COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

ＦｕＢａｏｌｉａｎ（付宝连）（ＲｅｃｅｉｖｅｄＮｏｖ．２２，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩ...     

ON EQUIVALENTS OF THE RECIPROCAL THEOREM TO SUPERPOSITION PRINCIPLES

In this paper in the terms of theory we have proved that the reciprocal theorem isequivalent to the superposition principle of displacements and is equivalent to thesuperposition principle of reactive forces. These equivalents have important theoreticalvalues and practical values.At the same time we also point out that Castigliano’s displacement equation can beapplied to solve the interior displacement of the region of the deformable body too.     

A NOTE ON THE MINIMUM COMPLEMENTARY ENERGY THEOREM

In this paper we propose a very simple and clear method whichcan prove that the minimum complementary energy theorem isequivalent to the condition of single-valued displacementsand displacement boundary condition of the deformable body.     

ON THE MODIFIED CASTIGLIANO"S THEOREM

This paper gives the modified Castigliano's theorem, which is more convenient and more extensive for applications than the classical Castigliano's theorem. The modifications to the classical Castigliano's theorem are in following two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load p of the complementary energy density in the clasical Castigliano's theorem is replaced by the expressions with teh products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second respect is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano's theorem, the modification provides the theoretical fundamental for solving the problems of various boundary conditions. We show also the method of how to apply the modified Castigliano's theorem to solve th     

FURTHER RESEARCH ON THE BENDING OF THE CANTILEVER RECTANGULAR PLATES UNDER A CONCENTRATED LOAD

In this paper we apply the reciprocal theorem to further research on the bendingproblem of the cantilever rectangular plate under a concentrated load acting atany of its points.This method is even simpler and more general.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)—CANTILEVER RECTANGULAR PLATES

In this paper,applying the method of the reciprocal theorem,we give the stationarysolutions of the forced vibration of cantilever rectangular plates under uniformly distributedharmonic load and concentrated harmonic load acting at any point of the plates,the figuresand tables of number value of bending moment and the deflection amplitudes as well.     

THE RECIPROCAL THEOREM AND LINEAR ELASTIC VARIATIONAL PRINCIPLES

In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.     

关于最小余能原理的一个注记

本文给出一个非常简明的方法,这个方法能够证明最小余能原理等价于变形体的位移单值条件和位移边界条件.     

应用功的互等定理计算矩形弹性薄板的自然频率

在文[1]的基础上,本文进一步推广功的互等定理的应用于计算矩形弹性薄板的自然频率.应用本法无需求解控制微分方程,只需在基本系统与实际系统之间应用功的互等定理后求解一简单的积分方程即可.使用了广义简支边的概念并且引入了频率矩阵,从而一并得到了两对边简支、另两对边为各种支持的矩形板的所有频率方程.这是计算矩形板自然频率的一个简便通用的方法.     

THE METHOD OF TRANSFORMATION OF THE BOUNDARIES FOR STRUCTURE THE ADMISSIBLE DISPLACEMENTS

In this paper the method of transformation of the boundaries for structure theadmissible displacements with various boundary conditions is presented What is called themethod of transformation of the boundaries is that. first we transform the actual systeminto the basic system and additional boundary forces and displacements on the basis of thesuperposition principle, then apply variational principles to the basic system,finally find thepermissible displacement of the actual system by means of the method of transformation ofthe series.In this paper, we also give mixed energy prinapies under Variation of boundaryconditions. The mixed energy principles as the potential and complementary energyprinciples under variation of boundary conditions are all the chief theoretical fundamentalof the method of transformation of the boundaries.Applying the method of transformation of the boundaries. we form the permissibledisplacements of rectangular plates of plane stress and bending problems with various edgeconditio