The Plastic Buckling of Axially Compressed Square Tubes

1992 ◽  
Vol 59 (2) ◽  
pp. 276-282 ◽  
Author(s):  
S. Li ◽  
S. R. Reid
Keyword(s):  
Deformation Theory ◽  
Buckling Analysis ◽  
Rectangular Plates ◽  
Plastic Buckling ◽  
Buckling Mode ◽  
Important Conclusion ◽  
Simply Supported ◽  
Edge Conditions ◽  
Crushing Behavior ◽  
Incremental Theory Of Plasticity

A plastic buckling analysis for axially compressed square tubes is described in this paper. Deformation theory is used together with the realistic edge conditions for the panels of the tube introduced in our previous paper (Li and Reid, 1990), referred to hereafter as LR. The results obtained further our understanding of a number of problems related to the plastic buckling of axially compressed square tubes and simply supported rectangular plates, which have remained unsolved hitherto and seem rather puzzling. One of these is the discrepancy between experimental results and the results of plastic buckling analysis performed using the incremental theory of plasticity and the unexpected agreement between the results of calculations based on deformation theory for plates and experimental data obtained from tests conducted on tubes. The non-negligible difference between plates and tubes obtained in the present paper suggests that new experiments should be carried out to provide a more accurate assessment of the predictions of the two theories. Discussion of the results herein also advances our understanding of the compact crushing behavior of square tubes beyond that given in LR. An important conclusion reached is that strain hardening cannot be neglected for the plastic buckling analysis of square tubes even if the degree of hardening is small since doing so leads to an unrealistic buckling mode.

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.

Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions

1972 ◽  
Vol 39 (2) ◽  
pp. 513-520 ◽  
Author(s):  
L. M. Keer ◽  
B. Stahl
Keyword(s):  
Integral Equations ◽  
Eigenvalue Problems ◽  
Coupled System ◽  
Mode Shapes ◽  
Fredholm Integral Equations ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Edge Conditions ◽  
Dual Series Equations

The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.

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.

VIBRATION AND BUCKLING OF SS-F-SS-F RECTANGULAR PLATES LOADED BY IN-PLANE MOMENTS

2001 ◽  
Vol 01 (04) ◽  
pp. 527-543 ◽  
Author(s):  
JAE-HOON KANG ◽  
ARTHUR W. LEISSA
Keyword(s):  
Beam Theory ◽  
Free Edge ◽  
Free Vibrations ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
One Dimensional ◽  
Simply Supported ◽  
Free Vibration Frequency ◽  
Edge Conditions

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon the Poisson's ratio (ν), results are shown for 0≤ν≤0.5, valid for isotropic materials.

On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates

2014 ◽  
Vol 14 (07) ◽  
pp. 1450020 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Boundary Conditions ◽  
Elasticity Theory ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Transversely Isotropic ◽  
Buckling Analysis ◽  
Transverse Shear Strain ◽  
Rectangular Plates

This paper presents the uniaxial and biaxial buckling analysis of rectangular plates based on new trigonometric shear and normal deformation theory. The theory accounts for the cosine distribution of the transverse shear strain through the plate thickness and on the free boundary conditions on the plate surfaces without using the shear correction factor. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The Navier type solutions for the buckling analysis of simply supported isotropic, transversely isotropic, orthotropic and symmetric cross-ply laminated composite rectangular plates subjected to uniaxial and biaxial compressions are presented. The effects of variations in the degree of orthotropy of the individual layers, side-to-thickness ratio and aspect ratio of the plate are examined on the buckling characteristics of composite plates. The present results are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT) and exact three-dimensional (3D) elasticity theory wherever applicable. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory.

Exact Solutions for the Free Vibrations and Buckling of Rectangular Plates With Linearly Varying In-Plane Loading

2001 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jae-Hoon Kang
Keyword(s):  
Solution Procedure ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Edge Conditions ◽  
Elastically Supported

Abstract 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.

Forced Vibrations of Thin, Elastic, Rectangular Plates with Edges Elastically Restrained Against Rotation

1977 ◽  
Vol 21 (01) ◽  
pp. 24-29
Author(s):  
E. A. Susemihl ◽  
P. A. A. Laura
Keyword(s):  
Bending Moment ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions ◽  
Approach Infinity ◽  
Square Plate ◽  
Elastic Rectangular Plate ◽  
Elastically Restrained ◽  
The Galerkin Method

Polynomial coordinate functions and the Galerkin method are used to determine the response of a thin, elastic, rectangular plate with edges elastically restrained against rotation and subjected to sinusoidal excitation. It is shown that when the flexibility coefficients approach infinity (simply supported edge conditions) the calculated results practically coincide with the exact solution in the case of a square plate when four terms of the expansion are used. Dynamic displacement and bending moment amplitudes are tabulated for different length-to-width ratios, flexibility coefficients, and frequency values.

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.

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