应用数学和力学

1995 Vol. 16, No. 12

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On the Error Estimate of h-Convergence in Quadrilateral Elements

Duan Mei, Miyamoto Yutaka, Zhou Benkuan, Chen Dapeng

1995, 16(12): 1043-1050.

Abstract(2192) PDF(605)

Abstract:
To provide a iheoreiical basis for h-type.finire elemenl analysis with quadrilateral elements,in the present paper,the h-convergence of quadrilateral elements is established.whose related lemmas and theorems being presented,and therefore,theerror estimate problems are investigated.

The Expliclt solution of the Matrix Equation AX-XB=C──To the memory of Prof

Chen Yuming, Xiao Heng

1995, 16(12): 1051-1059.

Abstract(5326) PDF(819)

Abstract:
Almost all of the existing results on the explicit solutions of the matrix equation AX-XB=C are obtained under the condition that A and B have no eigenvalues incommon For both symmetric or skewsymmetric matrices A and B.we shall give outthe explicit general solutions of this equation by using the notions of eigenprojections The results we obtained are applicable not only to any cases of eigenvalues regardlessof their multiplicities but also to the discussion of the general case of this equation.

Analytical Solution of Radiated Sound Pressure of Ring-Stiffened Cylindrical Shells in Fluid Medium

Xie Guanmo, Luo Dongping

1995, 16(12): 1061-1066.

Abstract(2376) PDF(556)

Abstract:
In this paper,analytical for mularions of radiated sound pressure of ring-stiffened cylindrical shells in fluid medium are derived by means of Hamilton's principle Huygens' principle and Green function.These formulations Can be used to compute the sound pressure of the shell's surface nearfield and farfield.

The lnteraction of Plane SH-Waves and Circular Cavity Surfaced with Lining in Anisotropic Media

Han Feng, Wei Yang, Liu Diankui

1995, 16(12): 1067-1077.

Abstract(2657) PDF(623)

Abstract:
In this paper.we use the complex function method for solving the problem of interaction of plane SH-waves and circular cavity surfaced with lining in anisotropic media.Anisotropic media can be used to simulate the conditions of the geology Thisproblem can be handled by using the method similar to that incorporated in Ref [5] todefine the scattering waves in media.added with the given boundary condition of the circular cavity.In this paper.as illustrated in the examples the results and discussions of numerical studies have been done for the interaction of plane SH-waves and two kinds of circular cavities surfaced with lining made up of different materials in anisotropic media.

The Variational Principle of Thin Shell in Stability

Huang Yan, Huang Reifang

1995, 16(12): 1079-1086.

Abstract(2064) PDF(486)

Abstract:
This paper gives the resultant forces and moments strain energy and work of external forces on the basis of the deformation theory of flexible body therefore in accordance with the principle of virtual displacement the energy criterion of critical lad is obtained and the equilibrium equations and boundary conditions of stability problem are derived.

On the Existence of Harmonic Solutions for Higher-Order Lienard Systems

Dong Qinxi, Huang Xiankai

1995, 16(12): 1087-1090.

Abstract(2237) PDF(517)

Abstract:
In this paper,by using of the theory of coincidence degree,we obtain the new conditions which guarantee the existence of harmonic solutions for Liénard Systems Our resuls do not require that the damping must be positive.

lnteraction of Turbulent Coherent Structures and Small Scale Structures

Liu Shihe, Liang Zaichao

1995, 16(12): 1091-1099.

Abstract(2955) PDF(1416)

Abstract:
In this paper experimental research is carried out for the existence of large andsmall scale.structures in turbulent boundary layer and the interactions between these structures.Based on the experimental results,a new method is suggested to discribe the coherent strucures in which the interactions between between the coherent and small-scale slructures are considered,Using this method a new pattern recognition method is suggested and used for the coherent structures in turbulent boundary layer in smooth and rough well conditions.The results show that the suggested method is reasonable.

Instability of Solution for a Class of the Third Order Nonlinear Differential Equation

Lu Deyuan

1995, 16(12): 1101-1114.

Abstract(2398) PDF(609)

Abstract:
In refercnce [1] the asymptotic stability of nonlinear slowly changing system has been discussed.In Ref [2] the instability of solution for the order linear differential equaiton with varied coefficient has been discussed.In this paper,we have discussed instability of solution for a class of the third order nonlinear diffeential equation by means of the metod of Refs [1] and [2].

Solving the Free Boundary Problem in Continuous Casing by Using Boundary Element Method

Li Yaoyong, Zhang Zili

1995, 16(12): 1115-1121.

Abstract(2611) PDF(513)

Abstract:
In this paper.the authors solve the free boundary problem(FBP) in continuous casiing by using boundary element method(BEM).First,we simplify the general mathematical model for continuous casting to a practicable model,and give the boundary integral equations with partial unknown boundary for this model,and describe in detail the steps of calculating this FBP by using the BEM.Next,wepresent the result of our numerical experiments,and discuss the stability,convergence and applicaiion of our method.At last.we simplify the former model so that it has ananalytic solution.and we compare its numerical solution resulted from our method withits analytic solution.

Unconditional Stable Solutions of the Euler Equations for Two and Three-D Wings in Arhitrary Motion

Gao Zhenghong

1995, 16(12): 1123-1134.

Abstract(2908) PDF(562)

Abstract:
The work presented here shows the unsteady inviscid results obtained for the twoand three-dimensional wings which are in rigid and flexible osciliations.The results are generated by a finite volume Euler method.It is based on theRunge-Kutta time stepping scheme developed by Jameson et al..To increase the timestep which is limited by the stability of Runge-Kutta scheme,the implicit residual smoothing which is modified by using variable coefficients in prerent the loss of flowphysics for the unsteady flows is engaged in the calculations.With this unconditional stable solver the unsteady flws about the wings in arbitrary motion can be received efficiently.The two-and three-dimensional rectangular wings which are in rigid andflexible pitching oscillations in the transonic flow are invesigated here,some of the computational results are compared with the experimental data.The influence of thereduced frequency for the two kinds of the wings are researched.All the results givenin this work are reasonable.

An Analysis of the Post-buckling of Laminated Pates of Symmetric Cross-ply

Weng Zongyi

1995, 16(12): 1135-1142.

Abstract(2531) PDF(568)

Abstract:
In this paper,general equations relating to the stability of laminated plates of symmetric cross-ply with initial imperfection factors are derived by using the variational principle.Taking the deflection as the perturbation parameter,the equilibrium path of the post-buckling path of a simply supported rectangular plate is investigated with the perturbation method.An approximation expression and a typical numerical example are presented to manifest the post-buekling behavior of the rectangular plate.