APPROXIMATE SOLUTION FOR BENDING OF RECTANGULAR PLATES—Kantorovich-Galerkin’s Method

This paper derives the cubic spline beam function from the generalized beamdifferential equation and obtains the solution of the discontinuous polynomial underconcentrated loads,concentrated moment and uniform distributed by using delta function.By means of Kantorovich method of the partial differential equation of elastic plates whichis transformed by the generalized function(δ function and σ function),whetherconcentrated load,concentratedmoment,uniform distributed load or small-square load canbe shown as the discontinuous polynomial deformed curve in the x-direction and the y-direction.We change the partial diffkerential equation into the ordinary equation by usingKantorovich method and then obtain a good approximate solution by using Glerkin’smethod.In this paper there are more calculation examples involving elastic plates withvarious bounndary-conditions,various loads and various section plates,and the classicaldifferential problems such as cantilever plates are shown.     

A GENERAL SOLUTION OF RECTANGULAR THIN PLATES IN BENDING

In this paper a general solution of rectangular plates in bending is given.The integralconstants are determined by means of boundary conditions.This method is simpler andeasier than the method of superposition.     

THE UNSYMMETRICAL BENDING OF CANTILEVER RECTANGULAR PLATES

This paper discusses the problems of the unsymmetrical bending of cantileverrectangular plates under various loads by the energy method.We illustrate numerouscalculating examples such as the plates which are subjected by the concentrated forces orconcentrated couples unsymmetrically on free sides and corner points and by a uniformly ornonuniformly distributed loads unsymmetrically on free edges and so forth.     

NONLINEAR BENDING OF SIMPLY SUPPORTED RECTANGULAR SANDWICH PLATES

In this paper,fundamental equations and boundary conditions of the nonlinearbending theory for a rectangular sandwicl plate with a soft core are derived by meansof the method of calculus of variations.Then the nonlinear bending for a simplysupported rectangular sandwich plate under the uniform lateral load is investigated byuse of the perturbation method and a quite accurate analytic solution is obtained.     

A GENERAL ANALYTICAL SOLUTION FOR ELASTIC VIBRATION OF RECTANGULAR THIN PLATES

A general solution of differential equation for lateral displacement function of rectangular elastic thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of rectangular plate with arbitrary boundaries. As an example. the frequency and its vibration mode of a rectangular plate with four edges free have been Solved.     

AN APPROXIMATE SOLUTION OF EIGEN－FREQUENCIES OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES WITH ELASTICAL RESTRAINTS

ＡＮＡＰＰＲＯＸＩＭＡＴＥＳＯＬＵＴＩＯＮＯＦＥＩＧＥＮ－ＦＲＥＱＵＥＮＣＩＥＳＯＦＴＲＡＮＳＶＥＲＳＥＶＩＢＲＡＴＩＯＮＯＦＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＷＩＴＨＥＬＡＳＴＩＣＡＬＲＥＳＴＲＡＩＮＴＳ（周叮）ＡＮＡＰＰＲＯＸＩＭＡＴＥＳＯＬＵＴ...     

THERMAL BENDING OF THICK RECTANGULAR PLATES OF BIMODULUS COMPOSITE MATERIALS

Weighted residual solutions are presented for thermal bending of laminated compositeplates.The material of each layer is assumed to be elastically and thermoelasticallyorthotropic and bimodular.The formulations are based on the thermoelastic version of thetheory of Whitney-Pagano laminated palte,which includes thickness shear deformations.The results are obtained for deflections and neutral-surface positions and are found to be ingood agreement with the closed-form solution.     

THE BENDING STABILITY AND VIBRATIONS OF CANTILEVER RECTANGULAR PLATES

This paper discusses the problems of the bending,stability and vibrations of cantileverrectangular plates by means of the variational method.In the text a good many calculatingexamples are illustrated.     

COMBINED LONGITUDINAL WITH LATERAL BENDING OF RECTANGULAR PLATES SUPPORTED AT POINTS OF CORNERS

This paper discusses the problems of combined longitudinal with lateral bending ofrectangular plates which are supported at four points of corners by means of the variationalcalculus.In the text the lateral bending and the stability of thin plates are also treatedrespectively.     

THE BENDING OF THIN RECTANGULAR PLATES WITH MIXED SUPPORTED SEGMENTS OF STRAIGHT EDGES

ＴＨＥＢＥＮＤＩＮＧＯＦＴＨＩＮＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＷＩＴＨＭＩＸＥＤＳＵＰＰＯＲＴＥＤＳＥＧＭＥＮＴＳＯＦＳＴＲＡＩＧＨＴＥＤＧＥＳＣｈｅｎＬｉ－ｚｈｉ（陈立志）（ＱｉｎｈｕａｎｇｄａｏＰｏｒｔＡｕｉｈｏｒｉｔｙ,Ｑｉｎｈｕａｎｇｄａ...     

A general solution of rectangular thin plates in bending

In this paper a general solution of rectangular plates in bending is given. The integral constants are determined by means of boundary conditions. This method is simpler and easier than the method of superposition.The author is grateful to mr. Chen Guang-nan for his assistance in calculation.     

CC series solution for bending of rectangular plates on elastic foundations

The analytical solution for the bending problem of the rectangular plates on an elastic foundation is investigated by using the Stockes' transformation of a double variables function. The numerical results for the rectangular plates with free edges on the elastic foundations under a concentrated force are given in the example. First Received Dec. 14 1993     

An exact solution for the bending of point-supported orthotropic rectangular thin plates

A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse load are arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.     

Reciprocal theorem method for solving the problems of bending of thick rectangular plates

ＲＥＣＩＰＲＯＣＡＬＴＨＥＯＲＥＭＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＰＲＯＢＬＥＭＳＯＦＢＥＮＤＩＮＧＯＦＴＨＩＣＫＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＦｕＢａｏ－ｌｉａｎ（付宝连）Ｔａｎｗｅｎ－ｆｅｎｇ（谭文锋）（ＹａｎｓｈａｎＵｎｉｒｅｒｓｉｔ...     

Symplectic system based analytical solution for bending of rectangular orthotropic plates on Winkler elastic foundation

This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.