Buckling Of Rings Research Articles

Influence of loading behavior on the post buckling of circular rings

(5) Finally, the loading energy of the hydrostatic pressure, which is equal to the product of the external pressure and the difference of the area of the buckled and unbuckled configuration, can be written as Trc = irb + P§(w— wv + vw) dtp (6) Considering the auxiliary condition (due to e = 0) 1 l r ? — (w — v) + ——— [ (w — i ) ) J H ( w + y ) ] = 0 (7) r 2r in eliminating w from Eq. (3), the following components of the potential functional JF= E TT= W2+ W3 + ... are obtained

Closure to “Inelastic Buckling of Rings with Residual Stresses”

Closure to “Inelastic Buckling of Rings with Residual Stresses”

Discussion of “Inelastic Buckling of Rings with Residual Stresses”

Discussion of “Inelastic Buckling of Rings with Residual Stresses”

Interactive design of large end rings on stiffened conical shells using composites

Design study methods and results are presented of a composite reinforced base ring for the conical aeroshell structure of the planetary lander vehicle for Project Viking, an unmanned mission to Mars. The aeroshell is a ring and stringer-stiffened conical shell structure having a half angle of 70° with a large base ring mounted at the outer edge of the cone and a large pay-load ring in the interior with many smaller rings spaced along the inside shell surface. The purpose of the structure is to develop the aerodynamic drag required to decelerate the lander in the Mars atmosphere to facilitate a soft landing. The shell, therefore, must be designed to resist external pressure loads during Martian entry. Unlike conventional shell structures, the Viking aeroshell has no connecting supports at its large diameter edge and, therefore, it must resist the external pressure as an unsupported inertially loaded shell. Very little design information is available on large shell structures under these loading conditions. The structural weight of the aeroshell must be reduced to the minimum possible level while still retaining structural integrity. A currently proposed design for this structure is all metal, and the base ring accounts for 41 per cent of the total aeroshell structural weight. One possible method of reducing the weight of the proposed design is to selectively apply filamentary composites to reinforce a redesigned base ring. The filamentary reinforced base ring must be designed to take into account all possible modes of failure under the maximum design load conditions. The possible modes of failure are local or general buckling of the shell, ring buckling, and exceedence of the maximum permissible stress levels. The design of a shell structure of this complexity requires the use of the latest technology available in a large general purpose shell buckling program. A large general purpose non-linear shell buckling program developed by Lockheed (BOSOR 2) was used. Since the amount of computational effort is considerable for such a study, the turnaround time for using such a program as an aid in the design process was reduced by adapting the program to an interactive real time graphical system using the facilities of the Langley Research Center CDC computer complex. This paper describes the shell structure model and the stability results of a large Langley Research Center Viking aeroshell model, the BOSOR 2 computer program and its adaptation to an interactive system, and the design strategy used to re-design the base ring and the weight savings achieveable by composite reinforcements.

Inelastic Buckling of Rings with Residual Stresses

Circular rings are commonly fabricated by cold rolling long straight bars of desired cross sections to the required radii and then completing them with a single butt weld. This process induces significant amount of residual stress in a ring which affects its in-service performance. Expressions which define the amount of residual stresses in a ring are derived in this paper and are subsequently used to develop inelastic buckling equations. Buckling pressures for rings with various radius-to-diameter ratios are computed for all available structural steels and are presented graphically. It is shown that reductions of up to 35% in buckling pressures occur due to the presence of residual stresses.

On one-dimensional finite-strain beam theory: The plane problem

The paper formulates a one-dimensional large-strain beam theory for plane deformations of plane beams, with rigorous consistency of dynamics and kinematics via application of the principle of virtual work. This formulation is complemented by considerations on how to obtain constitutive equations, and applied to the problem of buckling of circular rings, including the effects of axial normal strain and transverse shearing strain.

Thermal Buckling and Snapping of a Circular Ring

An analysis is made of the thermal buckling of flat rings and of shallow conical rings which are subjected to an axisymmetric temperature distribution. It is found that flat rings can buckle when there is a radial temperature variation only. Conical rings are subject to instability and snapping in the presence of either an axial temperature variation alone, or a combined axial and radial temperature variation, of the proper magnitude. Expressions are developed which give the temperatures at which buckling and snapping take place, as well as the temperature over-lap in a full thermostatic cycle of increasing and decreasing temperatures. Bimetallic conical rings at uniform temperature are examined, and snapping temperatures are determined for this type element.

