Brazier effect of single- and double-walled elastic tubes under pure bending

2015 ◽  
Vol 53 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Motohiro Sato ◽  
Yuta Ishiwata
2013 ◽  
Vol 81 (4) ◽  
Author(s):  
S.V. Levyakov

The paper discusses nonlinear equations of in-plane bending of curved tubes formulated by E. Reissner in terms of two unknown functions and two unknown parameters. To solve the equations, a numerical method based on the finite-difference approximations and Newton–Raphson iteration technique is proposed. Deformations and stresses in tubes of circular and noncircular cross sections are studied for a wide range of geometrical parameters. The accuracy of the equations is evaluated by comparing the numerical results with predictions obtained by a special shell finite element.


Author(s):  
M. Khurram Wadee ◽  
M. Ahmer Wadee ◽  
Andrew P Bassom ◽  
Andreas A Aigner

A variational model is formulated that accounts for the localization of deformation due to buckling under pure bending of thin-walled elastic tubes with circular cross-sections. Previous studies have successfully modelled the gradual process of ovalization of the cross-section with an accompanying progressive reduction in stiffness but these theories have had insufficient freedom to incorporate any longitudinal variation in the tube. Here, energy methods and small-strain nonlinear elastic theory are used to model the combined effects of cross-section deformation and localized longitudinal buckling. Results are compared with a number of case studies, including a nanotube, and it is found that the model gives rise to behaviours that correlate well with some published physical experiments and numerical studies.


1986 ◽  
Vol 14 (1) ◽  
pp. 3-32 ◽  
Author(s):  
P. Popper ◽  
C. Miller ◽  
D. L. Filkin ◽  
W. J. Schaffers

Abstract A mathematical analysis of radial tire cornering was performed to predict tire deflections and belt-edge separation strains. The model includes the effects of pure bending, transverse shear bending, lateral restraint of the carcass on the belt, and shear displacements between belt and carcass. It also provides a description of the key mechanisms that act during cornering. The inputs include belt and carcass cord properties, cord angle, pressure, rubber properties, and cornering force. Outputs include cornering deflections and interlaminar shear strains. Key relations found between tire parameters and responses were the optimum angle for minimum cornering deflections and its dependence on cord modulus, and the effect of cord angle and modulus on interlaminar shear strains.


Author(s):  
V.B. Zylev ◽  
◽  
P.O. Platnov ◽  
I.V. Alferov ◽  
◽  
...  

Author(s):  
Guoqing Jing ◽  
Du yunchang ◽  
Ruilin You ◽  
Mohammad Siahkouhi

Rubber concrete (RC) has been confirmed to be suitable for concrete sleeper production. This paper studies the cracking behaviour of conventional and rubber-reinforced concrete sleepers based on the results of an experimental program. The cracking behaviour in the pure bending zone was analysed up to a load of 140 kN. The crack mouth opening displacement (CMOD) was accordingly measured using a digital image correlation (DIC) method. The DIC results show that the rubber prestressed concrete sleeper (RPCS) has a resistance against crack initiation that is 20% greater than that of the conventional prestressed concrete sleeper (CPCS) under the same loading condition; however, due to the higher crack growth rate of the RPCS, the first crack detected by the operator forms at 60 kN, which corresponds to a strength approximately 9% lower compared with the 65 kN load at which the first crack is detected in the CPCS. Before the first crack (60 kN), the RPCS has a deflection 35% lower than that of the CPCS, but after cracking, at loads of 80 kN, 100 kN and 140 kN, the RPCS has a deflection 15%, 4% and 24% higher than that of the CPCS, respectively.


1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.


2006 ◽  
Vol 06 (04) ◽  
pp. 457-474 ◽  
Author(s):  
M. A. BRADFORD ◽  
A. ROUFEGARINEJAD ◽  
Z. VRCELJ

Circular thin-walled elastic tubes under concentric axial loading usually fail by shell buckling, and in practical design procedures the buckling load can be determined by modifying the local buckling stress to account empirically for the imperfection sensitive response that is typical in Donnell shell theory. While the local buckling stress of a hollow thin-walled tube under concentric axial compression has a solution in closed form, that of a thin-walled circular tube with an elastic infill, which restrains the local buckling mode, has received far less attention. This paper addresses the local buckling of a tubular member subjected to axial compression, and formulates an energy-based technique for determining the local buckling stress as a function of the stiffness of the elastic infill by recourse to a transcendental equation. This simple energy formulation, with one degree of buckling freedom, shows that the elastic local buckling stress increases from 1 to [Formula: see text] times that of a hollow tube as the stiffness of the elastic infill increases from zero to infinity; the latter case being typical of that of a concrete-filled steel tube. The energy formulation is then recast into a multi-degree of freedom matrix stiffness format, in which the function for the buckling mode is a Fourier representation satisfying, a priori, the necessary kinematic condition that the buckling deformation vanishes at the point where it enters the elastic medium. The solution is shown to converge rapidly, and demonstrates that the simple transcendental formulation provides a sufficiently accurate representation of the buckling problem.


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