UNIMODAL AMD BIMODAL OPTIMAL DESIGN OF ELASTIC TOROIDAL SHELLS SUBJECT TO BUCKLING UNDER EXTERNAL PRESSURE

1988 ◽  
Vol 16 (3) ◽  
pp. 359-386 ◽  
Author(s):  
Jacek Skrzypek ◽  
Jan Bielski
2000 ◽  
Vol 77 (3) ◽  
pp. 233-251 ◽  
Author(s):  
J Błachut ◽  
O.R Jaiswal

Author(s):  
G D Galletly

When perfect, externally pressurized complete circular toroidal shells buckle, the minimum buckling pressure pcr usually occurs in the axisymmetric n = 0 mode, with pcr for n = 2 being only slightly larger. In the present paper, the effects of axisymmetric initial geometric imperfections on reducing pcr for the perfect shell are investigated. Various types of imperfection are studied, i.e. localized flat spots, smooth dimples, sinusoids and buckling mode shapes. The principal geometry investigated was R/b = 10, b/t = 100, although other geometries were also considered. The maximum decrease in buckling resistance, Δ pcr, was found to be about 16 per cent at δ 0/t = 1 and it occurred with smooth dimples at the north (φ = 180°) and south (φ=0°) poles. This value of Δ pcr is not large. Circular toroidal shells thus do not appear to be very sensitive to axisymmetric initial geometric imperfections. The reductions in the buckling pressure of the above shell, arising because of initial imperfections having the shape of the n = 0 and the n = 2 buckling modes, were 12 and 9 per cent respectively for wo/t = 1. These decreases in the buckling resistance are smaller than that for the ‘two smooth dimple’ case mentioned above.


2001 ◽  
Vol 01 (01) ◽  
pp. 31-45 ◽  
Author(s):  
GERARD D. GALLETLY

This paper summarizes the results of numerical studies into the effects of initial geometric imperfections on the elastic buckling behaviour of steel circular and elliptic toroidal shells subjected to follower-type external pressure. The types of initial imperfection studied are (a) axisymmetric localized ones and (b) sinusoidal buckling modes. The principal localized imperfections studied are (i) circular increased-radius "flat spots" and (ii) smooth dimples. The buckling pressures pcr of circular toroidal shells were not very sensitive to initial imperfections. With elliptic toroids, whether the shell was sensitive to initial imperfections or not depended on the ratio k(≡ a/b) of major to minor radii of the section. The shells on the ascending part of the pcr versus k curve behaved like circular toroidal shells, i.e. they were not sensitive to initial imperfections. However, the behaviour of elliptic toroids on the descending part of the versus k curve was very different. The numerical results quoted in the paper are for limited ranges of the geometric parameters. It would be useful to extend these ranges, to explore the effects of plasticity and to conduct model tests on imperfect steel models to verify the conclusions of the numerical studies.


2011 ◽  
Vol 47 (5) ◽  
pp. 545-553 ◽  
Author(s):  
N. P. Semenyuk ◽  
N. B. Zhukova

1997 ◽  
Vol 119 (4) ◽  
pp. 494-497 ◽  
Author(s):  
M. Walker ◽  
T. Reiss ◽  
S. Adali

Finite element solutions are presented for the optimal design of hemispherically and flat-capped symmetrically laminated pressure vessels subjected to external pressure. The effect of vessel length, radius, and wall thickness, as well as bending-twisting coupling and hybridization on the optimal ply angle and buckling pressure are numerically studied. Comparisons of the optimal fiber angles and maximum buckling pressures for various vessel geometries are made with those for a hybrid pressure vessel. The well-known golden section method is used to compute the optimum angle in each case.


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