应用数学和力学

1997 Vol. 18, No. 5

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The First-order Approximation of Non-Kirchhoff-Love Theory for Elastic Circular Plate with Fixed Boundar under Uniform Surface Loading(Ⅲ)── Numerical Results

Chien Weizhang, Sheng Shangzhong

1997, 18(5): 385-393.

Abstract(2280) PDF(451)

Abstract:
Based upon the differential equations and their related boundary conditions givenin the previous papers^[1,2],using a global interpolation method,this paper presents anumerical solution to the axisymmetric bending problem of non-Kirchhoff-Love theoryfor circular plate with fixed boundary under uniform surface loading.All the numericalresults obtained in this paper are compared with that of Kirchhoff-Love classicaltheory^[3] and E.Reissner's modified theory^[4]

Notes on a study of vector Bundle Dynamical systems(Ⅱ)──Part 2

Liao Shantao

1997, 18(5): 395-412.

Abstract(2191) PDF(493)

Abstract:
In the part 2,theorem 3.1 stut ed in part 1^[15] is proved first.The proof is obtained via a way of changing variables to reduce the original system of differentialequations to a form concerning Standard systems of equations in the theory ofdifferentiable dynamical systems.Then by using theorem 3.1 together with thepreliminary theorem 2.l,foe main theorem of this paper announced in part 1 is proved.The definition of admissible perturbation is contained in the appendix of part 2.Themeanings of the main theorem is described in the introduction of part 1.

Interaction between a Rigid Line Inclusionand an Elastic Circular inclusion

Tang Renji, Tao Fangming, Zhang Minghuan

1997, 18(5): 413-420.

Abstract(2284) PDF(617)

Abstract:
In this paper,the interaction problem of a rigid line inclusion and an elasticcircular inclusion has been reduced to solve a normal Cauchy-type singular integralequation.The stress intensity factors at the ends of the rigid line inclusion and theinterface stresses of the inclusions are obtained.

Adjoint operator Method and Normal Forms of Higher order for Nonlinear Dynamical System

Zhang Wei, Chen Yushu

1997, 18(5): 421-432.

Abstract(3001) PDF(705)

Abstract:
Normal form theory is,a very effective method when we study degeneratebifurcations of nonlinear dynamical systems.In this paper by using adjoint operatormethod,normal forms of order 3 and 4 for nonlinear dynamical system with nilpotentlinear part and Z₂-asymmetry are computed.According to normal forms obtained,universal unfoldings for some degenerate bifurcation cases of codimension 3 and simpleglobal characterizations,are studied.

The Condition for Applying Slit island Method

Wei Yiqiang, Li Qingshi, Cai Zhongmin

1997, 18(5): 433-439.

Abstract(2229) PDF(496)

Abstract:
In this paper.in view of the discussion of the Hausdorff and Box fractaldimensions and measures which are frequently applied,the concept of the girth to areanormal ratio is introduced for the first time and the correct mathematical descriptionof SIM together with its proof,the sufficient condition for applying SIM and theimprovement version of SIM.

Direct Perturbation Method for Reanalysis of Matrix Singular Value Decomposition

Lü Zhenhua

1997, 18(5): 441-446.

Abstract(2345) PDF(641)

Abstract:
The perturbational reanalysis technique of matrix singular value decomposition isapplicable to many theoretical and practical problems in mathematics,mechanics,control theory,engineering,etc..An indirect perturbation method has previously beenproposed by,the author in this journal,and now the direct perturbation method hasalso been presented in this paper.The second-order perturbation results of nonrepeated singular values and the corresponding left and right singular vectors areobtained.The results can meet the general needs of most problems of various practicalapplications.A numerical example is presented to demonstrate the effectiveness of thedirect perturbation method.

Resonant Flow of a Fluid Past a Concave Topography

Zhu Yong

1997, 18(5): 447-450.

Abstract(2413) PDF(532)

Abstract:
In this paper,the resonant generation of nonlinear capillary-gravity waves in afluid system with the effecl of surface tension and the concave topography is examinedby using a perturbation method and numerical method.

Stochastic Boundary Element Method for ReliabilityAnalysis of Plate and Beams Composite Structures

Zhang Feier, Yuan Hong

1997, 18(5): 451-458.

Abstract(2352) PDF(506)

Abstract:
In this paper,the reliability of orthotropic plate and beams composite structures,which is under the actions of the stochastic loading and stochastic boundary conditions,have been analyzed by stochastic boundary element method.First,the boundaryintegral equation of orthotropic plate and beams composite structures is given in thispaper.and then based on the stochastic boundary element method,the method forreliability analysis of stochastic structures is establishes and formulas for computationof reliabilily index of orthotropic plate and beams composite structures are obtained.The computed examples show the efficienl of the method used in this paper.

Koiter-Boundary Layer Singular Perturbtion Method forAxial Compressed Stiffened Cylindrical Shells

Sun Haihong, Chen Tieyun

1997, 18(5): 459-467.

Abstract(2410) PDF(556)

Abstract:
The double singularities induced by bifurcation point and boundary layer in nondimensionalized nonlinear boundary-layer Karman-Donnell equations for axiallycompressed stiffened cylindrical shells can be treated by Koiter-boundary layersingular perturbation method in this paper.Based on the analysis of AS-2 shell,it is demonstrated that the method hashigh computing efficiency and accuracy and some new conclusions can be directiy obtained from the perturbation formulas.

The Corner Solution for Quasilinear Differential Equation with Two Parameters

Zhang Hanlin

1997, 18(5): 469-475.

Abstract(2333) PDF(442)

Abstract:
In this paper,the boundary value problem of quasilinear differential equationwith two parameters is studied via differential inequalities.The asymptotic solution isfound and the remainders is estimated.The asymptotic solution and estimated the remainders are given.

The Saint-Venant Problem of Plane Bar under an Axial Force

Huang Minfeng

1997, 18(5): 477-481.

Abstract(1792) PDF(467)

Abstract:
In the paper,the soluttion of Saint-Venant problem is obtained through assumptionof principal stress curves by means of the equilibrium equations which were deduced inpaper [1].The results show that the speed of shear approaching to zero is a³/y³ andaxial stress approaching to constant is a²/y².