Low Buckling Loads of Axially Compressed Conical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 384-392 ◽  
Author(s):  
M. Baruch ◽  
O. Harari ◽  
J. Singer
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Plane Boundary ◽  
Essential Difference ◽  
Physical Reason ◽  
Buckling Loads ◽  
Conical Shells ◽  
Simple Supports ◽  
Interaction Curves ◽  
The Stability

The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell-type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expression for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the “classical” ones are obtained for all but the stiffest simple supports SS4 (v = u = 0). Except for short shells, the effects do not depend on the length of the shell. The physical reason for the low buckling loads in the SS3 case is explained and the essential difference between cylinder and cone in this case is discussed. Buckling under combined axial compression and external or internal pressure is studied and interaction curves have been calculated for the 4 sets of in-plane boundary conditions.

General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure

1965 ◽  
Vol 16 (2) ◽  
pp. 187-204 ◽  
Author(s):  
M. Baruch ◽  
J. Singer
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Cross Section ◽  
Contact Surface ◽  
Critical Pressure ◽  
Boundary Work ◽  
Conical Shells ◽  
Circular Conical Shells ◽  
Simple Supports ◽  
The Stability

SummaryDonnell type equilibrium and stability equations are derived for stiffened thin conical shells. The stiffeners are considered closely spaced and are therefore assumed to be “distributed” over the whole surface of the shell. In the proposed theory the stiffeners and their spacing may vary in any prescribed manner, but here only equal and equally spaced stiffeners are dealt with. The force- and moment-strain relations of the combined stiffener-sheet cross section are determined by the assumption of identical normal strains at the contact surface of stiffener and sheet.The stability equations are solved for general instability under hydrostatic pressure by the method of virtual displacements. The solution used earlier for unstiffened conical shells, which satisfies some of the boundary conditions of simple supports only approximately, is again applied here. The effect of this incomplete compliance with boundary conditions is shown to be negligible by consideration of “boundary work”. The solution proposed for stiffened conical shells involves the concepts of “correcting coefficients” and minimisation of corresponding “error loads”.Typical examples are analysed and the effect of eccentricity of stiffeners is investigated. Simplified approximate formulae for the critical pressure of frame-stiffened conical shells are also proposed.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Buckling of Truncated Conical Shells Under Combined Axial Load, Pressure, and Heating

1985 ◽  
Vol 52 (2) ◽  
pp. 402-408 ◽  
Author(s):  
J. Tani
Keyword(s):  
Axial Load ◽  
Uniform Pressure ◽  
Uniform Heating ◽  
Buckling Mode ◽  
Load Pressure ◽  
Buckling Loads ◽  
Conical Shells ◽  
Shell Equations ◽  
The Difference ◽  
Interaction Curves

On the basis of the Donnell-type shell equations with the effect of nonlinear prebuckling deformations taken into consideration, a theoretical analysis is performed on the buckling of clamped truncated conical shells under two loads combined out of uniform pressure, axial load, and uniform heating. The problem is solved by a finite difference method. It is found that the interaction curves of buckling loads are changed remarkably by the difference in the shape of conical shells. This is due to the large nonlinear prebuckling deformation and the difference in the buckling mode between two cases of single load.

On the Buckling of Functionally Graded Cylindrical Shells Under Combined External Pressure and Axial Compression

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. Khazaeinejad ◽  
M. M. Najafizadeh ◽  
J. Jenabi ◽  
M. R. Isvandzibaei
Keyword(s):  
Axial Compression ◽  
Interaction Parameter ◽  
Numerical Study ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
External Pressure ◽  
Functionally Graded ◽  
Buckling Loads ◽  
Graded Material ◽  
The Stability

The stability problem of a circular cylindrical shell composed of functionally graded materials with elasticity modulus varying continuously in the thickness direction under combined external pressure and axial compression loads is studied in this paper. The formulation is based on the first-order shear deformation theory. A load interaction parameter is defined to express the combination of applied axial compression and external pressure. The stability equations are derived by the adjacent equilibrium criterion method. These equations are employed to analyze the buckling behavior and obtain the critical buckling loads. A detailed numerical study is carried out to bring out the effects of the power law index of functionally graded material, load interaction parameter, thickness ratio, and aspect ratio on the critical buckling loads. The validity of the present analysis was checked by comparing the present results with those results available in literature.

