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from Jan Blachut, Department of Mechanical Engineering, The University of Liverpool.
P is the external hydrostatic pressure.
P(bif.cyl) is the buckling pressure of a perfect short cylindrical shell of length L(o), thickness t(o) and radius R(o).
Delta is the amplitude of the outward bowing of the generators of the cylindrical shell.
The profile of the shell generator was searched for within the domain of generalized ellipses in order to maximize the critical hydrostatic pressure for each value of delta.
See the paper: J. Blachut & P. Smith, "Static stability of barrelled shells under hydrostatic pressure" Proceedings ICPVT-10, July 7-10, 2003, Vienna, Austria
ABSTRACT: The paper discusses the static stability of bowed out steel shells subjected to uniform external pressure. Parametric studies have indicated that the largest increase in the load carrying capacity is obtained for a single segment barrel. All multi-segment barrels appear to be weaker than an equivalent single segment barrel. As a result of detailed computations, two shell configurations have been identified for experimental benchmarking. Details about four laboratory scale, CNC-machined steel barrels are given in the paper.
Also see the paper: J. Blachut, "Optimum barreling of steel shells via simulated annealing algorithm", Computers & Structures, Vol. 81 (2003), pp. 1941-1956
ABSTRACT: The load carrying capacity, of externally pressurised and optimally shaped metallic shell, has been increased by 40% over the performance of an equivalent cylinder. The optimal geometry has been sought within a class of generalised ellipses by the application of simulated annealing algorithm.
The optimal solution has been verified experimentally by collapsing two, nominally identical, CNC-machined, mild steel shells at about 17 MPa. The wall thickness of the optimal shell was about 2.6 mm, its height was about 100 mm and its diameter was 200 mm. The effect of initial geometric imperfections on the ultimate load is also discussed. The comparison of theoretical and experimental results is good.
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