BENDING OF RECTANGULAR THIN PLATES WITH FREE EDGES LAID ON TENSIONLESS WINKLER FOUNDATION

In this paper,the bending problem of rectangular thin plates with free edges laid ontensionless Winkler foundation has been solved by employing Fourier series withsupplementary terms.By assuming proper form of series for deflection,the basicdifferential equation with given boundary conditions can be transformed into a set ofinfinite algebraic equations.Because the boundary of contact region can notbedetermined inadvance.these equations are weak nonlinear ones.They can be solved by using iterativeprocedures.     

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.     

THE BENDING, STABILITY AND VIBRATIONS OF RECTANGULAR PLATES WITH FREE EDGES ON ELASTIC FOUNDATIONS

This paper discusses the problems of the bending, stabilio, and vibrations of the rectangular plates with free boundaries on elastic foundations, In the present paper we select a flexural function, which satisfies not only all the boundary Conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem(MRT)is extended to solve thesteady state responses of rectangular plates under harmonic disturbing forces.A series ofthe closed solutions of rectangular plates with various boundary conditions are given andthe tables and figures which have practical value are provided.MRT is a simple,convement and general method for solving the steady state responsesof rectangular plates under vartous harmonic disturbing forces.The paper contains three parts:(Ⅰ)rectangular plates with four clamped edges andwith three clamped edges:(Ⅱ)rectangular.plates with two adjacent clamped edges:(Ⅲ)cantilever plates.We are going to publish them one after another.     

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.     

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.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)-RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plates under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided. MRT is a simple, convenient and general method for solving the steady state responses of rectangular plates under various harmonic disturbing forces. The paper contains three parts: (I) rectangular plates with four clamped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates. We are going to publish them one after another.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅱ)—RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES

In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two adjacent clamped edges under harmonicdistributed and concentrated loads.     

BENDING PROBLEM OF RECTANGULAR PLATES OF UNIDIRECTIONAL NONHOMOGENEITY AND VARIABLE THICKNESS WITH TWO OPPOSITE EDGES SIMPLY SUPPORTED UNDER ARBITRARY DISTRIBUTED LOADS

Using the step reduction method suggested by the first author of this paper, weinvestigate the problem indicated in the title and obtain the stepped approximatesolutions. As an example, the case of a square plate of linealy varying thicknesswith four edges simply supported under linearly distributed loads is calculatedThe obtained results agree well with those given in [3] and thus the exactness of thenew method is verified.     

Bending of rectangular plate with each edges arbitrary a point supported under a concentrated load

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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 stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates, the figures and tables of number value of bending moment and the deflection amplitudes as well.     

应用混合变量余能原理求解不同载荷作用下四边简支矩形板的弯曲

由功的互等定理导出了弯曲矩形板混合变量的总余能,应用混合变量余能原理求解四边简支矩形板弯曲问题,给出了四边简支矩形板的混合变量余能表达式,求解了不同载荷作用下四边简支矩形板的弯曲问题,并将计算的不同载荷作用下的挠度和弯矩值与ANSYS有限元的计算值比较,给出了一种求解四边简支矩形板的新方法。     

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

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A method using the reciprocal theorem to solve the bending of thin elastic semicircular plates

The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse defiectional equations of the plates.     

The bending,stability and vibrations of rectangular plates with free edges on elastic foundations

This paper discusses the problems of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations. In the present paper we select a flexural function, which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.     

Bending of uniformly loaded rectangular plates with two adjacent edges clamped, one edge simply supported and the other edge free

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The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

（黄家寅）（秦圣立）ＴＨＥＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＢＥＮＤＩＮＧＦＯＲＯＲＴＨＯＴＲＯＰＩＣＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳ￥ＨｕａｎｇＪｉａｙｉｎ;ＱｉｎＳｈｅｎｇｌｉ（ＱｕｆｕＮｏｒｍａｌＵｎ...     

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.     

On new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported

The symplectic geometry method is introduced for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported. The basic equations for the plates are first transferred into Hamilton canonical equations. The whole state variables are then separated. Using the method of eigenfunction expansion in the symplectic geometry, typical examples for plates with selected boundary conditions are solved and exact bending solutions obtained. Since only the basic elasticity equations of the plates are used, this method eliminates the need to pre-determine the deformation function and is hence more reasonable than conventional methods. Numerical results were presented to demonstrate the validity and accuracy of this approach as compared to those reported in other literatures.