POSTBUCKLING OF RECTANGULAR PLATES UNDER UNIAXIAL COMPRESSION COMBINED WITH LATERAL PRESSURE

Based on the nonlinear large deflection equations of von Karman plates,thee ateralpressure is first converted into an initial deflection by Galerkin method,the postbucklingbehavior of simply supported rectangular plates under uniaxial compression combined withlateral pressure is then studied applying perturbation method by taking deflection asperturbation parameter.Two types of in-plane boundary conditions and the effects of initial geometricimperfection are also considered.It is found that the theoretical results are in goodaccordance with experiments.     

Some Applications of Perturbation Method in Thin Plate Bending Problems

In this paper,problems of bending of thin plates under the combined action of lateral loadingand in-plane forces are studied by means of perturbation method.     

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.     

SOLUTION OF BENDING OF CANTILEVER RECTANGULAR PLATES UNDER UNIFORM SURFACE-LOAD BY THE METHOD OF TWO-DIRECTION TRIGONOMETRIC SERIES

The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the two-direction trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect.     

The solution of rectangular plates with large deflection by spline functions

In this paper, Von Karman ’s set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.     

THE SOLUTION OF RECTANGULAR PLATES WITH LARGE DEFLECTION BY SPLINE FUNCTIONS

In this paper,Von Kármán’s set of nonlinear equations for rectangular plates withlarge deflection is divided into several sets of linear equations by perturbation method,thedimensionless center deflection being taken as a perturbation parameter.These sets of linearequations are solved by the spline finite-point(SFP)method and by the spline finiteelement(SFE)method.The solutions for rectangular plates having any length-to-widthratios under a uniformly distributed load and with various boundary conditions arepresented,and the analytical formulas for displacements and deflections are given in thepaper.The computer programs are worked out by ourselves.Comparison of the results withthose in other papers indicates that the results of this paper are satisfactorily better.     

PERTURBATION ANALYSES FOR THE POSTBUCKLING OF SIMPLY SUPPORTED RECTANGULAR PLATES UNDER UNIAXIAL COMPRESSION

In this paper, applying perturbution method to yon Krmn nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the pa(?)buckloing behavior of simply supporied rectungular plates under umaxial compression is (?)igated. Two types of in-plane boundary conditions are now considered and the efferis of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments. The method suggested in this paper whieh has not been found in previons papers is rather simple and easy for the postbuckling analysis of rectangular plates.     

DYNAMIC BUCKLING OF STIFFENED PLATES UNDER FLUID-SOLID IMPACT LOAD

A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.     

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

This paper derives the cubic spline beam function from the generalized beam differential equation and obtains the solution of the discontinuous polynomial under concentrated loads, concentrated moment and uniform distributed by using delta function. By means of Kantorovich method of the partial differential equation of elastic plates which is transformed by the generalized function (δ function and σ function), whether concentrated load, concentrated moment, uniform distributed load or small-square load can be shown as the discontinuous polynomial deformed curve in the x-direction and the y-direction. We change the partial differential equation into the ordinary equation by using Kantorovich method and then obtain a good approximate solution by using Glerkin’s method. In this paper there ’are more calculation examples involving elastic plates with various boundary-conditions, various loads and various section plates, and the classical differential problems such as cantilever plates are shown.     

NONLINEAR BENDINGS OF SYMMETRICALLY LAYERED ANISOTROPIC RECTANGULAR PLATES

This paper has studied the nonlinear bendings of symmetrically layered anisotropic rectangular plates under various supports. The uniformly valid N-order asymptotic solutions of the defection and stress function are derived by the singular perturbation method offered in [1]. The analysis and calculations are given for simply and clamped supported, rectangular plates subjected to combined edge tensions and lateral loading in conjunction with the modified Galerkin procedure (a method of weighted residuals).     

