• Journal of Korean Society of Steel Construction
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• v.13 no.2
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• pp.191-200
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• 2001

This paper presents buckling analysis of the cylindrical shell subjected to axial loads using numerical method. The modeling method, appropriate element type, and number of element are recommended by comparing with analytical solution. Based on the parametric study, buckling stress decreases significantly as the diameter-thickness ratio increases. These results are different from those obtained from buckling analysis of columns. The number of buckling half-wave in circumferential direction decreases as the diameter-height ratio increases. Buckling stress increases 1~2% as the thickness of base plate increases. Therefore the effect of base plate on buckling strength for cylindrical shell can be disregarded. Buckling stress significantly decreases as the amplitude of initial geometric imperfection used for calculating buckling stress is developed and it shows a good agreement with numerical results.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.87-103
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• 2015

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake's length and thickness on the critical buckling load.

• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Journal of the Korean Society of Marine Environment & Safety
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• v.23 no.3
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• pp.313-319
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• 2017

Cylindrical shells are often used in ship structures at deck plating with a camber, side shell plating at fore and aft parts, and bilge structure part. It has been believed that such curved shells can be modelled fundamentally by a part of a cylinder under axial compression. From the estimations with the usage of cylinder models, it is known that, in general, curvature increases the buckling strength of a curved shell subjected to axial compression, and that curvature is also expected to increase the ultimate strength. We conduct series of elasto-plastic large deflection analyses in order to clarify the fundamentals in buckling and plastic collapse behaviour of cylindrical shells under axial compression. From the numerical results, we derive design formula for predicting the ultimate strength of cylindrical shell, based on a series of the nonlinear finite element calculations for all edges, simply supporting plating, varying the slenderness ratio, curvature and aspect ratio, as well as the following design formulae for predicting the ultimate strength of cylindrical shell. From a number of analysis results, fitting curve can be developed to use parameter of slenderness ratio with implementation of the method of least squares. The accuracy of design formulae for evaluating ultimate strength has been confirmed by comparing the calculated results with the FE-analysis results and it has a good agreement to predict their ultimate strength.

• Steel and Composite Structures
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• v.29 no.4
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• pp.557-567
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• 2018

Cylindrical shell structures buckle at service loads which are much lower than their associated theoretical buckling loads. The main source of this discrepancy is the presence of various imperfections which are created on the cylinder body during different processes as manufacturing, handling, assembling and machining. Many cylindrical shell structures are still designed against buckling based on the experimental data introduced by NASA SP-8007 as conservative lower bound curves. This study employed the numerical based Linear Buckling mode shape Imperfection (LBMI) method and modified it using a stochastic method to assess the effect of geometrical imperfections in more details on the buckling of cylindrical shells with and without the cutout. The comparison of results with those obtained from the numerical Simcple Perturbation Load Imperfection (SPLI) method for cylinders with and without cutout revealed a good correlation. The effect of two parameters of size and number of cutouts on the buckling load was investigated using the linear buckling and Modified LBMI methods. Results confirmed that in cylinders with a small cutout inserting geometrical imperfection using either SPLI or modified LBMI methods significantly reduced the value of the predicted buckling load. However, in cylinders with larger cutouts, the effect of the cutout is dominant, thus considering geometrical imperfection had a minor effect on the buckling loads predicted by both SPLI and modified LBMI methods. Furthermore, the modified LBMI method was employed to evaluate the combination effect of cutout numbers and size on the buckling load. It is shown that in small cutouts, an increasing in the cutout size up to a certain value resulted in a remarkable reduction of the buckling load, and beyond that limit, the buckling loads were constant against D/R ratios. In addition, the cutout number shows a more significant effect on decreasing the buckling load at small D/R ratios than large D/R ratios.

