计入膜力塑性耗散效应的矩形板塑性动力响应

从能量的观点在小挠度理论中引入表征膜力塑性耗散效应的修正因子,基于刚性板块的总体平衡给出矩形板大挠度塑性动力响应的完全运动方程组,分析了理想刚塑性简支和固支矩形板在矩形脉冲和冲击载荷下包括移行塑性铰相的完全大挠度响应过程。解决了当矩形板的挠度达到厚度量级时弯矩、膜力的联合作用问题,理论预报的结果在板的挠度为10倍板厚的量级与实验结果符合良好,改进了只考虑弯矩作用的小挠度理论结果和模态近似估计。     

Reduced-order models for nonlinear vibrations of fluid-filled circular cylindrical shells: Comparison of POD and asymptotic nonlinear normal modes methods

The aim of the present paper is to compare two different methods available for reducing the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD), and an asymptotic approximation of the nonlinear normal modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the partial differential equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed. The response is investigated also for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation. Bifurcation diagrams of Poincaré maps obtained from direct time integration and calculation of the maximum Lyapunov exponent have been used to characterize the system.     

Reduced-order models for control of fluids using the eigensystem realization algorithm

As sensors and flow control actuators become smaller, cheaper, and more pervasive, the use of feedback control to manipulate the details of fluid flows becomes increasingly attractive. One of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this article, we show that using the Eigensystem Realization Algorithm (ERA) (Juang and Pappa, J Guid Control Dyn 8(5):620?C627, 1985) one can theoretically obtain exactly the same reduced-order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.     

Nonlinear three-dimension analysis for axially symmetrical circular plates and multilayered plates

Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearily from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective.     

Perturbation analysis for the postbuckling of rectangular orthotropic plates

In this paper, applying perturbation method to von Kármán-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, thé postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.     

Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout

The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

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On the analysis of thick rectangular plates

Summary Thick rectangular plates are investigated using the method of initial functions proposed by Vlasov. The governing equations are derived from the three-dimensional elasticity equations using a MacLaurin series approach. As the governing equations can be obtained in the form of series, approximate theories of any desired order can be constructed easily by proper truncation. An exact solution is obtained for an allround simply supported thick plate using a Navier type solution. A Levy type solution for higher order theories is illustrated for the case of a thick plate with two opposite edges simply supported and other two edges clamped. Numerical results obtained are compared with those of classical, Reissner and Srinivas et al. solutions.

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Übersicht Mit Hilfe der Methode der Initial-Funktionen von Vlasov werden rechteckige Platten untersucht. Die zugehörigen Gleichungen werden aus den Gleichungen für das dreidimensionale Problem durch eine Entwicklung in MacLaurin-Reihen gewonnen. Durch Abbrechen dieser Reihen können Näherungen beliebiger Ordnung erhalten werden. Für den Fall einer allseitig einfach gelagerten dicken Platte wird eine exakte Lösung erhalten, bei der eine Lösung vom Navier-Typ verwendet wird. Eine Lösung vom Levy-Typ höherer Ordnung wird am Beispiel einer dicken Platte abgeleitet, von der zwei gegenüberliegende Ecken einfach gelagert, die anderen fest eingespannt sind. Die numerischen Ergebnisse werden mit den klassischen, von Reissner, Srinivas u. a. erhaltenen Resultaten verglichen.

     

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.     

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 for the orthotropic rectangular thin plates under various supports

In this paper, the nonlinear bendings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement w and stress function are derived by the perturbation offered in [1].     

Three-dimensional elastic solutions for functionally graded circular plates

Three-dimensional elastic solutions are obtained for a functionally graded thick circular plate subject to axisymmetric conditions. We consider a isotropic material where the Young modulus depends exponentially on the position along the thickness, while the Poisson ratio is constant. The solution method utilises a Plevako’s representation form which reduces the problem to the construction of a potential function satisfying a linear fourth-order partial differential equation. We write this potential function in terms of Bessel functions and we pointwise assign mixed boundary conditions. The analytic solution is obtained in a general form and explicitly presented by assuming transversal load on the upper face and zero displacements on the mantle; this is done by superposing the solutions of problems with suitably imposed radial displacement. We validate the solution by means of a finite element approach; in this way, we highlight the effects of the material inhomogeneity and the limits of the employed numerical method near the mantle, where the solution shows a large sensitivity to the boundary conditions.