应用数学和力学

1989 Vol. 10, No. 6

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The Displacement Wave Theory of Blood Vessel

Yuan Fan, Wu Wang-yi

1989, 10(6): 469-476.

Abstract(1730) PDF(1130)

Abstract:
On the basis of the medical and mechanical analysis and explanations in this paper the visco-elastic simply supported beam model is proposed to treat the displacement wave of the blood vessels. The relationships between the displacement wave and blood vessel elasticity as well as the viscous dissipation of the blood and blood vessel are obtained. The corresponding relations of such kinds of pulses in the traditional Chinese medicine as smooth pulse, surface pulse and deep pulse to the displacement waves of blood vessels are also found. The computational results are in good agreement with those acquired in the experiments with ultrasonic wave.

Topologieal Degree Theofy and Fixed Point Theorems in Probabilistic Metric Spaces

Zhang Shi-sheng, Chen Yu-qing

1989, 10(6): 477-486.

Abstract(2046) PDF(705)

Abstract:
The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.

The Curved Beam Element and Its Convergence Rate

Lü He-xiang, Tang Li-min, Liu Xiu-lan

1989, 10(6): 487-498.

Abstract(1977) PDF(598)

Abstract:
The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam clement. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approxtmately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l²) and when regular elements are used. l is the element length.

The Stability and Convergence of the Finite Analytic Method for the Numerical Solution of Convective Diffusion Equation

Sun Yu-ping, Wu Jiang-hang

1989, 10(6): 499-505.

Abstract(1818) PDF(733)

Abstract:
In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.

Incremental Analysis for Nonlinear Rubber-Like Materials by Hybrid Stress Finite Element

Fan Jia-qi, Yang Xiao-xiang

1989, 10(6): 507-515.

Abstract(1790) PDF(524)

Abstract:
In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.

A Hybrid FEM Algorithm for Fluid Flow in a Visco-Elastic Pipe

Chen Yao-song, Cao Nian-zheng

1989, 10(6): 517-622.

Abstract(1684) PDF(445)

Abstract:
A variational principle of hybrid FEM is proposed to solve the flow in a visco-elaslic pipe. As an example, the influence of an axisymmetrical stenosis on an artery vibrating flow with a single frequency is calculated.

The Interaction of a Shock Wave with the Boundary Layer in a Reflected Shock Tunnel

Xu Li-gong

1989, 10(6): 523-529.

Abstract(1933) PDF(720)

Abstract:
The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

Hopf-Landau Bifurcations of Higher Dimensional Tori

Cheng Chong-qing

1989, 10(6): 531-538.

Abstract(1605) PDF(456)

Abstract:
The existence of degenerate bifurcations from T^m to P_m+1 is provedunder the condition of quasi-periodic critical points.

Torsion of Circular Cylinders Containing n Circular Holes

Yin Chang-yan

1989, 10(6): 539-546.

Abstract(1769) PDF(472)

Abstract:
In the present paper by using complex variable methods in linear elasticity and by-means of analytic continuation, the author obtains for this problem a complex torsional function, shear stress components, displacement components,the lorsional rigidity and shear stresses on boundaries expressed in terms of series.

A Note on the Completeness of Hu Hai-chang’s Solution

Wang Min-zhong, He Bei-chang

1989, 10(6): 547-552.

Abstract(1846) PDF(572)

Abstract:
In this paper it is showed that Hu Hai-chang's solution for the isotropic is complete in case of regions convex in z-direction.

The Asymptotic Expansions of Singularly Perturbed Boundary Value Problems

Zhou Qin-de, Li Yong

1989, 10(6): 553-557.

Abstract(1861) PDF(544)

Abstract:
In this paper we study the singularly penurbed boundary value problem:εy"=f(t,y,ε), y(0)=ξ(ε),y(1)=η(ε), where ε is a positive small parameter In the conditions:f_y(0,y,0)≥m₀,f_y(1,y,0)≥m₀ and f_y(t,y,ε)≥0, we prove the existences, and uniformly valid asymptotic expansions of solutions for the given boundary value problems, and hence we improve the existing results.