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Research Papers

Evaluation of Reissner’s Equations of Finite Pure Bending of Curved Elastic Tubes

[+] Author and Article Information
S.V. Levyakov

Department of Engineering Mathematics,
Novosibirsk State Technical University,
Novosibirsk 630092, Russia

Manuscript received July 1, 2013; final manuscript received September 3, 2013; accepted manuscript posted September 12, 2013; published online October 16, 2013. Assoc. Editor: George Kardomateas.

J. Appl. Mech 81(4), 041014 (Oct 16, 2013) (9 pages) Paper No: JAM-13-1268; doi: 10.1115/1.4025414 History: Received July 01, 2013; Revised September 03, 2013; Accepted September 12, 2013

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.

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Figures

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Fig. 1

Cross sections used in the analysis: (a) circular section (A = 0); oval or two-lobe section (A = 0.5 and n = 2); (c) three-lobe section (A = 0.5 and n = 3)

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Fig. 2

Meridional stress distribution over the circular cross section

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Fig. 3

Longitudinal stress distribution over the circular cross section

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Fig. 4

Meridional stress distribution over the oval cross section

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Fig. 5

Longitudinal stress distribution over the oval cross section

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Fig. 8

Half of the cross section as an arch under squeezing load

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Fig. 7

Longitudinal stress distribution over the three-lobe cross section

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Fig. 6

Meridional stress distribution over the three-lobe cross section

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