• Magazine of the Korean Society of Agricultural Engineers
• /
• v.35 no.1
• /
• pp.59-66
• /
• 1993

Ring Sector Plate Supported by Elastic Beam Although all the reinforced concrete circular ring sector plates are elastically supported, it is conventional to simplify their supporting conditions as fixed or simply-supported ones assuming that their supporting beam has infinite stiffness. However, in order to obtain a precise solution, it should be required to consider the stiffness of their supporting beam. As a methodological improvement to the precise analysis, "Reinforced Concrete Model" previously developed by the author was applied to the structural analysis of the reinforced concrete circular ring sector plates with elastically supported beam. The results of analysis in the cases under various conditions of open angle, steel ratio, relative stiffness(EI/DL) between plate and supporting beam were summarized as follows ; 1.Although the effect of relative stiffness between plate and supporting beam varies depending on the magnitude of open angle, in general, it shows the largest when not more than 5.0 and negligible when not less than 10.0. Therefore, it would be considered as fixed supporting condition :in the case of its open angle of 0$^{\circ}$rectangular plates), its stiffness ratio being not less than 10.0 and in the other case of its open angle of 30$^{\circ}$, its stiffness ratio being not less than 5.0. 2.In the rectangular plates, the effect of steel ratio is considerable in no supporting condition, but neglible in the supporting condition. So, the effect of steel ratio should be negligible in the case of the elastically supported circular ring sector plates. 3.However, the effect of steel ratio is much more considerable in the case of the fixed supported circular plates, especially, when steel ratio being not more than 1.0% and stiffness ratio being smaller. So, the effect of steel ratio should be considered in the analysis of reinforced concreate circular ring sector plates with fixed conditions. 4.The effect of open angle is greater in the case of without-supporting beam conditions. However, in the other case of with-supporting beam conditions, the effect is a little bit when open angle of not more than 300 and negligible when open angle of not more than 30$^{\circ}$.

• Computational Structural Engineering
• /
• v.10 no.1
• /
• pp.135-148
• /
• 1997

The main objective of this paper is to analyze the rectangular stiffened plates with two opposite ends elastically restrained and the others simply supported subjected to in-plane bending by Finite Element Method. Another objective is to develope Classical Method analyzing the unstiffened rectangular plates with the above boundary conditions. In order to validate finite element and classical methods, the buckling strengths of the rectangular plates with four simply supported ends, and with two simply supported and the others fixed ends by finite element method and classical method are compared with those of references. In finite element method, elastically restrained ends can be obtained as considering torsional and warping rigidities of end stiffeners. The buckling strengths of the rectangular plates with elastically restrained ends by finite element and classical methods are calculated and compared with each other. In case of stiffened plates, to validate finite element method, the buckling strengths of the rectangular stiffened plates with four simply supported ends, and with two simply supported and the others fixed ends are also compared with those of references. The buckling strengths of the rectangular stiffened plates with elastically restrained ends by finite element method are calculated as solving eigenvalue problems which are obtained as assembling rectangular plate elements and beam elements considered torsional and warping rigidities. The buckling strengths of rectangular stiffened plates according to various positions of rectangular intermediate stiffener, J and I/sub w/ of end stiffeners are also obtained, which are compared to determine the efficient position of intermediate stiffener.

• Structural Engineering and Mechanics
• /
• v.7 no.5
• /
• pp.503-512
• /
• 1999

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer's viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.13 no.1
• /
• pp.25-35
• /
• 2000

The superstructure of general bridge like slab bridge and slab on girder bridge is composed of elastically supported isotropic plate. The objective of this study is to develop the new analysis method for elastically supported plate with general edge beam or girder(boundaries) under arbitrary out of plane loading. The displacement solutions for the macro-element of plate and beam are obtained by solving for the unknown interactive forces and moments at the beam or nodal line locations after satisfying equilibrium equation along the nodal line. The displacement functions for macro-elements ate proposed in single Fourier series using harmonic analysis, and the equilibrium equations of nodal line are composed by using slope-deflection method. The proposed analysis method is programmed by MS-Fortran and can be applied to all types of isotropic decks with bridge-type boundaries. Numerical examples involving elastically supported plates with various aspect ratio, loading cases, and bridge-type boundary conditions are presented to demonstrate the accuracy of this program. The major advantage of this new analysis method is the development of a simple solution algorithm, leads to obtain rapidly responses of bridge deck system. This proposed method can be used in parametric study of behavior of bridge decks.

