应用数学和力学

An Analytic Solution of Dense Two-Phase Flow in a Vertical Pipeline

Lin Duo-min, Tsai Shu-tang

1990, 11(12): 1027-1034.

Abstract(1708) PDF(484)

Abstract:
According to a mathematical model for dense two-phase flows presented in the previous pape^[1],a dense two-phase flow in a vertical pipeline is analytically solved,and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived.The results show that when the drag force between two phases depends linearly on their relative velocity,the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall,and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.

Formulation of Boundary Element-Linear Complementary Equation for the Ffictional Elastic Contact Problems

Sha De-song, Sun Huan-chun, Xu Shou-ze

1990, 11(12): 1035-1041.

Abstract(1737) PDF(580)

Abstract:
Boundary element-linear complementary equations are formulated to solve elastic contact problems with Coulomb frictions.It is also a new attempt to solve free boundary problems in solid mechanics by means of boundary element-mathematical programming techniques.

A New Approach to Inverse Problems of Wave Equations

Ding Hua, Zheng Zhe-min, Xu Shou-ze

1990, 11(12): 1043-1047.

Abstract(1881) PDF(394)

Abstract:
We introduce a multi-cost-functional method for solving inverse problems of wave equations.This method has its simplicity,efficiency and good physical interpretation.It has the advantage of being programmed for two-or three-(space) dimensional problems as well as for one-dimensional problems.

An Application of Topological Method to Analysing the Three-Dimensional Flow in Cascades(Ⅱ)—— Topological Analysis on the Vector Field Patterns of Skin-Frictions and Section Streamlines

Kang Shun, Wang Zhong-qi

1990, 11(12): 1049-1056.

Abstract(1824) PDF(615)

Abstract:
With an application of topologial analysis,in this paper the skin-friction line patterns on compressor and turbine cassade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross section of a curved pipe and a turbine cascade are drawn under given conditions.In addition the structures of vortices within three-dimensional viscous flow fields in cascades are analysed.

Dynamic Response of Underground Structures by Time Domain SBEM and SFEM

Zhu Jian-xiong, Cao Zhi-yuan, Li Guo-hao

1990, 11(12): 1057-1065.

Abstract(1738) PDF(421)

Abstract:
The dynamic interaction problems of three-dimensional lineqr elastic structures with arbitrary shaped section embedded in a homogeneous,isotropic and linear elastic half space under dynamic disturbances are numerically solved.The numerical method employed is a combination of the time domain semi-analytical boundary element method(SBEM) used for the semi-infinite soil medium and the semi-analytical finite element method(SFEM) used for the three-dimensional structure.The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface.Displacements,velocities,accelerations and interaction forces at the interface between underground structure and soil medium produced by the diffraction of wave by an underground structure for every time step are obtained.In dynamic soil-structure interaction problems,it is advantageous to combine the SBEM and the SFEM in an effort to produce an optimum numerical hybrid scheme which is characterized by the main advantages of the two methods.The effects of the thickness,the ratio of length and diameter of underground structure and the soil medium on dynamic responses are discussed.

Qualitative Investigation and Monotonic Iterative Solutions for Nonlinear Bending of Polar Orthotropic Circular Plates

Shang Xin-chun, Cheng Chang-jun

1990, 11(12): 1067-1081.

Abstract(1831) PDF(462)

Abstract:
This paper presents a systematical investigation of the nonlinear bending of polar orthotropic circular plates under arbitrarily axisymmetric loads and a variety of boundary conditions.Firstly,the oundary value problem reduces to the equivalent integral equations,and the so tions to the linearized problem are given by means of generalized functions.Secondly,the general properties of the solutions of the nonlinear integral equations are investigated in detail,such as,wrinkling,non-negativity,and singularity etc.Then,the monotonic iterative solutions are formally given and the convergence criteria and the global uniqueness of the solutions are discussed.The error estimate of the iterative process is obtained.Finally,a special example is discussed,which shows that the conclusions and methods of this paper are valid.Several results in the paper are presented for the first time.

Buckling and Postbuckling Behavior of Antisymmetrically Angle-Ply Laminated Composite Plates

Shen Hui-shen

1990, 11(12): 1083-1092.

Abstract(2072) PDF(511)

Abstract:
The buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression have been studied by perturbation technique which takes deflection as its perturbation parameter.In this paper,the effects of in-plane boundary conditions,angles,total number of layers and initial geometric imperfection on the postbuckling behavior of laminated plates have been discussed.

Numerical Simulation of the Flow Field in a Thermal Plasma Reactor

Li Guo-yan

1990, 11(12): 1093-1097.

Abstract(1722) PDF(542)

Abstract:
A numerical simulation is presented for a thermal plasma reactor with particle-trajectory model in this paper.Turbulance is considered by using simple SGS model.The governing equations are solved by means of the algorithm of SIMPLER.The calculated results give the velocity and the temperature fields within plasma reactor,and the trajectories of the injected particles.

A Catastrophic Model for Vib rational Buckling of Elastic Arches

Shea Mao-shan, Wei De-min

1990, 11(12): 1099-1102.

Abstract(2007) PDF(729)

Abstract:
This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures.The authors not only obtain a catastrophic model of vibrational buckling of elastic arches,but also give the critical condition of losing stability.

Refined Differential Equations of Deflections in Axial Symmetrical Bending Problems of Spherical Shell and Their Singular Perturbation Solutions

Fan Cun-xu

1990, 11(12): 1103-1112.

Abstract(1820) PDF(566)

Abstract:
This paper deals with the research of accuracy of differential equations of deflections.The basic idea is as follows.Firstly,considering the boundary effect the meridian midsurface displacement u=0,thus we derive the deflection differential equations;secondly we accurately prove that by use of the deflection differential equations or the original differential equations the same inner forces solutions are obtained;finally,we accurately prove that considering the boundary effect the meridian surface displacement u=0 is an exact solution.In this paper we give the singular perturbation solution of the deflection differential equations.Finally we check the equilibrium condition and prove the inner forces solved by perturbation method and the outer load are fully equilibrated.It shows that perturbation solution is accurate.On the other hand,it shows again that the deflection differential equation is an exact equation. The features of the new differential equations are as follows: 1.The accuracies of the new differential equations and the original differential e-quations are the same. 2.The new differential equations can satisfy the boundary conditions simply. 3.It is advantageous to use perturbation method with the new differential equations. 4 We may obtain the deflection expression (ω) and slope expression (dw/da) by using the new differential equations. The new differential equations greatly simplify the calculation of spherical shell.The notation adopted in this paper is the same as that in Ref.[1].

An Efficient Iteration Algorithm of Mixed Boundary/Finite Element Method and Application to Free Torsional Vibration Analysis of Bodies of Revolution

Wang Xiu-xi, Chen Feng, Qian Jiang

1990, 11(12): 1113-1119.

Abstract(1528) PDF(389)

Abstract:
In this paper,the general formulation of a new proposed iteration algorithm of mixed BEM/FEM for eigenvalue problems of elastodynamics is described.Approximate fundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEM equations.The accuracy of solutions is progressively improved by the iteration procedure.Not only could the awkwardness of non-algebraic eigenvalue equations be avoided but also the accuracy of numerical solutions is almost independent of the interior meshing.All these give many advantages in numerical calculation.The algorithm is applied to free torsional vibration analysis of bodies of revolution.A few cases are studied.All of the numerical results are very good.

1990 Vol. 11, No. 12