应用数学和力学

Stress Analysis of Hyperbolic Shells of Revolution with Non Axisymmetrical Geometric Imperfections

Tong Guang-shan, Kye J. Han

1986, 7(10): 867-876.

Abstract(1986) PDF(595)

Abstract:
In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed; the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability.A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under dead load and wind load conditions by the equivalent load method. A direct analysis of the imperfect shell is also made by a specialized finite element program. Through numerical studies, the accuracy qnd applicability of the equivalent load method are examined.

Analysis of Adhesive Lap Joint

Zhang Fu-fan

1986, 7(10): 877-885.

Abstract(1927) PDF(570)

Abstract:
This paper is to solve the interlaminar stresses of adhesive lap joint by the energy method without considering the adhesive layer. The joint is made of two identical narrow plates. Two cases are discussed: one is for the isotropic material and the other is for orthotropic material. Because of the different materials forming the joint, the length of distribution and the magnitude of the interlaminar stresses for the two cases will be very different.

Bending Problem of Rectangular Plates of UnidirectionalNonhomogeneity and Variable Thickness with Two Opposite Edges Simply Supported underArbitrary Distributed Loads

Yeh Kai-yuan, Wang Ying-bang

1986, 7(10): 887-895.

Abstract(1790) PDF(552)

Abstract:
Using the step reduction method^[1,2] suggested by the first author of this paper, we investigate the problem indicated in the title and obtain the stepped approximate solutions. As an example, the case of a square plate of linearly varying thickness with four edges simply supported under linearly distributed loads is calculated. The obtained results agree well with those given in [3] and thus the exactness of the new method is verified.

Study of the Closing Mechanism of Natural Heart Valves

Lei Ming, Kang Zhen-huang

1986, 7(10): 897-905.

Abstract(1810) PDF(671)

Abstract:
At present, then are still some controversial considerations on the closing mechanism of natural heart valves. In this area, a lot of phenomena still remain mysterious, particularly for the mechanism of earlier partial closure of the valve while the blood ejection is still in its acceleration phase. It is the purpose of this study to focus on the problem of earlier closure mechanism of heart valves hy using both theoretical analysis and experimental verifications. A certain two-dimensional mathematical model of closure with all contributing factors and the whole operating process being considered is in vestigated with a new analytical method. Several new conclusions were found. The main points are as follows:1. During the opening phase. the main factor of motion of the valve is the accelerating flow, and the decelerating flow plays a main role during most the of time of the deceleration phase. But during the quasi-steady phase of blood ejection, it is the vortex in the sinus that controls the valve closure.2. For the earlier partial closure of the valve during the acceleration phase, the vortex is a decisive factor, hut its function is limited. It is found in the same time that without the vortex, the valve can still close in a similar manner, but there will be no earlier closure during the acceleration phase which characterizes the situation of being with vortex.3. It is ascertained that the existence of the sinus is essential to the effective closure of the valve.In addition, the effects of the valve length, frequency and peak flow rate of the motion of the valve are studied in this paper. Such studies are useful for the design of artificial heart valves.

Existence and Uniqueness of Global Strong Solutions of Two Models in Atmospheric Dynamics

Mu Mu

1986, 7(10): 907-912.

Abstract(1601) PDF(475)

Abstract:
In this paper, the author proves by the methods of energy estimates the existence and uniqueness of global strong solutions of barotropic nondivergent model and baroclinic quasi-geostrophic quasi-nondivergent model.The two models are fundamental ones in atmospheric dynamics. The results here generalize the outcome given by the author in [3]-[5] and verify a conjecture posed by Zeng Qing-cun in [1].

Toupin-Berdichevskii Theorem Can’t Be Considered as a Mathematical Expression of Saint-Venant’s Principle

Zhao Jian-zhong

1986, 7(10): 913-916.

Abstract(2091) PDF(1073)

Abstract:
In this paper the condition and the conclusion of Toupin-Berdichevskii Theorem is examined, where by it is explained and demonstrated with an example that the theorem can't be considered as a mathematical expression of Saint-Venant's Principle in Elasticity.

Further Research on the Bending of the Cantilever Rectangular Plates under a Concentrated Load

Zhu Yan-bin, Fu Bao-lian

1986, 7(10): 917-928.

Abstract(1978) PDF(597)

Abstract:
In this paper we apply the reciprocal theorem^[1] to further research on the bending problem of the cantilever rectangular plate under a concentrated load acting at any of its points. This method is even simpler and more general.

Finite Element Analysis of Non-Newtonian Fluid Flow in 2-D Branching Channel

Su Ming-de

1986, 7(10): 929-936.

Abstract(1845) PDF(588)

Abstract:
This paper presents finite element analysis of non-Newtonian fluid flow in 2-d branching channel. The Galerkin method and mixed finite element method are used. Here the fluid is considered as incompressible, non-Newtonian fluid with Oldyord differential-type constitutive equation. The non-linear algebraic equation system which is formulated with finite element method is solved by means of continuous differential method. The results show that finite element method is suitable for the analysis of non-Newtonian fluid flow with complex geometry.

On the Surface Instability of Elastic Half Spaces

Cao Guang-zhong

1986, 7(10): 937-945.

Abstract(1863) PDF(659)

Abstract:
In this paper, we present some work on the surface instability of elastic half spaces. An analysis of surface instability of an incompressible half space under biaxial loading is summarized, and the critical condition for the onset of surface buckling is given. As an example in the case of compressible materials, the axisymmetric problem of surface instability for a half space made of a standard material is analyzed, and the dependence of buckling parameters on the material is revealed.

The Axial Symmetrical Edge Problems for Thin Walled Shells of Revolution

Chen Guo-dong

1986, 7(10): 947-957.

Abstract(1850) PDF(567)

Abstract:
In this paper, the uniformly valid asymptotic solutions for the axial symmetrical edge problems of thin-walled shells of revolution in bending are given.

1986 Vol. 7, No. 10