STUDY OF CIRCULAR PLATES OF NON.UNIFORM THICKNESS WITH CENTRAL-HOLE

Abstract

A detailed analytical study of circular plates of non-uniform thickness is made in the present investigation with particular reference to the problem of analysis and design of circular raft foundation slabs, encountered in circular struct- ures like tall elevated water towers, chimney stacks etc. Circular plates with and without a concentric hole with an axi-symmetrical thickness variation are considered and analy-ses of these are obtained for two different types of loading viz., uniformly distributed load p which is axi-symmetrical and linearly varying load which is anti-symmetrical about a diameter. The four cases of the problem thus solved are (a) circular plate with hole subject to an axi-symmetric load (b) circular plate with hole subject to an anti-symmetric load (o) circular plate without hole subject to an axi-symmetric load and (d) circular plate without hole subject to an anti-symmetric load. In all the cases, the plates are simply supported on an intermediate concentric ring support. Solutions of the ordinary and partial, fourth-order linear differential equations governing the problem in the two cases of loading respectively are obtained numerically by finite-difference technique employing the first-order approximations. The scope of solutions attempted is strictly limited to the thin-plate small-deflection theory based on Kirchhoff-Love formulation, For the purposes of analysis four different ratios of the variables involved in the problem are considered. They are, the vi ratios of the thicknesses at the outer and inner boundaries of the plate to the thickness at the ring beam, and the ratios of the radii of the hole and the ring beam support to the plate radius. A wide range of these four ratios is considered for analysis to facilitate a comprehesive study of the problem, A huge number of sets of linear algebraic equations resulting from the finite-difference analysis, embracing the four parts of the problem in question, is solved by employing an algorithm specially suited for band-type matrices. The entire analysis is carried out on a cigital computer and four 'Utility• programs are prepared which can be run on a small computer like IBM 1620, with slight modifications. The results of the analy- - sis of the problem under investigation are presented graphically in a form suitable for utilisation by designers. The suitability of the application of the numerical method and the computer programs is indicated for the analysis of circular plates having any boundary condition at the edge and any thickness variation, 6ubjectod to any type of loading, that can be expressed mathematically; all of these being subject to certain limitations.