Research Papers

On the Stability and Postbuckling Behavior of Shells With Corrugated Cross Sections Under External Pressure

[+] Author and Article Information
Nikolai P. Semenyuk

SP Timoshenko Institute of Mechanics,
National Academy of Sciences of Ukraine,
ul.Nesterova 3,
Kiev 03057, Ukraine
e-mail: mikolasem@mail.ru

Alexandre I. Morenko

The Chair of Higher Mathematics and IT,
Surgut State Pedagogical University,
Artema St. 9,
Surgut 628400, Russia
e-mail: alexandremorenko@hotmail.com

Michael J. A. Smith

Department of Mathematics,
The University of Auckland,
Private Bag 92019,
Auckland 1012, New Zealand
e-mail: m.smith@math.auckland.ac.nz

1Corresponding author.

Manuscript received August 16, 2012; final manuscript received March 20, 2013; accepted manuscript posted March 21, 2013; published online August 22, 2013. Assoc. Editor: George Kardomateas.

J. Appl. Mech 81(1), 011002 (Aug 22, 2013) (8 pages) Paper No: JAM-12-1402; doi: 10.1115/1.4024077 History: Received August 16, 2012; Revised March 20, 2013; Accepted March 21, 2013

The problem of determining the deformation of a longitudinally corrugated, long cylindrical shell under external pressure is considered. The topics that are covered can be summarized as follows: the formulation of a boundary value problem for the incremental approach as a normal system of differential equations under appropriate boundary conditions, the determination of postbuckling behavior characteristics for cylindrical shells using the discrete orthogonalization method, and an analysis of deformation for both closed and open cylindrical shells. In particular, we consider the stability and postbuckling behavior of both isotropic and composite shells. The solution is based on the relationships for the cubic version of nonlinear Timoshenko-type shell theory. A comparison is made with the well-established quadratic version, as well as analytical solutions where applicable. The necessity for using more precise equations to examine the postbuckling behavior of shells is shown. Using this higher-order approach, it is possible to determine the postbuckling behavior with much greater accuracy.

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Fig. 1

Cross section of a cylindrical shell corrugated in the longitudinal direction (N = 5)

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Fig. 2

Arc segment of a cylindrical corrugated shell for the nth iteration

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Fig. 3

Arc segment of a cylindrical corrugated shell for the (n + 1)th iteration

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Fig. 4

Cross section of a cylindrical shell for γ0 = 17π/18, N = 18

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Fig. 5

Relationship between loading and the interior angle γ0

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Fig. 6

Relationship between loading and the number of arc segments N

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Fig. 7

Deformed (dashed curve) and undeformed buckling (solid curve) over the interval π/3 < ϕ < 2π/3

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Fig. 8

Relationship between the deflection and load at the points ϕ = π/2 (curve 1) and ϕ = 3π/4 (curve 2)




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