应用数学和力学

1991 Vol. 12, No. 9

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Second-Order Effect of an Elastic Circular Shaft during Torsion

Chen Mian Chen Zhi-da

1991, 12(9): 769-776.

Abstract(2052) PDF(496)

Abstract:
In this paper we deal with the second-order effect of an elastic circular shaft during torsion.The analysis is based on the method of co-moving coordinates and the strain-rotation decomposition theorem^[1] in continuum mechanics.By using asymptotic expansion methods,we comfirm that the effect of axial elongation and distortion of plane cross-section exists in an elastic circular shaft during large torsion and give the expressions of the axial force and the torque.

Expressions for Pressure-Velocity-Gradient Correlations

Lin Duo-min, Cai Shu-tang

1991, 12(9): 777-785.

Abstract(2224) PDF(527)

Abstract:
The term for pressure-velocity-gradient correlation was initiated by Ratio's^[21] rewriting the correlation between the pressure fluctuation gradient and velocity fluctuation.However,it is very difficult to consider the effect of this term.Since Rotta's work,Launder et al^[7] has made some estimates of this term.In this paper according to the equations for velocity fluctuation,the pressure fluctuation is solved so that the average value of the product of the pressure fluctuation and the velocity fluctuation gradient is obtained.Thus,the whole expressions for the pressure-velocity-gradient correlation are derived.The result explains that the limited expressions by Rotta and Launder are reasonable to a certain degree.The whole expressions in this paper are discussed respectively in two situations: one is without a separate consideration of large and small vortexes; the other is with a separate consideration of three kinds of vortexes.Therefore,the paper gives the whole expressions for pressure-velocity-gradient correlation to the Reynolds stress turbulence model^[7] and the three-vortex turbulence model^[13].

An Analytical Method for a Mixed Boundary Value Problem of Circular Plates under Arbitrary Lateral Loads

Zheng Xiao-ping Ye Tian-qi Chen Bai-ping

1991, 12(9): 787-793.

Abstract(2131) PDF(509)

Abstract:
In this paper by using the concept of mixed boundary funetions,an analytical method is proposed for a mixed boundary value problem of circular plates.The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system.Three examples are presented to show the stability and high convergence rate of the method.

Theremoelastic Problems in the Half Space An Application of the General Solution in Elasticity

Wang Min-zhong Huang Ke-fu

1991, 12(9): 795-806.

Abstract(2094) PDF(568)

Abstract:
In this paper,some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations.The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.

Generalized Variational Inequalities and Minimax Theorems

Yan Xin-li, Li Bing-you

1991, 12(9): 807-812.

Abstract(1860) PDF(465)

Abstract:
In the present paper we discuss the variational problem of operator which may a Hausdorff topological linear space into a Riesz space^[6] We give absolute inequality and elative inequality respectively.

The General Solution for Axial Symmetrical Bending of Nonhomogeneous Circular Plates Resting on an Elastc Foundation

Ji Zhen-yi

1991, 12(9): 813-820.

Abstract(2243) PDF(474)

Abstract:
In this paper,a new method,the exact analytic method,is presented on the basis of step reduction method.By this method,the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting,on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions.The uniform convergence of the solution is proved.This general solution can also he applied directly to the bending of circular plates without elastic foundation.Finally,it is only necessary to solve a set of binary linear algebraic equation.Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

The Effects of Roughness Change on the Surface Layer of the Atmosphere(Ⅰ) the Variations of Wind Speed and Shear Stress

Xu Da-peng, Julian Hunt

1991, 12(9): 821-830.

Abstract(1893) PDF(464)

Abstract:
A general four-layer structure linear theory for predicting the effects of arbitrarily distributed roughness change on the variations of wind speed and shear stress in the surface layer of 3D and 2D atmospheres was presented.The results derived by the theory were agreeable to the previous ones.

A Coupling Method of Difference with High Order Accuracy and Boundary Integral Equation for Evolutionary Equation and Its Error Estimates

Yang Dan-ping

1991, 12(9): 831-844.

Abstract(1784) PDF(420)

Abstract:
In the present paper,a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied,combining difference method with high accuracy with boundary integral equation method.The numerical approximate schemes for both problems on a bounded or unbounded domain in R³ are proposed and their prior error estimates are obtained.

Extended Airy Function and Differential Equations with n-Turning Points

Zhang Ju-ling

1991, 12(9): 845-862.

Abstract(2168) PDF(536)

Abstract:
This paper studies a second order linear ordinary differential equation with n-turning points Where q₁=(x-µ₁)(x-µ₂)…(x-µ_n)ƒ(x)≠0,and λ is a large parameter.The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method.By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.

Generalized Noether’s Theorem of Nonholonomic Nonpotential System in Noninertial Reference Frames

Luo Shao-kai

1991, 12(9): 863-870.

Abstract(2431) PDF(686)

Abstract:
The new Lagrangian of the relative motion of mechanical system is constructed,the varialional principles of Jourdain's form of nonlinear nonlwlonomic nonpotential system in noninertial reference frame are established,the generalized Noether's theorem of the system above is presented and proved,and the conserved quantities of system are studied.