Ring Buckling of Inflated Drag Bodies

Buckling instability may occur in at least three types of aerodynamic decelerators, toroidal drag bodies, drag cones, and the tucked-back balloon-parachute (Ballute).f Buckling criteria for inflated compression members are reviewed, and tests of inflated columns of Mylar, Dacron-neoprene, and stainless steel-silicone fabrics are reported in support of the theoretical development. The theory is then extended to the buckling of a ring in and out of the plane of its centerline. A drag body consisting of a simple torus connected by a skirt to a forebody is used as an illustrative example.

Erratum: “On the Buckling of Rings Under Constant Directional and Centrally Directed Pressure” (Journal of Applied Mechanics, 1970, 37, pp. 215–218)

Erratum: “On the Buckling of Rings Under Constant Directional and Centrally Directed Pressure” (Journal of Applied Mechanics, 1970, 37, pp. 215–218)

The n.m.r. spectra and conformations of cyclic compounds part V. Mechanism of CH·CH coupling in heterocyclic compounds

The 1H spectra of some five-membered heterocyclic olefins and related compounds are reported and analysed. The observation of some weak, hitherto ignored transitions in the AA′BB′ spectrum of the CH2·CH2 groups removes the deceptive simplicity of the spectrum and gives well determined and non-equal values of Jcis and Jtrans.The mechanisms contributing to the CH·CH couplings in these systems are considered in detail. It is concluded that (a) ring buckle and the known dihedral angle dependence satisfactorily accounts for the values in carbocyclic rings; (b) these contributions plus angle deformations and the orientation of the electronegative substituents account for the values in saturated five-membered heterocyclics. (c) No reasonable combination of these mechanisms provides a quantitative explanation of the large couplings observed in the five-membered heterocyclic olefins investigated.Possible reasons for this are given.

On the Buckling of Rings Under Constant Directional and Centrally Directed Pressure

On the Buckling of Rings Under Constant Directional and Centrally Directed Pressure

On the Buckling of Rings Subject to Impulsive Pressures

It is shown in this paper that previous, independent analyses of the phenomena of dynamic elastic instability and dynamic plastic-flow buckling of circular cylindrical shells can be combined in a single approach leading to results consistent with those that follow from these analyses. The response of the shell in both cases is governed by the interaction between the fundamental radial, purely extensional mode of deformation and inextensional flexural modes always present in the response. An analytical procedure is given for the determination of dominant modes in the elastic and plastic phases of the response, and the results of this procedure are verified by comparison with numerical and experimental data.

Elastic Stability of Radically Nonhomogeneous Rings

A variational theory of elastic stability is applied to the problem of in-plane buckling of rings in which the elastic constants are step functions of the radius, as in sandwich or layer construction. Normally and centrally directed uniform loading conditions are considered. The strain energy is described using the nonlinear theory of elasticity to provide for the effects of ring thickness and nonhomogeneity. Instability criteria are determined by investigating the character of the second variation of the potential energy. Based on numerical examples of the analytical results, design curves for the determination of the critical pressure for two and three element ring configurations are presented. The results of tests using nonhomogeneous specimens composed of nickel, glass fiber-epoxy, and urethane foam are presented.

Bending and Buckling of Thin-Walled Open-Section Rings

The Wagner theory for the bending and buckling of straight bars of thin-walled open section is extended to circular curved bars and rings. The differential equations of equilibrium are determined by a summation of force components, whereas the natural boundary conditions are derived by the minimum potential energy principle. The effects of nonuniform torsion, unsymmetrical loading, elastic foundation, and axial extension are included. The buckling of a ring subjected to a uniform external pressure is treated. The critical pressure is found to be the root of a cubic characteristic equation. Simplified solutions are found by restricting the generality, thereby reducing the characteristic equation to the first order.

A Refinement of the Theory of Buckling of Rings Under Uniform Pressure

Abstract A general variational theory of elastic stability that was originated by E. Trefftz (1) is applied to the problem of buckling of rings of rectangular cross section subjected to uniform external pressure. The theory is believed to be more rigorous than previous treatments of the problem, since it avoids conventional assumptions of curved-beam theory, such as the assumptions that plane sections remain plane and that radial stresses vanish. The classical result of Levy (2) is confirmed for a ring of infinitesimal thickness. New results are obtained which show the effect of the finite thickness of a ring on the coefficients in the buckling formula.

On The Buckling of Elastic Rings

Journal of Mathematics and PhysicsVolume 26, Issue 1-4 p. 94-103 Article On The Buckling of Elastic Rings G. F. Carrier, G. F. Carrier Brown UniversitySearch for more papers by this author G. F. Carrier, G. F. Carrier Brown UniversitySearch for more papers by this author First published: April 1947 https://doi.org/10.1002/sapm194726194Citations: 48AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume26, Issue1-4April 1947Pages 94-103 RelatedInformation