• Composites Research
• /
• v.12 no.3
• /
• pp.17-25
• /
• 1999

In this paper, we present the analytical study results of buckling behavior of elastically restrained orthotropic plates. In the study the boundary conditions of the plate are simply supported at all four edges and elastically restrained by the elastic medium at opposite two longitudinal edges. The energy method is employed in the solution of the problems in which method the buckling coefficient is calculated from the condition that the work-done by the external forces during buckling is equal to the stored elastic strain energy. The results are presented in the graphical from. The equations derived for the orthotropic plate in this study are compared with existing isotropic ones and identical results were observed.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.15 no.2
• /
• pp.1-11
• /
• 1978

Using the elliptical cylindrical function, the added masses of thin rectangular plates vibrating elastically in an infinite ideal fluid are calculated. For the boundary conditions of the plates, two models are adopted. The plate which is simply-supported on two opposite edges while the other edges are clamped is one and the other is the plate which is simply-supported on two opposite edges while the other edges are free. Same examples are calculated numerically for the fundamental mode in each cases. And the effect of the boundary condition on the added mass are investigated by comparing these data with those of Kim's[4] which were calculated for the simply-supported plates by the same method. It is concluded that it is possible to predict the added mass of a rectangular plate, whose boundary condition is not treated in this report, by using the result of this investigation.

• Journal of Korean Association for Spatial Structures
• /
• v.4 no.4 s.14
• /
• pp.99-111
• /
• 2004

An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

• Structural Engineering and Mechanics
• /
• v.62 no.4
• /
• pp.431-441
• /
• 2017

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.18 no.1
• /
• pp.1-8
• /
• 1981

To contribute to the preventive measures against local vibrations of ship's deck panels, some investigations into the prediction method of the natural frequency of the vibration of stiffened plates were done. Firstly, an analytical method based on the orthotropic plate analogy and the Rayleigh method using eigenfunctions of the Euler beam was shown, and numerical results of a regularly stiffened plate were compared with experimental results. And then, the method was extended to stiffened plates having one or two irregular stiffeners to obtain an approximate formula showing the relation between the change of the natural frequency and the size of the irregular stiffeners. The latter case was investigated for the purpose of providing a convenient design manual applicable to cure of local resonant vibrations of ships' deck panels by additional reinforcement of one or two stiffeners. In the analytical development the boundary was assumed to be rigidly supported and elastically restrained against rotation. In the experiment, however, only an extreme case i.e. simply supported boundary was investigated. The results of the investigation show that there is a fairly good conformity between the analytical results and the experimental ones in the first case, and that the approximate formula for the second case is confirmed also to be reliable for the design purpose. Considering that actual boundary conditions of deck panels in ship structures lie mostly somewhere between the simple support and the fixed, the authors discussed problems of the joint efficiency at the boundary of deck panels from the viewpoint of the practical application of the formulae.

• Composites Research
• /
• v.16 no.5
• /
• pp.28-38
• /
• 2003

In this study, the analytical investigation of orthotropic rectangular plate is presented. The loaded edges are assumed to be simply supported and the unloaded edges could have elastically restrained boundary conditions including the extreme boundary condition such as simple, fixed, and free. Using the closed-form solutions, the buckling analyses of orthotropic plate with arbitrary boundary conditions are performed. Based on the data obtained by conducting numerical analysis, the simplified form of equation for finding the buckling coefficient of plate with elastically restrained boundary conditions at the unloaded edges is suggested as a function of aspect ratio, elastic restraint. and material properties of the plate. The results of buckling analyses by closed-form solution and simplified form of solution are compared for various orthotropic material properties. It is confirmed that the difference of results is less than 1.5%.