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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 102
Application of Simulated Annealing to Optimal Barreling of Externally Pressurised Shells J. Blachut
Department of Mechanical Engineering, The University of Liverpool, United Kingdom Full Bibliographic Reference for this paper
J. Blachut, "Application of Simulated Annealing to Optimal Barreling of Externally Pressurised Shells", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 102, 2001. doi:10.4203/ccp.73.102
Keywords: buckling, external pressure, pressure hull, simulated annealing, shell.
Summary
Various optimisation techniques would normally be needed to deal with problems
encountered in practice and these techniques may be classified in a variety of ways.
A useful approach could be based on the type of information that must be provided
in order to find the optimum, e.g. whether the information on gradients of the
objective and constraints is required. A class of methods, requiring only function
values, is collectively known as zero-order search methods. The emphasis has
recently been directed toward new zero-order techniques, which have arisen, at
least in part, from a study of nature and they include, amongst others, genetic
algorithms, simulated annealing and tabu search. This paper applies one of these
methods, i.e. simulated annealing, SA, to structural optimisation of a pressure hull
component.
The paper begins with an overview of the current use of the simulated annealing
technique in structural optimisation. After a brief discussion of generic parameters,
the paper highlights a method, which allows the SA to be used for continuous
domain problems. Next, the shape optimisation of metallic, doubly curved shells
subjected to static external pressure is attempted. The maximum load carrying
capacity is sought within a class of shells with the positive Gaussian curvature in
which the meridional profile is described by generalised ellipses. Both geometrical
non-linearity and material non-linearity are taken into account. It is assumed that
shells are made from mild steel with Young's modulus E = 217 GPa, Poisson's
ratio
Standard SA algorithm with a geometric schedule for lowering temperature has
been adopted. A variable step length was used for generation of a candidate
configuration with the average percentage of accepted moves at about 50% per
temperature level. The epoch length of 20 was assumed and it was kept constant at
all temperature levels. The stopping criterion was based on no change of the cost
function for 10 consecutive iterations. Computational effort of a single re-analysis
is such that a predominantly sequential optimisation tool, such as SA, was capable
to navigate through the non-convex design space in an affordable amount of time.
Whilst it is not certain whether the obtained solution is a global maximum, it offers
some 40% increase over the reference geometry's load bearing capacity. Yielding
of the optimal geometry starts on the inner surface of the barrel at both top and
bottom edges and the maximum, effective, plastic strain at the collapse reaches
3.2%. Calculations have shown that 90% of the cross section has yielded at the
collapse load.
The optimal solution has been verified experimentally by collapsing two,
nominally identical shells. Models, designated here as E1 and E1a, were CNC-
machined from thick, mild steel tube with 180 mm and 310 mm inner and outer
diameters, respectively. Shells were machined with integral top and bottom rings.
After machining to over-sized dimensions both shells were stress relieved at
600
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