应用数学和力学

A Screw Dislocation by Nonlinear Continuum Mechanics

Pan Ke-lin, Chen Zhi-da

1994, 15(12): 1037-1045.

Abstract(1668) PDF(497)

Abstract:
Based on the nonlinear geometry field theory of continuum mechanics, this paper analyses the stress field due to a serew dislocation in an infinite an infinite medium. The results reveal the high-order effect of the stress field. When this effect is small, the result can be reduced to one of the classical linear elasticity. The body couple field of the serew dislocation is also investigated in this paper. The analytiecal expression of the body couple due to a serew dislocation is obtained with small rotation deformation. As the application of theoretical results. the stress and the body couple at the interface of the crystals are calculated when the serew dislocation is near the interface.

Stress-Anlysis of Thick Ring Shell Sumitted to the Action of Internal Pressure

Zhao Xing-hua

1994, 15(12): 1047-1055.

Abstract(1972) PDF(457)

Abstract:
In this paper, from asymptotic equations of thicking shell obtained on the basis of the equations of three dimensional elastic mechanics using geometric small parameter a=r₀/R₀. we find the solutions of the stresses and the deformations of thick ring shell submitted to the action of internal pressure q.

Plane Elasticity Sectorial Donain and the Hamiltonian System

Zhong Wan-xie

1994, 15(12): 1057-1066.

Abstract(1732) PDF(471)

Abstract:
The governing equations of plane elasticity in sectorial domain are derived to be in Hamiltoinan form via variable substitutes and variationl principles. The method of separation of variables and eigenfunction expansion method are derive to solve the finite element analytically for the sectorial domain elasticity problem, so that such kind of analytical element can be installed into FEM program systems. It demonstrates the potential of the Hamiltonian system theory and symplectic mathematics.

A Stability Study of Navier-Stokes Equations(Ⅲ)

Shi Wei-hui

1994, 15(12): 1067-1073.

Abstract(2025) PDF(530)

Abstract:
In this paper, the necessary conditions of the existence of C² solution. in someinitial problems of Navier-Stokes equations are given. and examples of instability ofinitial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equationvarious authors studies this problem and contributed a number of results.J.Leray.a French professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions.In this paper,with certain rigorously defined key concepts,based upon the basic theory of J.Hadmard partial differential equanous[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to reference.[4].

A Mixed Method for the Creep of a Skin Layer

Huang Li-du, Wang Qin-que, Mak Fak-tat Arthur

1994, 15(12): 1075-1082.

Abstract(1750) PDF(490)

Abstract:
The creep of a skin layer under a distributed surface pressure was solved by ananalysical method using Hankel transform and Laplace transform.The surface stress boundary conditions lead to a Volterra integral equation of the first kind, which was then solved by a numerical method.The IMSL subroutines DINLAP and DGORUL were employed to numerically obtain the Hankel-Laplace inversion. The calculated displacements at two distinctive moments were compared respectively with those obtained by an elastic solution for either in compressible or compressible solid. The transient creep responses of the skin layer were also presented.

The Stress Analysis of Vessel wall in the Entrance Region of a Tapered Vessel

Cen Ren-jing, Tan Zhe-dong, Chen Zheng-zong

1994, 15(12): 1083-1090.

Abstract(1691) PDF(533)

Abstract:
The present paper deals with the flow in an entrance region of a tapered vessel.Pressure distribution formula, axial and radial distribution formulas,shear stress distribution formula of flow field and shear stress distribution formula of vessel wallare derived. Relative numerical computations are made and analyzed.Discussion of the effects of tapered angle on the pressure distribution and vessel wall stress distribution are emphasized.

1994, 15(12): 1091-1105.

Abstract(1640) PDF(562)

Abstract:

Spatlal-Temporal Discrete Coordination of FEM and Direct Integral Method for Transient Dynamic Problems

Wang Huai-zhong

1994, 15(12): 1111-1117.

Abstract(1894) PDF(393)

Abstract:
In this paper, the coordination of spatial-temporal discrets of FEM and direct integral method is investigates.By analyzing the numespatial-temporal discrete,the principle of balancing the principle of balancing the energy error induced by spatial discrete and the energy error induced by temporal discrete is presented, and the prioriprocess and adaptive method for the coordination of spatial discerand temporal discrete is obtained.

A Modified Method of Averaging for Solving a Class of Nonlinear Equations

Zhang Bao-shan

1994, 15(12): 1119-1126.

Abstract(1837) PDF(476)

Abstract:
In this paper, we studied a method of averaging which decide a uniform valid solution for nonlinear equation and got the, modified forms for KB, method (Krylov-Bogoliubov method)and KBM method (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and there by the applied area of the method of averaging are extended.

1994 Vol. 15, No. 12