Buckling of Thin Cylindrical Shell Under Hoop Stresses Varying in Axial Direction

1957 ◽  
Vol 24 (3) ◽  
pp. 405-412
Author(s):  
N. J. Hoff
Keyword(s):  
Cylindrical Shell ◽  
Thermal Stresses ◽  
Axial Direction ◽  
Elastic Buckling ◽  
Thin Cylindrical Shell ◽  
Simply Supported ◽  
Buckling Stress ◽  
Compressive Stresses ◽  
Hoop Stresses ◽  
Approximate Formulas

Abstract The buckling of a thin cylindrical shell simply supported along the perimeter of its end sections is analyzed under hoop compressive stresses varying in the axial direction. The thermal stresses arising from a uniform increase in the temperature of the cylinder are determined. It is found that such thermal stresses are not likely to cause elastic buckling. Simple approximate formulas are developed for buckling stress and thermal stress.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Response of Pressurized Cylindrical Shells Subjected to Moving Loads

1972 ◽  
Vol 39 (1) ◽  
pp. 227-234 ◽  
Author(s):  
E. N. K. Liao ◽  
P. G. Kessel
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Axial Direction ◽  
Biaxial Stress ◽  
Steady State Response ◽  
Moving Loads ◽  
Simply Supported ◽  
State Response ◽  
Critical Velocities

This paper presents a theoretical analysis of the dynamic response of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial biaxial stress and subjected to a radial point force that moves uniformly either along the axial direction or the circumferential direction. The analytical solutions are obtained in explicit form for the transient response of the first problem and the steady-state response of the latter problem. Critical speeds are given for both problems. Numerical results for both problems show the effects of the various relevant parameters. The effects of initial biaxial stress on the radial displacement and the critical velocities are presented. The behavior of cylinders beyond the lowest critical velocity is also pointed out.

Theory of Plastic Buckling of Plates and Application to Simply Supported Plates Subjected to Bending or Eccentric Compression in Their Plane

1956 ◽  
Vol 23 (1) ◽  
pp. 27-34
Author(s):  
P. P. Bijlaard
Keyword(s):  
Reduction Factor ◽  
Elastic Buckling ◽  
Plastic Buckling ◽  
Simply Supported ◽  
Buckling Stress ◽  
Plate Buckling ◽  
Eccentric Compression ◽  
Finite Difference Equations ◽  
Longitudinal Bending ◽  
Plate Width

Abstract After some general considerations on the plastic buckling of plates, the plastic buckling stresses are calculated for long plates, subject to longitudinal bending or eccentric compression in their plane, and simply supported at their unloaded edges. The solutions are based on the author’s theory of plastic plate buckling and are obtained by reducing the governing partial differential equation to ordinary finite-difference equations. Second-order finite differences are used, with a spacing equal to one ninth of the plate width. A simple design formula is presented for the plastic reduction factor with which the elastic buckling stress has to be multiplied for obtaining the plastic buckling stress.

The Application of Long and Short Cylindrical Shell Solutions for Stress and Flexibility Determination in a Single Mitred Bend

2016 ◽  
Author(s):  
Igor Orynyak ◽  
Andrii Bogdan ◽  
Iryna Selivestrova
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Bending Moment ◽  
Axial Direction ◽  
Piping System ◽  
Structural Elements ◽  
Thin Cylindrical Shell ◽  
Straight Pipe ◽  
Pipe Bend ◽  
Short Shell

The continuous pipe bend behavior is well elaborated in literature. It is characterized by local ovalization of each cross section during bending which results in enhanced flexibility of it as compared to straight pipe. When pipe bend approaches some other structural elements of a piping system the end effect take place which can be described by so called long shell solution. This long solution is, in fact, a semi-membrane Vlasov’s solution when the derivative of any geometrical or force function in axial direction is much smaller than in the circumferential one [1]. Mitred bend is formed by conjunction by welding of two oblique sections of initially straight pipes. Its behavior during loading by pressure or bending moment is not evident and poorly described in standards. The goal of this paper is to give a set of general functions within a thin cylindrical shell theory which will give the opportunity to consider the mitred bend as an element of a piping system. Here we additionally introduce the so called short solution when the derivative of any parameter in axial direction is much bigger than that in circumferential one. Its main goal is to give the local behavior of stress in the vicinity of the oblique weld. Each of these two solutions satisfy by differential equations of forth order. The complete theoretical solution for a particular mitred bend is compared with a) existing analytical solutions and formulas; b) numerical results obtained by FEM with distinction of the zones of influence of a long as well as short shell solution; c) experimental data on real mitred bends given in the literature.

Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

A new approach for pre-stressing of rail-end-bolt holes

2016 ◽  
Vol 231 (12) ◽  
pp. 2275-2283 ◽  
Author(s):  
JT Maximov ◽  
GV Duncheva ◽  
IM Amudjev ◽  
AP Anchev ◽  
N Ganev
Keyword(s):  
Fatigue Life ◽  
Fatigue Cracks ◽  
New Technology ◽  
Innovative Technology ◽  
Bolted Joint ◽  
Compressive Stresses ◽  
Process Formation ◽  
Technology Process ◽  
Bolt Holes ◽  
Hoop Stresses

Bolted joint railroad is the subject matter of this paper. Rail joint elements are subjected to cyclic and impact loads as a result of the passage of trains, which causes the origination and growth of fatigue cracks occurring, in most cases, around the bolt holes. Fatigue failure around rail-end-bolt holes is particularly dangerous because it leads to derailment of trains and, consequently, to inevitable accidents. Moreover, the cracking at rail-ends, which starts from bolt hole surface, causes premature rails replacement. The presence of residual compressive hoop stresses around the bolted holes, which is achieved by prestressing of these holes, extends the fatigue life of bolted joint railroads. This article presents an innovative technology for pre-stressing of rail-end-bolt holes, implemented on a vertical machining centre of Revolver vertical (RV) type. Two consecutive operations are involved in the manufacturing technology process: formation of the hole by drilling, reaming and making of a chamfer through a new combined cutting tool; cold hole working by spherical motion cold working through a new tool equipment, which minimizes the axial force on the reverse stroke. The new technology introduces beneficial residual compressive stresses around the bolted holes thereby preventing the fatigue cracks growth and increasing the fatigue life of these openings.

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