EQUATION IN COMPLEX VARIABLE OF AXISYMMETRICAL DEFORMATION PROBLEMS FOR A GENERAL SHELL OF REVOLUTION

In this paper,the equation of axisymmetrical deformation problems for a general shellof revolution is derived in one complex variable under the usual Love-Kirchhoff assumption.In the case of circular ring shells,this equation may be simplified into the equation given byF.Tolke(1938).R.A.Clark(1950 )and V.V.Novozhilov(1951 ).When the horizontalradius of the shell of revolution is much larger than the average radius of curvature o_jmeridian curve,this equation in complex variable may be simplified into the equation forslander ring shells.If the ring shell is circular in shape,then this equation can be reducedinto the equation in complex variable for slander circular ring shells given by this author(1979).If the form of elliptic cross-section is near a circle,then the equation of slanderring shell with near-circle ellipitic cross-section may be reduced to the complex variableequation similar in form for circular slander ring shells.     

厚管板的等效弹性常数

本文考虑了厚管板界条之间的约束条件和界条断面上存在着相应的双力矩,并由此导出了三角形排列厚管板的等效弹性系数公式和等效波桑系数公式。由该公式计算的结果和Sampson R.C.的实验值、Slot T.的数值解是一致的。     

VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

Since 1979,a series of papers have been published concerning the variational principlesand generalized variational principles in elasticity such as[1](1979),[6](1980),[2,3](1983)and[4,5](1984).All these papers deal with the elastic body with linear stress-strainrelations.In 1985,a book was published on generalized variational principles dealing withsome nonlinear elastic body,but never going into detailed discussion.This paper discussesparticularly variational principles and generalized variational principles for elastic bodywitk nonlinear stress-strain relations.In these discussions,we find many interestingproblems worth while to pay some attention.At the same time,these discussions are alsoinstructive for linear elastic problems.When the strain is small,the high orde terms may beneglected,the results of this paper may be simplified to the well-known principles inordinary elasticity problems.     

圆板在匀布重压下所生之挠曲

本文所研究者,为一周缘夹紧之圆板,在匀布之侧向重压下所生之巨大挠曲。本文用圆板中点之挠曲距离与板厚之比率为参数,逐步求得本题之近似解答,藉此避免前人Way氏之幂级数法中繁重之数字计算。圆板周缘呈现委屈现象之条件,亦可求得,其结果与McPherson,Ramberg及Levy诸氏之实验,完全吻合。本法亦可适用于一圆板在其它周缘条件及其它荷重情况下之诸问题。     

不用Kirchhoff－Love假定的三维弹性板近似理论及其边界条件

经典弹性板理论采用了着名的克希霍夫(Kirchhoff)[1]-拉甫(Love)[2]的经典基本假定,在卡氏张量坐标x_i(ι=0,1,2)中,这些基本假定是:(1)略去横向即x₀轴向正应变,即假定e₍₀₀₎=0;(2)略去横向剪应变,即假定e_0α=0,其中α=1,2;(3)略去横向正应力,即假定σ₀₀=0.人们利用这些假定,建立了应变位移关系和应力位移关系,再利用应力平衡的三维方程,通过跨厚度的积分,找到弹性板中面上的各待定量所应满足的经典理论方程。前文[3,4,5],曾在不用克希霍夫-拉甫经典假定的弹性板三维理论中建立了一种近似理论,但并未证明这种近似理论的唯一性,也没有研究相应的近似边界条件。本文将用三维弹性体的广义变分原理[6]研究相同的问题。本文通过变分驻值条件,求得唯一的近似方程和相应的近似边界条件。本文详细研究了一级近似的平衡方程和近似边界条件。     

非线性弹性体的弹性力学变分原理

作者自1978年以后,曾发表了一系列有关弹性力学的变分原理和广义变分原理的文章如[1](1978),[6](1980),[2]、[3](1983),[4]、[5](1984),都是指线性应力应变关系的线性弹性体的.在1985年出版的广义变分原理中,初步推广至非线性弹性体,但并未进行较全面的探讨.本文特别讨论非线性应力应变关系的弹性体的变分原理和广义变分原理,这里有不少问题是值得注意的,有时,它对线性弹性体的变分原理,有指导意义.当应变很小,其高次项可以略去时,本文所得结论,都能近似地化简为通常线性理论的结果.     

The numerical simulation of turbulent flows of Newtonian and a sort of non-Newtonian fluid in 180-degree square sectioned bend

Using k-εmodel of turbulence and measured wall functions.turbulent flows ofNewtonian(pure water)and a sort of non-Newtonian fluid(dilute,drag-reduction solutionof polymer in a180-degree curved bend were simulated numerically.The calculated resultsagreed well with the measured velocity profiles.On the basis of calculation andmeasurement,appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.     

Variational principles and generalized variational principles for nonlinear elasticity with finite displacement

In a previous paper (1979)^[1], the minimum potential energy principle and stationary complementary energy principle for nonlinear elasticity with finite displacement, together with various complete and incomplete generalized principles were studied. However, the statements and proofs of these principles were not so clearly stated about their constraint conditions and their Euler equations. In somecases, the Euler equations have been mistaken as constraint conditions. For example, the stress displacement relation should be considered as Euler equation in complementary energy principle but have been mistaken as constraint conditions in variation. That is to say, in the above mentioned paper, the number of constraint conditions exceeds the necessary requirement. Furthermore, in all these variational principles, the stress-strain relation never participate in the variation process as constraints, i.e., they may act as a constraint in the sense that, after the set of Euler equations is solved, the stress-strain relation may be used to derive the stresses from known strains, or to derive the strains from known stresses. This point was not clearly mentioned in the previous paper (1979)^[1]. In this paper, the high order Lagrange multiplier method (1983)^[2] is used to construct the corresponding generalized variational principle in more general form. Throughout this paper, V/.V. Novozhilov's results (1958)^[3] for nonlinear elasticity are used.     

对合变换和薄板弯曲问题的多变量变分原理

本文利用拉氏乘子法把薄板弯曲问题的最小位能原理和最小余能原理的变分约束条件解除.从而导出了常见的广义变分原理.为了降低泛函中变量导数的阶次.我们用对合变换引进新的正则变量.于是,我们可以进一步利用拉氏乘子法,把这些对合变换当作变分约束而予以消除,从而导出了各种多变量的薄板弯曲广义变分原理.事实证明,使用上述拉氏乘子法,并不能消除一切变分约束;为此,我们进一步引用高阶拉氏乘子法消除这些剩下来的约束条件,从而导得了薄板弯曲问题的更一般的广义变分原理.     

Variational principles and generalized variational principles in hydrodynamics of viscous fluids

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.