction between molecular diffusion and convection.The negative diffusion,when it occurs,causes a concentration and focusing of energy within the decaying slug,acting as a role of reversing natural decays.

Bifurcation and Stability of Spatially Periodic Solutions of Nonlinear Evolution Equations with Integral Operators

Lu Qi-shao

1987, 8(11): 985-995.

Abstract(1841) PDF(453)

Abstract:
A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially periodic static bifurcating solutions and their stability.At first,the necessary condition and the sufficient condition for the existence of bifurcation are studied respectively.The stability of the equilibrium solutions is analyzed by the method of semigroups of linear operators.We also obtain the principle of exchange of stability in this case.As an example of application,a concrete result for a special case with integral operators of exponential type is presented.

On Exact Solution of Karman’s Equations of Rigid Clamped Circular Plate and Shallow Spherical Shell under a Concentrated Load

Zheng Xiao-jing, Zhou You-he

1987, 8(11): 997-1006.

Abstract(2147) PDF(491)

Abstract:
It is extremely difficult to obtain an exact solution of von Karmán's equations because the equations are nonlinear and coupled.So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet.In this paper,first of all,we reduce the von Kármán's equations to equivalent integral equations which are nonlinear,coupled and singular.Secondly the sequences of continuous function with general form are constructed using iterative technique.Based on the sequences to be uniformly convergent,we obtain analytical formula of exact solutions to von Karman's equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.

On Perfectly Stress Field at a Mixed-Mode Crack Tip under Plane and Anti-Plane Strain

Yuan Yi-wu

1987, 8(11): 1007-1014.

Abstract(1711) PDF(593)

Abstract:
In[1],under the condition that all the perfectly plastic stress components at a crack tip are functions of θ only,making use of equilibrium equations,stress-strain rate relations,compatibility equations and yield condition,Lin derived the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain.But in[1] there were several restrictions on the proportionality factor λ in the stress-strain rate relations,such as supposing that λ is independent of θ and supposing that λ=cor cr^-1.In this paper,we abolish these restrictions.The cases in[1],λ=crⁿ(n=0 or-1) are the special cases of this paper.

Bending of a Circular Cylinder Containing a Crack

Yin Chang-yan, Zu Cheng-de

1987, 8(11): 1015-1026.

Abstract(2142) PDF(483)

Abstract:
The study of bending of cracked circular cylinders is of more significance.The bending of cylinders containing radical crack or cracks was discussed by refs.[1]-[4] and that of concentrically craked circular cylinders was studied by[5].Continuing[6] and using complex variable methods in elasticity,this paper deals with the bending problems of a circular cylinder,containing an internal linear crack at any position under an acting force perpendicular to the crack.The general forms of displacements,stresses,and stress-intensity factors,expressed in terms of series,are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed.Finally,the twist angle per unit length and the center of bending for the radically cracked circular cylinder,one of whose crack-tips is located at the origin,have been computed and the results are almost the same as that calculated in[1].

The Unsymmetrical Bending of Contilever Rectangular Plates

Cheng Xiang-sheng

1987, 8(11): 1027-1033.

Abstract(2028) PDF(445)

Abstract:
This paper discusses the problems of the unsymmetrical bending of cantilever rectangular plates under various loads by the energy method.We illustrate numerous calculating examples such as the plates which are subjected by the concentrated forces or concentrated couples unsymmetrically on free sides and corner points and by a uniformly or nonuniformly distributed loads unsymmetrically on free edges and so forth.

A Discussion on “Representing General Solution of Equations in Theory of Elasticity by Harmonic Functions”

Zhou Qing, Wang Min-zhong

1987, 8(11): 1035-1038.

Abstract(2016) PDF(421)

Abstract: