On some problems for unsymmetrical lateral buckling of rectangular plates

The present paper investigates several problems for unsymmetrically lateral instability of rectangular plates by the energy method. In the text we discuss the minimum critical load of rectangular plates which possess the unsymmetrical supporters and to which the lateral buckling occurs unsymmetrically under a concentrated force, uniformly distributed load and the concentrated couples respectively.     

On buckling of cantilever rectangular plates under symmetrical edge loading

The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by lite varialional calculus. We are going to find out the minimum critical loading for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We’ll discuss the least critical loadings when the buckling of rectangular plates acted on bv a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.     

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.     

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.     

Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的辛叠加解

研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性.     

确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应

建立了一种普遍的解析理论用于求解确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应。首先通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程，给出了计算其自由振动的精确方法，并导出了Timoshenko弯扭耦合薄壁梁自由振动主模态的正交条件。然后利用简正模态法研究了确定性载荷作用下单对称Timoshenko薄壁梁的弯扭耦合动力响应，该弯扭耦合梁所受到的荷载可以是集中载荷或沿着梁长度分布的分布载荷。最后假定确定性载荷是谐波变化的，得到了各种激励下封闭形式的解，并对动力弯曲位移和扭转位移的数值结果进行了讨论。     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论,考虑材料物性参数随坐标和温度变化的特性,研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题,基于一维DQ法和Galerkin技术,给出了一对边固支、另对边任意约束时板弯曲问题的半解析解.以Si3N4/SUS304板为例考察了材料组份、温度场、面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响.     

Large deplection of corrugated circular plate with a plane central region under the action of concentrated loads at the center

This paper solves the problem of large deflections for corrugated circular plates with a plane central region under the action of concentrated loads at the center by means of the non-linear bending theory for anisotropic circular plates. Using the modified iteration method, the characteristic relation of the plate is obtained. This formula may be applied directly to design of elastic elements of measuring instruments.     

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     

域内具有支承及集中质量的薄板自由振动的边界元分析

本文基于薄板小挠度弯曲问题的基本解,建立了任意边界条件、域内具有支承及附有征意个集中质量的薄板自山振动的边界积分方程,文中计算了若干算例,其精度是实际工程中所允许的。     

VIBRATIONS OF STEPPED RECTANGULAR THIN PLATES ON WINKLER’S FOUNDATION

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A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.     

Load’s temporal characteristics for annulling forced vibrations of linear elastic plates

We consider trapezoidal load-time pulses with linearly increasing and affinely decreasing durations equal to integer multiples of the time period of the first bending mode of vibration of a linearly elastic structure. For arbitrary spatial distributions of loads applied to monolithic and laminated orthotropic plates, it is shown through numerical solutions that plates’ vibrations become miniscule after the load is removed. This phenomenon is independent of the dwell time (i.e., the time duration between the rising and the falling portions) during which the load is kept constant. The primary reason for this response is that for such time-dependent loads, nearly all of plate’s strain energy is concentrated in deformations corresponding to the fundamental bending mode of vibration. Thus plate’s deformations can be studied by taking the mode shape of the 1st bending mode as the basis function and reducing the problem to that of solving a single second-order ordinary differential equation. We have verified this postulate by comparing strain energies computed from the 3-dimensional deformations of different plate geometries and boundary conditions with those determined by using the single degree of freedom (DoF) model. Thus for trapezoidal time-dependent loads applied on plates, the 1 DoF model provides reasonably accurate results and saves considerable computational effort.     

A free rectangular plate on elastic foundation

This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a fiexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions.     

Steady-state motion of a plate with a discontinuous mass

An “exact” solution employing the normal mode approach is presented for the steady-state motion of a plate of arbitrary shape and with arbitrary boundary conditions that is provided with a discontinuous mass. The plate is viscously damped and the excitation is furnished in the form of distributed and/or concentrated loads that vary sinusoidally. The rigid mass, which may act as a vibration damper, can be applied to any point in the structure. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported square plates subjected to base excitation and discrete loads. The effects of all system parameters, including damper location and mass ratio, mode shapes, viscous damping, and excitation frequency are determined. It is found that the system under consideration is an efficient device for reducing the vibration of plates, particularly cantilevered ones.     

Large deflections of heterogeneous anisotropic rectangular plates

An approximate solution is presented for large deflections of clamped, uniformly loaded, unsymmetrically laminated, anisotropic, rectangular plates. Expressing the load and displacements in the form of series, the von Karman-type nonlinear differential equations and immovable boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. The solution obtained by successive approximations can reduce to some existing solutions for large deflections of homogeneous plates. Numerical results based on the first three terms of the truncated series are graphically presented for unsymmetrical cross-ply and angle-ply plates having various values of fiber-reinforced material, number of layers, and aspect ratio. The results in small deflections of coupled laminates are compared with available data.     

BOUNDARY INTEGRAL EQUATIONS FOR BENDING PROBLEM OF REISSNER'S PLATES ONTWO-PARAMETER FOUNDATION

I.IntroductionThickplatesonelastict'oundationarewidelyusedinengineering,suchasthebottomplatesofoffShorestructures,surfaceplatesonrunwayofairportsandfoundationsofhigh-risebuildingsandthelike.Itisextremelydifficulttoobtainanalyticalsolutiontarathickplatewithcomplicatedshapeorcomplicatedboundaryconditiononelasticfoundation.Inrecentyears,theboundaryelementmethod(BEM)hasbeensuccessl'ullyusedtoanalyzethebendingproblemofplatesoneverykindofelasticfoundation(Ref.[l,2.3]).Butthereareonlyfewreferences…     

A free rectangular plate on elastic foundation

In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the differential equation, the boundary conditions of the edges and the free corners. Thus we are led to a system of infinite simultaneous equations. The problem solved is for a plate with a concentrated load at its center. The reactive forces from the foundation should be made to be in equilibrium with the concentrated force to see whether our calculation is correct or not.     

Radial basis functions collocation and a unified formulation for bending,vibration and buckling analysis of laminated plates,according to a variation of Murakami’s zig-zag theory

In this paper, we propose a variation of the use of Murakami’s zig-zag theory for the analysis of laminated plates. The new theory accounts for through-the-thickness deformation, by considering a quadratic evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions. This paper considers the analysis of static deformations, free vibrations and buckling loads on laminated composite plates.     

Nonlinear bendings of unsymmetrically layered anisotropic rectangular plates

An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under verious supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem.