Buckling of a Cylindrical Shell Subjected to Nonuniform External Pressure

1962 ◽  
Vol 29 (4) ◽  
pp. 675-682 ◽  
Author(s):  
B. O. Almroth
Keyword(s):  
Cylindrical Shell ◽  
Lateral Pressure ◽  
Circular Cylindrical Shell ◽  
External Pressure ◽  
Buckling Analysis ◽  
Graphical Form ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Ritz Procedure ◽  
The Stability

A buckling analysis is presented for a circular cylindrical shell subjected to nonuniform external pressure. The general approach is not restricted with respect to the distribution of the lateral pressure. However, the final formulation is specialized for the case in which the pressure distribution is of the form p = p0 + p1 cos φ within a centrally located circumferential band. In the buckling analysis the stability criterion is based on the principle of minimum potential energy, and the Rayleigh-Ritz procedure is used to expand the displacement components in trigonometric series. Buckling pressures are computed in terms of nondimensional parameters and are presented in graphical form.

The Flexure of a Uniformly Pressurized, Circular, Cylindrical Shell

1958 ◽  
Vol 25 (4) ◽  
pp. 453-458
Author(s):  
J. D. Wood
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Cross Section ◽  
Circular Cylindrical Shell ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
The Cross ◽  
The Moment

Abstract This paper presents the moment-curvature relationship and the components of displacement in the cross section of a uniformly pressurized, long, closed, circular, cylindrical shell. The shell is loaded in one of its principal planes by two equal and opposite terminal couples: First, the shell undergoes small initial displacements. These are formed by superimposing pressurization displacements upon Saint Venant displacements. Second, from this deformed position the shell is perturbed into a system of additional small displacements. A Rayleigh-Ritz technique is used to find the latter displacements from the theorem of minimum potential energy. The point at which the moment-curvature relationship becomes nonlinear is shown by several curves in this paper.

Carrying Capacity of an Elastic-Plastic Cylindrical Shell With Linear Strain-Hardening

1958 ◽  
Vol 25 (1) ◽  
pp. 79-85
Author(s):  
P. G. Hodge ◽  
S. V. Nardo
Keyword(s):  
Cylindrical Shell ◽  
Carrying Capacity ◽  
Circular Cylindrical Shell ◽  
Maximum Load ◽  
Isotropic Hardening ◽  
Linear Strain ◽  
Minimum Potential Energy ◽  
Rigid Plastic ◽  
Plastic Cylindrical Shell ◽  
Minimum Potential

Abstract The approximate capacity of a thin-walled closed circular cylindrical shell, simply supported at each end and subjected to a uniform hydrostatic pressure, is determined. Elastic and plastic strains are considered, and the latter are assumed to follow a linear law of isotropic hardening. The principle of minimum potential energy is used to determine an approximate solution for the stress resultants, displacements, and maximum load. In an example, it is found that the carrying capacity is considerably lower than that predicted by either rigid-plastic theory or elasticity theory.

Buckling Analysis of a Bi-Directional Strain-Gradient Euler–Bernoulli Nano-Beams

2020 ◽  
Vol 20 (11) ◽  
pp. 2050114
Author(s):  
Murat Çelik ◽  
Reha Artan
Keyword(s):  
Potential Energy ◽  
Gradient Elasticity ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Minimum Potential Energy ◽  
End Conditions ◽  
Graded Material ◽  
Minimum Potential ◽  
Gradient Elasticity Theory ◽  
Basic Equations

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

1971 ◽  
Vol 93 (4) ◽  
pp. 998-1006
Author(s):  
H. S. Ho ◽  
D. P. Updike
Keyword(s):  
Cylindrical Shell ◽  
Velocity Field ◽  
Axial Force ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Yield Condition ◽  
External Pressure ◽  
Tresca Yield Condition ◽  
Stress States ◽  
Range Of Values

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

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.

Nonlinear Buckling Analysis of Long-Span Suspended Latticed Intersected Cylindrical Shell

2014 ◽  
Vol 919-921 ◽  
pp. 169-176 ◽  
Author(s):  
Ming Liang Zhu ◽  
Yan Sun
Keyword(s):  
Cylindrical Shell ◽  
Bearing Capacity ◽  
Single Layer ◽  
Ultimate Bearing Capacity ◽  
Buckling Analysis ◽  
Nonlinear Buckling ◽  
Long Span ◽  
The Stability ◽  
Nonlinear Buckling Analysis ◽  
Material Nonlinear

The Suspended Latticed Intersected Cylindrical Shell (SLICS) is a new structural system, composed by the single layer Latticed Intersected Cylindrical Shell (LICS) and the prestressed cable-strut system. Mechanical properties of this structure were investigated through nonlinear buckling analysis by the consistent imperfect buckling analysis method, compared with the single layer LICS. Structure parameters including prestress level, member section, length of bar, rise-span ratio, obliquity were analyzed. And the effect of material nonlinearity on the stability was studied. Results show that the ultimate bearing capacity of the SLICS is improved as the introduction of prestress. However the prestress level has a limited impact on the ultimate bearing capacity. And the material nonlinear is very important to the stability of the SLICS.

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