Buckling of Axially Compressed Long Cylindrical Shell With Elastic Core

1962 ◽  
Vol 29 (2) ◽  
pp. 329-334 ◽  
Author(s):  
J. C. Yao
Keyword(s):  
Cylindrical Shell ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Buckling Mode ◽  
Elastic Core ◽  
Long Cylindrical Shell ◽  
Special Case

This paper presents a theoretical solution to the problem of determining the buckling characteristics of an axially compressed, long, cylindrical shell which contains a solid or elastic core with a modulus lower than that of the shell. The buckling mode is assumed to be sinusoidal in both the axial and circumferential directions, with the bellows mode taken as a special case. Numerical results are obtained for the buckling characteristics of cylinders with solid cores. These results are found similar to those of P. Seide, who considered the bellows buckling mode.

Buckling of a long cylindrical shell containing an elastic core

AIAA Journal ◽  
1965 ◽  
Vol 3 (9) ◽  
pp. 1710-1715 ◽  
Author(s):  
G. HERRMANN ◽  
M. J. FORRESTAL
Keyword(s):  
Cylindrical Shell ◽  
Elastic Core ◽  
Long Cylindrical Shell

Analysis of the buckling of long cylindrical shells embedded in an elastic medium using the energy method

2002 ◽  
Vol 37 (5) ◽  
pp. 375-383 ◽  
Author(s):  
S. L Fok
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Linear Elasticity ◽  
Energy Method ◽  
Surrounding Medium ◽  
Far Field ◽  
Buckling Mode ◽  
Linear Elasticity Theory ◽  
Present Solution ◽  
Long Cylindrical Shell

Buckling of a long cylindrical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure, is reanalysed using the energy method together with a Rayleigh-Ritz trial function. For simplicity, linear elasticity theory is employed and inextensional buckling is assumed. An expression is derived relating the pressure load to the buckling mode number, from which the critical load can be determined. The solution is similar to that given by Forrestal and Hermann using a more elaborate approach. However, the present solution predicts lower buckling load if Poisson's ratio of the surrounding medium is less than 0.5 and hence seems to provide better agreement with experiments.

Buckling of Pipelines With Inconstant Corrosion Subjected to External Hydrostatic Pressure

2006 ◽  
Author(s):  
Jianghong Xue
Keyword(s):  
Cylindrical Shell ◽  
Asymptotic Expansion ◽  
Hydrostatic Pressure ◽  
Equilibrium Analysis ◽  
Constant Thickness ◽  
External Hydrostatic Pressure ◽  
Buckling Mode ◽  
Buckling Modes ◽  
Nominal Thickness ◽  
Long Cylindrical Shell

Methodology to derive analytical solutions for the buckling of pipelines with inconstant corrosion subjected to external hydrostatic pressure is presented. The corroded pipeline is modeled as a non-uniform, infinitely long cylindrical shell with two regions: Region 1 of nominal thickness and Region 2 of reduced, inconstant thickness. Eigen-functions to determine the buckling pressure for the corroded pipeline are derived using asymptotic expansion. Symmetric and anti-symmetric buckling modes are found to occur for pipelines when the corrosion is symmetric about its centerline. In particular, solutions of the buckling mode and the eigenvalues for buckling pressure of the corroded pipeline are obtained when Region 2 has a reduced and constant thickness and are found to converge to the validated solutions obtained from equilibrium analysis.

Shear Buckling of a Clamped Infinitely Long Plate Reinforced by a Stiffener Mesh

1966 ◽  
Vol 17 (3) ◽  
pp. 302-309
Author(s):  
H. W. Parsons ◽  
I. T. Cook
Keyword(s):  
Shear Stress ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Numerical Results ◽  
Theoretical Solution ◽  
The Other ◽  
Clamped Plate ◽  
Longitudinal Stiffeners ◽  
Shear Buckling ◽  
Special Case

SummaryA theoretical solution to the initial buckling under shear stress of a long clamped plate with parallel edges reinforced by a stiffener mesh is obtained. The mesh is formed by two families of stiffeners each evenly spaced. One family consists of longitudinal stiffeners parallel to the edges of the plate and the other consists of diagonal stiffeners inclined to the parallel edges. The flexural and torsional rigidity of the stiffeners are included in the analysis. Numerical results are given for the special case in which the longitudinal stiffeners are absent and the diagonal stiffeners have flexural rigidity only.

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

On the Stresses in a Notched Strip

1952 ◽  
Vol 19 (2) ◽  
pp. 141-146
Author(s):  
Chih-Bing Ling
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Experimental Results ◽  
System Of Linear Equations ◽  
Transverse Bending ◽  
Longitudinal Tension

Abstract In a previous paper by the author (1), a theoretical solution for a notched strip under longitudinal tension is given. The result demands the solution of an infinite system of linear equations. A considerable amount of labor is involved in solving such a system. It seems, however, that the labor can be diminished by adapting to the solution a process known as the promotion of rank. In this paper such a process is described and then applied to solve the problem of a notched strip under transverse bending. The solution of this problem seems also to be new. The numerical results obtained are compared graphically with the experimental results available.

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