• Earthquakes and Structures
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• v.27 no.2
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• pp.97-111
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• 2024

In this paper, buckling conditions and retrofitting of cylindrical steel water storage tanks with different roof types and wall thicknesses were investigated by using finite element method. Four roof types of cylindrical steel tanks which are open-top, flat-closed, conical-closed and torispherical-closed and three wall thicknesses of 4, 6 and 8 mm were considered in FE modeling of cylindrical steel tanks. The roof shapes significantly affect load distribution on the tank shell under the seismic action. Composite FRP materials are widely used for winding thin-walled cylindrical steel structures. The retrofitting efficiency of cylindrical steel water tank is tested under the seismic loading with the externally bonded CFRP laminates. In retrofitting of cylindrical steel tank, the CFRP composite material coating method was used to improve of seismic performance of cylindrical steel tanks. ANSYS software was used to analyze the cylindrical steel tanks and maximum equivalent (von-Mises) and directional deformation were obtained. Equivalent (von-Mises) stresses significantly decreased due to the coating of the tank shell with FRP composite material. In thin-walled steel structures, excessive stress causes buckling and deformations. Therefore, retrofitting led to decrease in stress, reductions in directional and buckling deformation of the open-top, flat-closed, conical-closed and torispherical-closed tanks.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.1
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• pp.1-8
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• 1985

The buckling characteristics of cylindrical shells with a circular hole, under axially compressed loads, have been analyzed and the results have been compared with existed experimental results. Deflection function with decay factor is assumed, and stress distribution around a circular hole in tensioned infinite plate is used for formulating buckling energy function. Applying Rayleigh Ritz procedure to this energy function, characteristic equation of eigenvalue problem is determined. Buckling load is defined by the minimum value of eigenvalues calculated according to several decay factors, and as the radius ratios of a circular hole (a/R) and shell thickness ratios (R/t) are varied, the reducing characteristics of buckling load are studied. As a result, buckling loads are reduced by about 50% according to some radius ratios ($a/R{\geq}0.15$) of circular hole and are not nearly affected by shell thickness ratio(R/t).

• Steel and Composite Structures
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• v.22 no.2
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• pp.301-321
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• 2016

The objective of this paper is to investigate buckling behavior of composite laminated cylinders by using semi-analytical finite strip method. The shell is subjected to deformation-dependent loads which remain normal to the shell middle surface throughout the deformation process. The load stiffness matrix, which is responsible for variation of load direction, is also throughout the deformation process. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on the first-order shear deformation theory with Sanders-type of kinematic nonlinearity. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridional direction and truncated Fourier series along with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, which is responsible for variation of load direction, is also derived for each strip and after assembling, global load stiffness matrix of the shell is formed. The numerical illustrations concern the pressure stiffness effect on buckling pressure under various conditions. The results indicate that considering pressure stiffness causes buckling pressure reduction which in turn depends on various parameters such as geometry and lay-ups of the shell.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.5
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• pp.150-156
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• 2000

The objective of this study is to investigate effects of prebuckling on the buckling of laminated composite cylindrical shells. Axial compression and lateral pressure are considered for laminated composite cylindrical shells with the ratios of length to radius. The shell walls are made of a laminate with several symmetric ply orientations. The study was made using finite difference energy method, utilizing the nonlinear bifurcation branch with nonlinear prebuckling displacements. The results are compared to the buckling loads determined when membrane prebuckling displacements are considered. Review the influence of nonlinear prebuckling for the buckling loads, the difference between the actual and classical buckling loads are increased as the increments with the ratios of length to radius, for which is applied the axial compression, but almost same for the lateral pressure.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.3
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• pp.13-20
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• 1994

The effects of prebuckling on the buckling of laminated composite cylindrical shells are investigated. Both axial compression and lateral pressure are considered for laminated composite cylindrical shells with length to radius ratios usually associated with container vessels. The shell walls are made of a laminate with several symmetric ply orientations. The study was made using finite difference energy method, utilizing the nonlinear bifurcation branch with nonlinear prebuckling displacements. The results are compared to the buckling loads determined when prebuckling displacements are neglected.