应用数学和力学

1991 Vol. 12, No. 6

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The Relation of the Threshold Velocity of Coal Dust to Its Size and Humidity

Lin Duo-min, Tsai Shu-tang

1991, 12(6): 485-490.

Abstract(1827) PDF(515)

Abstract:
On the ground of wharf and a station where coal is piled up, the sources polluting the atmosphere are mainly the raised coal dust. According to the principle of mechanics, with the consideration of the gravities of coal dust particles and liquid droplets, coal dust size and humidity, under the condition of force balance when the coal dust was raised, the authors obtaineda theoretical formula for the threshold velocity of coal dust with humidity.Finally, the theoretical values from the formula gave a good agreement with the experimental data from some wind tunnels.

Computation of Unsteady Flow past Blunt Bodies

Yao De-Hang, Bian Yin-gui

1991, 12(6): 491-499.

Abstract(2007) PDF(550)

Abstract:
In accordance with the recent experimental research for flow visualization, the unsteady behavior of the starting period is investigated numerically for flow past blunt bodies. Finite difference methods are employed to solve the unsteady two-dimensional incompressible Navier-Stokes equations. A short discussion is presented of explicit, implicit and ADI methods. Finally, the explicit and ADI schemes are used to study the flow field in the starting period for flow past mountain-shaped and rectangular bodies.

The Flow Structure of Dilute Gas-Particle Suspensions behind a Shock Wave Moving along a Flat Surface

A. N. Osiptsov, S. L. Veselyi, V. A. Kulikovskii, Wang Bai-yi

1991, 12(6): 501-507.

Abstract(2031) PDF(420)

Abstract:
The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented. The Saffman lift force acting on a particle in a shear flow is taken into account. It is shown that particle migration across the boundary layer leads to intersections of particle trajectories. The corresponding modification of dusty gas model is proposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at a constant speed are obtained by using the method of matched asymptotic expansions. The method of the calculation of particle phase parameters in Lagrangian coordinates is described in detail. Some numerical results for the case of small particle concentration are given.

The Linear Stability of PSane Poiseuille Flow under Unsteady Distortion

Zhou Zhe-wei

1991, 12(6): 509-514.

Abstract(1770) PDF(499)

Abstract:
This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show that in the initial period of disturbance development, the distortion profiles presented by paper [1] will make the disturbances grow up, thus augmenting the possibility of instability.

An Analysis of the Large Deflection of an Elastic-Plastic Cantilever Subjected to an Inclined Concentrated Force

Luan Feng, Yu Tong-xi

1991, 12(6): 515-522.

Abstract(2518) PDF(904)

Abstract:
Based on the Plastica theory (see ref. [12]), the large deflection of an elastic-perfectly plastic cantilever subjected to an inclined concentrated force at its tip, before the unloading in the plastic region occurs, is analyzed in this paper. The emphasis of the analysis is put on the effects of the angle of inclination of the concentrated force upon the deformed shape, the load-deflection relationship and the length of the plastic region. Both analytical and computed results are given.

Instability of Toroidal Membrane with Large Tensile Deformation

Shang Xin-chun, Cheng Chang-jun

1991, 12(6): 523-530.

Abstract(2224) PDF(521)

Abstract:
In this paper, the problem of large axisymmetric deformation of hyperelastic membrane is reformulated on the basis of the general theory of finite elasticity. From the fundamental equations derived here, the tensile instability of toroidal rubberlike membrane with Mooney-Rivlin's model constitutive relation is solved by using the shooting method. The upper and lower limit loads and the response curve of the displacement to the load are given.

Structural Function Theory of Generalized Variational Principles for Linear Elastic Materials with Voids

Pi Dao-hua, Jin Li-hua

1991, 12(6): 531-540.

Abstract(1870) PDF(455)

Abstract:
In this paper, we have obtained generalized variational principles for linear elastic materials with voids from structural function theory. Correspondent relations between structural functions and generalized variational principles are given.

Parametric Quadratic Programming Method for Viscoplasticity

Zeng Pan, Qian Ling-xi

1991, 12(6): 541-545.

Abstract(2155) PDF(540)

Abstract:
Perzyna model in viscoplasticity has. been studied by the parametric variational principle, which could be transformed into solving the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.

Large Amplitude Vibration of Thin Annular Plates

Li Dong

1991, 12(6): 547-556.

Abstract(2247) PDF(590)

Abstract:
A pure analytic solution of the axisymmetric large amplitude free vibration of thin annular plates is presented in this paper. By using the modified iteration method, we derive an analytic relation for the amplitudes vs. frequencies of vibrations. The present paper shows the great potentiality of this method to tackle the large amplitude vibration problems of plates.

Transient Temperature Fields and Residual Stress Fields of Metallic Materials under Welding

Yuan Fa-rong, Sun Hua-dong

1991, 12(6): 557-561.

Abstract(1903) PDF(536)

Abstract:
Based on the situation of welding thermal conduction and thermo-elasto-plasticity research, this paper explores some problems in this field. First, the boundary element method for nonlinear problems is improved by linearization of nonlinear problems and used in welding thermal conduction analysis. Second, the thermo-elasto-plastic finite element method is used for the welding stress calculation, in which the phase transformation is considered by the "equivalent linear expansion coefficient method".The comparison of the calculated results with experimental data shows that the methods provided in this paper are available.

Fringe Multiplication by Reflection

An Li-qian

1991, 12(6): 563-566.

Abstract(1998) PDF(529)

Abstract:
A new method of fringe multiplication is presented in this paper. The method is simple and applicable. Only one polarizer and one quarter-wave plate are adopted to get fringe multiplication by reflection.

Bending Problems of Rectangular Reissner Plate with Free Edges Laid on Tensionless Winkler Foundations

Bu Xiao-ming, Yan Zong-da

1991, 12(6): 567-578.

Abstract(2128) PDF(575)

Abstract:
In this paper, an analytical method for solving the bending problems of rectangular reissner plate with free edges under arbitrary loads laid on tensionless Winkier foundations is proposed. By assuming proper form of Fourier series with supplementary terms, which meet derivable conditions, for deflection and shear force functions, the basic differential equations with given boundary conditions can be transformed into a set of simple infinite algebraic equations. For common Winkier foundations, this set of equations can be solved directly and for tensionless Winkler foundations, it is a set of weak nonlinear algebraic equations, the solution of which can be obtained easily by using iterative procedures.