The Analysis of Cooling Towers by the Matrix Finite Element Method

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Abstract
As a necessary first step towards the large displacement analysis of the cooling tower structure by the finite element method, an account of the small displacement theory of the SABA family of elements has been given in the first part of the paper. It may be worth repeating the basic considerations which influenced the philosophy in the design of the element: for an economical large displacement analysis to be successful it is essential that the structure should be represented by as few displacement parameters as possible, consistent with an accurate description of the structural behaviour. The SABA element is an axi-symmetrical thin shell element which describes the displacement variation in the circumferential direction by a Fourier series, each term of which is associated with a polynomial for interpolation in the meridional direction. By the devise of interpolating the meridional geometry in the same way, no strain is induced in a rigid-body movement, thus achieving true equilibrium and avoiding serious error in a large displacement calculation. Results of the small displacement analysis by this element for various examples given in Part I agreed accurately with existing solutions by other methods.

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