Effects of Shearing Loads and In-Plane Boundary Conditions on the Stability of Thin Tubes Conveying Fluid

1979 ◽  
Vol 46 (4) ◽  
pp. 779-783 ◽  
Author(s):  
J. Tani ◽  
H. Doki
Keyword(s):  
Boundary Conditions ◽  
Fourier Integral ◽  
Integral Theory ◽  
Plane Boundary ◽  
Simply Supported ◽  
Thin Walled ◽  
Shell Equation ◽  
Divergence Velocity ◽  
The Stability ◽  
Conveying Fluid

The hydroelastic stability of short, simply supported, thin-walled tubes conveying fluid is examined with an emphasis on the effects of shearing loads and in-plane boundary conditions. The Donnell shell equation is used in conjunction with linearized, potential flow theory. The solution is obtained by using Fourier integral theory and Galerkin’s method. It is found that an increase of the shearing load reduces the critical divergence velocity and raises the corresponding number of circumferential waves. A change in the in-plane boundary conditions exerts the significant effect on the critical divergence velocity of short tubes.

Buckling of Truncated Cones With Localized Imperfections

2012 ◽  
Author(s):  
J. Błachut
Keyword(s):  
Axial Compression ◽  
Wall Thickness ◽  
External Pressure ◽  
Buckling Load ◽  
Buckling Loads ◽  
Conical Shells ◽  
Buckling Strength ◽  
Shape Deviations ◽  
Combined Action ◽  
Axisymmetric Shape

The paper shows that both the inward and outward bulge-type axisymmetric shape imperfections can significantly lower the buckling strength of steel conical shells. The FE results are provided for: (i) axial compression, (ii) external pressure, and (iii) combined action of both loads. Sensitivity of buckling loads to outward bulges has not been generally known or expected. It is shown that the sensitivity of buckling load depends not only on the shape, amplitude but also on the position of the imperfection along the slant. Geometry of recently tested cones was also used in order to assess the influence of measured shape deviations on the buckling strength. The amplitudes of imperfections in these machined models were small (up to 5 % of wall thickness). As a result their influence on the buckling strength was found to be negligible.

scholarly journals Buckling of Joined Composite Conical Shells Using Shear Deformation Theory under Axial Compression

2019 ◽  
pp. 574-584
Author(s):  
Mohammad Hadi Izadi ◽  
Hosseini Hashemi Shahrokh ◽  
Moharam Habibnejad Korayem
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Axial Compression ◽  
Deformation Theory ◽  
Separation Of Variables ◽  
Shear Deformation Theory ◽  
Power Series Method ◽  
Buckling Loads ◽  
Conical Shells ◽  
First Order

This paper investigates critical buckling loads in joined conical shells under axial compression. An analytical approach has been applied to study classical linear buckling of joined cones that are made of cross-ply fiber reinforced laminates. The governing equations have been extracted using first-order shear deformation theory (FSDT), and an analytical solution has been applied to extract critical buckling loads. Accordingly, the system of partial differential equations has been solved via separation of variables using Fourier expansion and power series method. The effects of the number of layers, lamination sequences, semi-vertex angles, shell thicknesses, shell lengths and boundary conditions on the stability of joined cones have been examined. For validation, the specific examples of the present study have been compared to previous studies. Using ABAQUSE/CAE software (a FEM-based software), the results of finite element have been extracted. The present method is in good agreement with the finite element and other research results. Finally, the differences in classical shell theory (CST) of Donnell type and first-order shear deformation theory have been discussed for different shell thicknesses.

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