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     

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

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

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.     

Application of the method of the reciprocal theorem to finding displacement solutions of cubes

In this paper the method of reciprocal theorem is extended to find solutions of three-D problems of elasticity. First we give the basic solution of the cube with six surfaces fixed as the basic system and then using the reciprocal theorem between the basic system acted on by unit concentrated loads and the actual system with prescribed surface displacements, we find displacement solution of the actual system.     

The symmetrical bending of an elastic circular plate supported atK internal points

This paper treats the symmetrical bending of a uniformly loaded circular plate supported at k internal points. The boundary displacement and slope are expanded in Fourier seriesr. The method proposed by [6] is applied. As both the governing differential equation and boundary conditions are satisfied exactly, we therefore obtain the analytic expression of the transverse deflectional equation of the circular plate. This is an easy and effective methed.     

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.     

Energy theorems for solving equations of deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano’s Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.     

Further research on the bending of the cantilever rectangular plates under a concentrated load

In this paper we apply the reciprocal theorem^[1] to further research on the bending problem of the cantilever rectangular plate under a concentrated load acting at any of its points. This method is even simpler and more general.