Combined ring element/quadrilateral element method for the analysis of shells of revolution with geometric imperfections

Fonseka, Merrennege Chinthaka Manoranjan (1989) Combined ring element/quadrilateral element method for the analysis of shells of revolution with geometric imperfections. University of Southampton, Doctoral Thesis.

Abstract

A Combined Method of Analysis based on the principle of substructuring is developed for the analysis of shells of revolution with geometric imperfections with special reference to hyperbolic cooling tower shells. In this analysis, the shell is basically divided into two parts that is, the Primary structure and the Substructure. The primary structure is modelled with axysymmetric isoparametric ring elements and the substructure is modelled with quadrilateral shell elements which have similar characteristics to the ring element. The two structures are stitched together using the compatibility conditions at the connecting boundaries. The primary structure properties are formulated using a suitable Fourier series (harmonic analysis). The shells of revolutions are generally axisymmetric but if a shell contains localised non-axisymmetric parts such as local geometric imperfections, then the substructure is used to model these parts since the substructure elements are not restricted by the axisymmetric property. This is an efficient way of peforming the analysis rather than modelling the whole structure with quadrilateral elements just because of localised imperfect areas. The Linear Static analysis of shells of revolution using the Combined Method of Analysis gave successful results. A hyperbolic cooling tower structure (Ardeer cooling tower) with axisymmetric and non-axisymmetric imperfections was used in testing the workability of this model. This method has the capability of using the geometric simulation technique to model the imperfection whether it is axisymmetric or non-axisymmetric by amalgamating the assumed geometry of the imperfection pattern with the theoretical shell equations to obtain the necessary geometric parameters in the imperfect zones. Using this model the behaviour of stresses when there are geometric imperfections in the shell can be studied which is very useful in design purposes. These sorts of studies are recommended in the design specifications for cooling tower shells. The Geometrically Non-linear Static analysis of shells of revolution using the Combined Method of Analysis could not be successfully performed because proper convergence could not be obtained when ring elements were used in the analysis. Also the harmonic terms are coupled with each other in the non-linear analysis and this coupling of harmonics makes the analysis complicated and the computer time consumed rises very sharply.

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