Shape and thickness optimization of thin-walled pressure vessel end closures

CATEGORY: PRESSURE VESSELS
EngOpt 2012 – 3rd International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 01 - 05 July 2012.
Shape and thickness optimization of thin-walled pressure vessel end closures
Jacek KruŜelecki and Rafał Proszowski
Jacek.Kruzelecki@pk.edu.pl
Proszowski.Rafal@gmail.com
Cracow University of Technology, Jana Pawła II 37, 31-864 Kraków, Poland
Abstract
Authors investigate the problem of shape and thickness optimization of thin-walled pressure vessel heads. They look for optimal geometry of a closure, which minimizes the design objective containing both depth and capacity or both depth and volume of the material of a closure (two variants) in the class of the uniform strength structures.  They consider three types of optimization problems are considered: the optimal shape is sought for a prescribe wall thickness, the optimal wall thickness is sought for a prescribed shape of a closure and the case when they look for both shape functions.
Domes consisting of both two- and one-arc are considered. The optimal solutions are obtained using the simulated annealing algorithm.
Introduction
Circular cylindrical pressure vessels can be closed at the ends by different types of closures. Most pressure vessels are closed by convex torispherical, ellipsoidal, or hemispherical heads. Geometry for the heads mentioned above is defined by two different meridional curvatures. Hence, such domes are called two-arc pressure vessel heads. On the other hand, ellipsoidal and hemispherical domes are called one-arc heads. Such structural elements are, in general, standardized but they can also be manufactured as special designs. In such cases, shape of the middle surface as well as thickness of the closure can differ from those prescribed in the standards. Smooth and appropriately supported, axially symmetric shells under uniform pressure can be considered as structures in the membrane stress state. However, at the junction between a cylindrical shell and a vessel head there is discontinuity of meridional curvatures.
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