This web page has been created as part of a civil engineering MEng thesis at the University of Edinburgh. The work undertaken in this project is a contribution towards real ongoing research in the field of thin dome shells.
A thin dome shell structure is defined
as a shell with a thickness that is very small relative to its other dimensions
and has a geometry that is spherical or domed in shape.
Background
The analysis in to the buckling strength of thin dome shell structures has
become of increased importance within the last couple decades. This can be
attributed to several reasons; Firstly, the number of applications that these
structures can be applied to has increased in such areas as fuel tanks, water
tanks, silos, storage buildings, roof structures, spacecraft, rockets and submarines. Secondly, advancements in computer technology
has allowed designers to develop and expand on previous methods for analysing
shell structures in order to produce more effective and efficient models.
Finally, a greater knowledge of the behaviour of structures in general has allowed
designers to better their understanding in this area of the engineering field.
History
Engineers as far
back as 537AD have exploited the geometry of the dome shape to span large areas
in structures due to its effectiveness in carrying loads, evident in the mosque
of Hagia Sophia in present day Istanbul.
Another famous, but more recent example of this dome shape
is St.Paul’s Cathedral in London which was completed in 1710 by Sir Christopher
Wren.Some of the first calculations of the buckling pressures of complete
spherical shells were made by Zoelly (1915) and Scherwin (1922) who considered displacements as being symmetrical
with respect to diameter, and van der Neut (1932) who considered unsymmetrical
displacements. An extensive investigation in to the behaviour of
the clamped shallow shell began in 1954 with Kaplan and Fung, partly
because it presented some unique problems of its own and partly because
many of the practical applications involved partial rather than complete
shells.
With
advancements in electronic computing technology came increased interest
in to the analytical solutions of the problem. In 1959 Bernard
Budiansky obtained an analytical prediction for symmetrical buckling of
clamped spherical shells which closely resembled the behaviour of
experimental results. Budiansky concluded that the strange behaviour of
the shell was due to interferences between the prebuckled deformation
and succeeding buckling modes. He also determined the influence of an
initial imperfection mode and concluded that an investigation in to the
effect of non-symmetric deflections should take place.
Recent numerical parametric studies using a series of geometrically nonlinear elastic analyses has been carried out by Wunderlich and Albertin (2002). The study examined geometrically perfect and imperfect shells of constant wall thickness and made of elastic-plastic material, provided with different boundary conditions, and subjected to uniform external pressure.
This emphasises, in
part, the difficulty of the problem as engineers and designers have yet to produce a
model that easily predicts the behaviour of these structures despite extensive analysis.
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