应用数学和力学

1989 Vol. 10, No. 2

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On the Objective Stress Rate in Co-Moving Coordinate System

Shang Yong, Chen Zhi-da

1989, 10(2): 95-104.

Abstract(1864) PDF(678)

Abstract:
The objective stress rate is a rather important problem in mechanics of finite deformation. In this paper, the objective stress rate in co-moving coordinate is derived by applying nonlinear geometric field theory of deformation. Problems, such ax targe extension coupled with rotation, and large shear deformation, are exemplified by using the new formula. Comparing with Jaumann's stress rate and other formulae presented in current literature, the new result appears to be the reasonable one in co-moving coordinate system.

Nonlinear Buckling Analysis of Hyperbolic Cooling Tower Shell with Ring Stiffeners

Li Long-yuan, Lu Wen-da

1989, 10(2): 105-110.

Abstract(1961) PDF(540)

Abstract:
This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are-length method is suggested. Finally, some conclusions having important significance for practice engineering are given.

Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle

Zhang Shi-sheng, Luo Qun

1989, 10(2): 111-113.

Abstract(2407) PDF(611)

Abstract:
This paper proposes a formally stronger set-valued Caristi's fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland's variational principle and thin set-valued Caristi's fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].

On the Stability of Distorted Laminar Flow(Ⅰ)——Basic Ideas and Theory

Zhou Zhe-wei

1989, 10(2): 115-129.

Abstract(2148) PDF(590)

Abstract:
This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability.

Bäcklund Transformations for the Equation ∂²u/∂x¹∂x¹+∂²u/∂x²∂x²=f(u)

Li Yan-guang

1989, 10(2): 131-135.

Abstract(2210) PDF(412)

Abstract:
Bäcklund transformations for the equation ∂²u/∂x¹∂x¹+∂²u/∂x²∂x²=f(u) is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d²f/du²=λf is sufficient for the existence of Bäcklund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt^[1,2].

The Application of Compatible Stress Iterative Method in Dynamic Finite Element Analysis of High Velocity Impact

Song Shun-cheng

1989, 10(2): 137-143.

Abstract(1774) PDF(467)

Abstract:
There is a common difficulty in elastic-plastic impact codes such as EPIC^[2,3] NONSAP^[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.

A Numerical Model of Left Ventricle and Aortic Valve Function of Its Afterload(I)

Liu Zhao-rong, Yin Yong-yi

1989, 10(2): 145-154.

Abstract(1660) PDF(408)

Abstract:
Due to the study of the function of heart and aoritic valve, we set up a physical model of left ventricle, aortic valve and afterload and derive theoretical equation of each part from the model. Then we calculate the basic equations within phystology and impair parameters. Based on this, we will discuss fully in the next paper the effect of left ventricular afterload on valve opening, ejection and valve function,etc.

Conditions for Incipient Cavitation Formation

Huang Jing-quan

1989, 10(2): 155-159.

Abstract(2113) PDF(596)

Abstract:
The growth, equilibrium and stabilization of free gas nucleus are analyzed. It is shown that the cavitation results from growth of free gas nucleus to critical radius and conditions of cavitation have been derived.

Research on the Complicated Dynamical Behaviors of Nonlinear Ecosystems(Ⅱ)

Zan Ting-quan

1989, 10(2): 161-166.

Abstract(1478) PDF(467)

Abstract:
This paper is a further study of reference [1]. In this paper, we mainly discuss the complicated dynamical behaviors resulting from a simple one-dimensional model of nonlinear ecosystems: fixed point motion, periodic motion and chaotic motion etc., and briefly discuss the universality of the complicated dynamical behaviors, which can be described by the first and the second M. Feigenbaun constants. At last, we discuss the "one-side lowering phenomenon" due to near unstabilization when the nonlinear ecosystem approaches bifurcation points from unbifurcation side. It is of important theoretical and practical meanings both in the development and utilization of ecological resources ar.d in the design and management of artifilial ecosystems.

The Dynamic Computation of Closed Cylindrical Shell under impact Load

Cheng Xiang-sheng

1989, 10(2): 167-172.

Abstract(1583) PDF(490)

Abstract:
This article discusses the dynamic computation of the closed cylindrical shell under impact load. In the text we analyse the changes of the momenta and the energy on each stage in the impact process, take into account the effect of the mass of impact object and the system of the closed cylindrical shell by impact, and transform the distributed mass of the whole cylindrical shell into an only concentrated "equivalent mass" by the method of reduced mass. Consequently we derive the dynamic factor of the closed cylindrical shell due to impact load.The method proposed in this paper is of practical worth and is more convenient in calculations.

Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces

Li Bing-you

1989, 10(2): 173-178.

Abstract(1746) PDF(502)

Abstract:
Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:
d(Tx,Ty)≤ad(x,y)+b{d(x,Tx)+d(y,Ty)}+c{d(x,Ty)+d(y,Tx)},∀x,y∈K
for all x,y in K,where 0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1, then T has a unique fixed point in K.

Using Generalized Variational Principles to Resolve the St. Venant’s Torsional Bar with a Crack

Fan Xiu-chang

1989, 10(2): 179-186.

Abstract(1652) PDF(524)

Abstract:
According to generalized variational principles suitable for linear elastic incompatible displacement elements given by Professor Chien Wei-zang, using crack tip singular element and isoparametric surrounding element given by the author of this paper, we will study the St. Venant's torsional bar with a radial vertical crack and compare the present computed results with the results of reference [2], The present computed results show that, using the method provided in this paper, satisfactory convergent solution can be obtained under lower degree of freedom.