whole_RishRaphaelFoner1971_thesis.pdf (6.2 MB)

# Some studies in elastic shell structures

thesis

posted on 2023-05-27, 16:17 authored by Rish, RFSECTION A CHAPTER ONE introduces differential equations applied to the bending of a beam on simple supports. The solution is taken in the form of a Fourier series, each term of which satisfies the boundary conditions of the beam. It is shown that a solution of this form produces no constants of integration. The more advanced problem of the beam on elastic supports is then studied and it is shown how the solution to the differential equation is obtained and a table of derivatives drawn up. Particular problems are then solved by consideration of the boundary conditions. CHAPTER TWO considers the , stresses and deformations of a complete cylindrical shell with axi-symmetric loading. The differential equation is derived and shown to be of the same form as that for the beam on an elastic foundation. The solution is used to explain the anticlastic bending of a plate. CHAPTER THREE derives the simplest form of the shell roof equation, that due to Schorer, and introduces an improved method for obtaining the derivatives of the solution. A direct design approach is introduced which is suitable for teaching an undergraduate class the design of a roof with post tensioned edge beams. CHAPTER FOUR develops the membrane theory of cooling towers built up of a number of conical sections. Published results of tests on a model cooling tower are reanalysed to give better agreement with the theory than was obtained at the time. The theory is extended in the form of a computer program to deal with hyperboloid shells. The failures at Ferrybridge are considered and attributed to the analysis of cone-toroid shells as hyperboloids. CHAPTER FIVE applies Schorer's equation to the deformation of a complete cylindrical shell with unsymmetrical loadings. A fourth order differential equation is derived similar to that of the axi-symmetrically loaded case but with smaller roots. The inextensional bending solution for open tanks is developed and used in place of the particular integral in a number of problems of practical interest. CHAPTER SIX describes a method by which the roots of Flugge's equation for complete cylindrical shells can be extracted. It is shown that two sets of roots are obtained, the first identical to the shell with an axi-symmetrical load, the second identical to the shell with an unsymmetric load. SECTION B The method of chapter six is applied to Flugge's shell roof equation and gives rise to a new characteristic equation with explicit roots. A shell roof with post tensioned edge beams is analysed using a Fourier series for the post-tension which converges rapidly. An edge correction is applied to retain compatibility at the ends of the edge beam.

## History

## Publication status

- Unpublished

## Rights statement

Copyright 1971 the author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Thesis (PhD) - University of Tasmania, 1971. Bibliography: l. 75-76## Repository Status

- Open

## Usage metrics

## Categories

No categories selected## Licence

## Exports

RefWorks

BibTeX

Ref. manager

Endnote

DataCite

NLM

DC