复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降     

The effect of large rotation on post-buckling of annular plates

On the basis of the axisymmetrical finite deformation theory on Rissner's plates, the post-buckling behaviour of annular plates and the effect of large rotation are qualitatively and numerically discussed by the method of the bifurcation theory.The project is supported by the National Natural Science Foundation of China     

A new approach of predicting bifurcation points of elastic-plastic buckling of plates and shells

The paper proposes a new approach of predicting the bifurcation points of elastic-plastic buckling of plates and shells, which is obtained from the natural combination of the Lyaponov's dynamic criterion on stability and the modified adaptive Dynamic Relaxation (maDR) method developed recently by the authors. This new method can overcome the difficulties in the applications of the dynamic criterion. Numerical results show that the theoretically predicted bifurcation points are in very good agreement with the corresponding experimental ones. The paper also provides a new means for further research on the plastic buckling paradox of plates and shells.     

Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance

Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method.The rectangular thin plate is subject to transversal and in-plane excitation.A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach.A one-toone internal resonance is considered.An averaged equation is obtained with a multi-scale method.After transforming the averaged equation into a standard form,the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics,which can be used to explain the mechanism of modal interactions of thin plates.A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits.Furthermore,restrictions on the damping,excitation,and detuning parameters are obtained,under which the multi-pulse chaotic dynamics is expected.The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.     

中厚矩形板的非线性动力屈曲分叉

建立考虑横向剪切与转动惯量影响的矩形板的动力控制方程，应用Ｇａｌｅｒｋｉｎ方法将其化为Ｍａｔｈｉｅｕ方程，然后根据Ｌｙａｐｕｎｏｖ－Ｓｃｈｍｉｄｔ方法得到了系统在参数激励下的１／２亚谐分叉特性，并给出了四边简支与四边固支弹性薄板的非线性动力屈曲分叉条件。     

FUNDAMENTAL RESONANCE AND BIFURCATION OF LARGE GENERATOR END WINDING WHEN ITS CLAMPING PLATES ARE LOOSE

Introduction Theendwindingunderelectromagneticforcewillvibratewhenthegeneratorisrunning. Becauseofeffectofmanyfactors,suchasmanufacturetechniqueandpracticalrunningcondition, thevibrationmayresultinabrasion,fatigueandfractureoftheendwindinginsulation,even makecoilshortcircuited.Thisisoneofthedifficultiesthatpuzzledpeopleinengineeringfield.Forexample,someelectricpowerstationshavehadaccidentssuchasendwindinginsulation frettedwhichresultedinshortcircuitbecauseclampingplatesareloose;Clipofdown_lea…     

A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

Global bifurcations in the motion of parametrically excited thin plates

In this paper we investigate global bifurcations in the motion of parametrically excited, damped thin plates. Using new mathematical results by Kovai and Wiggins in finding homoclinic and heteroclinic orbits to fixed points that are created in a resonance resulting from perturbation, we are able to obtain explicit conditions under which Silnikov homoclinic orbits occur. Furthermore, we confirm our theoretical predictions by numerical simulations.     

层合板分叉方程的Lyapunov—Schmidt约化分析

采用广义傅立叶级数法建立了具有弹性约束的复合材料矩形层板在面内载荷作用下的非线性稳定性控制方程,并简化为矩阵形式。利用分叉理论和泛函知识,对有限维的该分叉方程进行了Lyapunov-Schmidt约化,获得了三种典型的分叉图形式,同时指出当非齐次项等于零时必然发生分叉。数值计算结果表明了三种分叉图分别所对应的典型的力学模型,主要因素在于边界条件、铺层方式及初始缺陷三方面。     

联合载荷作用下简支矩形板的屈曲和过屈曲

本文研究了简支正交各向异性矩形板在两对板受中面压力作用下的屈曲和过屈曲性态,得到了载荷的稳定性区域,证明了临界载荷最多为二重的。利用多参数摄动方法求得临界载荷附近板的过屈曲状态的渐近解,分析了在二重临界载荷附近,当载荷按比例变化时,板的可能的过屈曲状态及其与参数的依赖关系。