Axisymmetrical Buckling of Circular Cones Under Axial Compression

1956 ◽  
Vol 23 (4) ◽  
pp. 625-628
Author(s):  
Paul Seide

Abstract The axisymmetrical buckling of right circular cones under axial compression is investigated. A simple expression is obtained for long cones of constant thickness, relating the cone buckling load to the buckling load of a long cylinder of equal thickness and the cone semivertex angle.

2011 ◽  
Vol 11 (02) ◽  
pp. 215-236 ◽  
Author(s):  
MATTEO BROGGI ◽  
ADRIANO CALVI ◽  
GERHART I. SCHUËLLER

Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.


1974 ◽  
Vol 18 (01) ◽  
pp. 55-61
Author(s):  
Vincent Volpe ◽  
Youl-Nan Chen ◽  
Joseph Kempner

A stability analysis of an infinitely long web-stiffened, circular cylindrical sandwich shell under uniform axial compression is presented. The formulation begins with the establishment of a set of suitable large-deflection shell equations that forms the basis for the subsequent development of the buckling equations. The mathematical model corresponds to two face layers that are considered as thin shells and a thick core that is capable of resisting both transverse shear and circumferential extension. The associated eigenvalue problem is solved. Results show that the lowest buckling load is associated with the axisymmetric mode and is less than one half the buckling load of an equivalent single-layer shell.


2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.


1969 ◽  
Vol 36 (4) ◽  
pp. 791-798 ◽  
Author(s):  
M. M. Lei ◽  
Shun Cheng

A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.


2017 ◽  
Vol 17 (03) ◽  
pp. 1750034 ◽  
Author(s):  
Jin-Song Lei ◽  
Wei-Bin Yuan ◽  
Long-Yuan Li

In this paper, the axial compression buckling problem of castellated columns about the major axis when exposed to a fire is investigated. An analytical formula for calculating the critical buckling load of castellated columns is derived, which considers not only the shear deformation effect of web openings but also the non-uniform cross-section temperature distribution due to non-symmetric fire exposure. The results show that for the same average temperature, the critical buckling load of a castellated column with non-uniform temperature distribution is smaller than that of a castellated column with uniform temperature distribution. The web shear effect caused due to web openings can significantly reduce the critical buckling load of the castellated column, particularly for the columns with shorter lengths or wider flanges. However, the change of the shear effect on the critical load with different temperature distributions is very small and can be generally ignored.


1965 ◽  
Vol 9 (02) ◽  
pp. 9-10
Author(s):  
William P. Vafakos

Sufficient conditions are presented under which an increase (decrease) of the flexural, torsional, or extensional stiffness in any part of a structure cannot result in a decrease (increase) of the classical buckling load. A problem of axisymmetric buckling of a ringstiffened circular cylindrical shell under axial compression is considered for illustration.


1986 ◽  
Vol 53 (1) ◽  
pp. 130-134 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
N. Olhoff

We consider columns attached to elastic foundations and compressed by axial end loads. Pinned-pinned, clamped-clamped, and pinned-clamped boundary conditions are treated. The columns have rectangular sandwich cross sections with a fixed lightweight core and identical face sheets of variable thickness. For given total volume, we optimize the variation of the thickness along the column so as to maximize the buckling load. In most cases, the optimal design is bimodal (i.e., associated with two buckling modes). The optimal designs depend on the foundation stiffness, and the largest increase in buckling load relative to a column with constant thickness is 22 percent.


1956 ◽  
Vol 23 (2) ◽  
pp. 191-194
Author(s):  
Paul Seide

Abstract The torsional rigidity of rectangular sandwich plates of constant thickness is calculated, with cross sections assumed free to warp. The faces are isotropic and of equal thickness while the core may be orthotropic, the axes of orthotropy coinciding with co-ordinate axes of the structure.


2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Eduards Skukis ◽  
Olgerts Ozolins ◽  
Janis Andersons ◽  
Kaspars Kalnins ◽  
Mariano A. Arbelo

Applicability of the vibration correlation technique (VCT) for nondestructive evaluation of the axial buckling load is considered. Thin-walled cylindrical shells with and without circular cutouts have been produced by adhesive overlap bonding from a sheet of aluminium alloy. Both mid-surface and bond-line imperfections of initial shell geometry have been characterized by a laser scanner. Vibration response of shells under axial compression has been monitored to experimentally determine the variation of the first eigenfrequency as a function of applied load. It is demonstrated that VCT provides reliable estimate of buckling load when structure has been loaded up to at least 60% of the critical load. This applies to uncut structures where global failure mode is governing collapse of the structure. By contrast, a local buckling in the vicinity of a cutout could not be predicted by VCT means. Nevertheless, it has been demonstrated that certain reinforcement around cutout may enable the global failure mode and corresponding reliability of VCT estimation.


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