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.   


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.




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.