BUCKLING OF RECTANGULAR PLATES WITH INTERNAL HINGE

2001 ◽  
Vol 01 (02) ◽  
pp. 169-179 ◽  
Author(s):  
Y. XIANG ◽  
C. M. WANG ◽  
C. Y. WANG
Keyword(s):  
Design Parameters ◽  
Elastic Buckling ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Wide Range ◽  
Benchmark Solutions

This paper is concerned with the elastic buckling of uniaxially/biaxially loaded rectangular plates with an internal hinge and two opposite sides simply supported. The buckling problem is solved analytically using the Levy method. The exact buckling solutions furnished by the Levy method provide benchmark solutions for such plates with an internal hinge. Extensive buckling results are presented for plates of a wide range of aspect ratios, hinge locations and in-plane loading configurations. Based on these results, the buckling behaviour of plates with an internal hinge may be observed with respect to the aforementioned design parameters.

scholarly journals Semi-Analytical Solution Based on Strip Method for Buckling and Vibration of Isotropic Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohamed A. El-Sayad ◽  
Ahmed M. Farag
Keyword(s):  
Transition Matrix ◽  
Isotropic Plate ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Analytical Results ◽  
Present Technique ◽  
Benchmark Solutions ◽  
Good Agreement

The present paper achieves a semianalytical solution for the buckling and vibration of isotropic rectangular plates. Two opposite edges of plate are simply supported and others are either free, simply supported, or clamped restrained against rotation. The general Levy type solution and strip technique are employed with transition matrix method to develop a semianalytical approach for analyzing the buckling and vibration of rectangular plates. The present analytical approach depends on reducing the strips number of the decomposed domain of plate without escaping the results accuracy. For this target, the transition matrix is expressed analytically as a series with sufficient truncation numbers. The effect of the uni-axial and bi-axial in-plane forces on the natural frequency parameters and mode shapes of restrained plate is studied. The critical buckling of rectangular plate under compressive in-plane forces is also examined. Analytical results of buckling loads and vibration frequencies are obtained for various types of boundary conditions. The influences of the aspect ratios, buckling forces, and coefficients of restraint on the buckling and vibration behavior of rectangular plates are investigated. The presented analytical results may serve as benchmark solutions for such plates. The convergence and efficiency of the present technique are demonstrated by several numerical examples compared with those available in the published literature. The results show fast convergence and stability in good agreement with compressions.

Some Observations on the Compressive Buckling of Rectangular Plates

1963 ◽  
Vol 14 (1) ◽  
pp. 17-30 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Rate Of Change ◽  
Infinite Strip ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Stress Coefficient ◽  
Wide Range ◽  
Elastically Restrained

SummaryThe problem considered is the buckling of a rectangular plate under uniaxial compression. The ends may be either both clamped, both simply-supported or a mixture of the two. The sides may be elastically restrained against both deflection and rotation with any stiffnesses whatsoever. It is shown that the curve of buckling stress coefficient versus side ratio can be deduced in a simple manner from that of a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength for an infinite strip with the same side conditions are known. Some correlations between the curves for the three types of end condition are discussed. It is also shown that if, for some given side ratio, the buckling mode is known, then it is always possible to deduce the rate of change of buckling stress coefficient with side ratio at that point. The argument is based upon an assumption which is shown to give very accurate results in a wide range of cases.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Effect of Shear Deformations on the Bending of Rectangular Plates

1960 ◽  
Vol 27 (1) ◽  
pp. 54-58 ◽  
Author(s):  
V. L. Salerno ◽  
M. A. Goldberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Classical Plate Theory ◽  
Simply Supported ◽  
Wide Range

The three partial differential equations derived by Dr. E. Reissner2, 3 have been reduced to a fourth-order partial differential equation resembling that of the classical plate theory and to a second-order differential equation for determining a stress function. The general solution for the two partial differential equations has been applied to a simply supported plate with a constant load p and to a plate with two opposite edges simply supported and the other two edges free. Numerical calculations have been made for the simply supported plate and the results compared with those of classical theory. The calculations for a wide range of parameters indicate that the deviation is small.

scholarly journals Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

1994 ◽  
Vol 208 (5) ◽  
pp. 307-319 ◽  
Author(s):  
C W Bert ◽  
M Malik
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Free Vibrations ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Classical Boundary ◽  
Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

Deflection and Moment Data for Rectangular Plates of Variable Thickness

1972 ◽  
Vol 39 (3) ◽  
pp. 814-815 ◽  
Author(s):  
P. Petrina ◽  
H. D. Conway
Keyword(s):  
Variable Thickness ◽  
Rectangular Plates ◽  
Direction Parallel ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Plates Of Variable Thickness

Numerical values of deflections and moments are given for uniformly loaded rectangular plates with a pair of opposite sides simply supported and the others either simply supported or clamped. The plates are tapered in a direction parallel to the simply supported sides. Data are given for two tapers and for plate aspect ratios equal to 1 (square plates), 1.5 and 2.

Effect of Nonhomogeneity on Vibration of Orthotropic Rectangular Plates of Varying Thickness Resting on Pasternak Foundation

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Roshan Lal ◽  
Dhanpati
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
The Other ◽  
Thickness Variation ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness ◽  
Aspect Ratios ◽  
Displacement Mode

Free transverse vibrations of nonhomogeneous orthotropic rectangular plates of varying thickness with two opposite simply supported edges (y=0 and y=b) and resting on two-parameter foundation (Pasternak-type) have been studied on the basis of classical plate theory. The other two edges (x=0 and x=a) may be any combination of clamped and simply supported edge conditions. The nonhomogeneity of the plate material is assumed to arise due to the exponential variations in Young’s moduli and density along one direction. By expressing the displacement mode as a sine function of the variable between simply supported edges, the fourth order partial differential equation governing the motion of such plates of exponentially varying thickness in another direction gets reduced to an ordinary differential equation with variable coefficients. The resulting equation is then solved numerically by using the Chebyshev collocation technique for two different combinations of clamped and simply supported conditions at the other two edges. The lowest three frequencies have been computed to study the behavior of foundation parameters together with other plate parameters such as nonhomogeneity, density, and thickness variation on the frequencies of the plate with different aspect ratios. Normalized displacements are presented for a specified plate. A comparison of results with those obtained by other methods shows the computational efficiency of the present approach.

Relationship Between the Elastic Buckling of Square Tubes and Rectangular Plates

1990 ◽  
Vol 57 (4) ◽  
pp. 969-973 ◽  
Author(s):  
S. Li ◽  
S. R. Reid
Keyword(s):  
Cross Section ◽  
Elastic Buckling ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Tube Cross Section ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Edge Conditions

The buckling behavior of axially compressed square tubes is investigated by introducing realistic edge conditions for the panels which correspond to symmetry or antisymmetry in the modes of deformation of the tube cross-section with regard to the diagonals of the section. The results show a number of differences between the buckling behavior of square tubes and of simply-supported plates. This vanishes only for very thin tubes and plates. The comparison between the buckling mode for thinner and thicker tubes suggests an explanation for the existence of compact and noncompact crushing modes in the subsequent crushing of tubes.

Simply supported annular plates transversely loaded by a concentrated force applied at an arbitrary point

1995 ◽  
Vol 30 (3) ◽  
pp. 211-215
Author(s):  
A Strozzi ◽  
E Dragoni ◽  
V Ciavatti
Keyword(s):  
Series Solution ◽  
Annular Plate ◽  
Arbitrary Point ◽  
Experimental Tests ◽  
Concentrated Force ◽  
Simply Supported ◽  
Annular Plates ◽  
Aspect Ratios ◽  
Wide Range ◽  
Plate Geometry

An analysis is performed for a thin, annular plate, simply supported at its inner boundary, free at its periphery, and loaded by a concentrated force applied at any plate position. A purely flexural model is adopted, for which a series solution is obtained with the aid of an algebraic manipulator. Experimental tests are carried out for a specific plate geometry and the results obtained are compared to the analytical forecasts. A diagram is presented which summarizes the plate theoretical deflection by the loaded point for a wide range of aspect ratios of the annular plate and of normalized loaded positions.

Bending of normally loaded simply supported rectangular plates in the large-deflection range

1969 ◽  
Vol 4 (3) ◽  
pp. 190-198 ◽  
Author(s):  
A Scholes ◽  
E L Bernstein
Keyword(s):  
Linear Equations ◽  
Rectangular Plates ◽  
Algebraic Equations ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Out Of Plane ◽  
Linear Differential ◽  
Good Agreement

Means of solving the non-linear differential equations of plate bending are revieweed and a method based on minimizing the corresponding energy integral is selected as offering most advantages. The energy intergral can be approximated either by using finite-difference approximatons or by assuming a form of displacement variation. Two sets of non-linear algebraic equations (in the in-plane and out-of-plane deflections) are thus formed and, by substitution alternately in each set, the resulting linear equations are solved. Results for simply supported rectangular plates have been worked out in some detail; these are compared with tests made on plates of various aspect ratios. Good agreement on maximum values of stress and deflection was obtained.

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