The nonlinear behaviour of shallow spherical shells

Hossack, John D.W (1965) The nonlinear behaviour of shallow spherical shells. PhD thesis, University of Glasgow.

Abstract

The subject matter of the thesis concerns the instability of shallow spherical shells. It presents an analytical and experimental investigation of the elastic, nonlinear, axisymmetric behavior of such shells under the action of uniform pressure and point loading at the apex. Chapter I is a critical survey of the relevant published literature. The survey cutlines the development of the theoretical aspects of shell buckling and shows how this was influenced by the results of experimental investigations. It further outlines the development of highly refined experimental techniques which reduced the scatter of results characteristics of previous work. It is then shown that even experimental work using these refined techniques, provides only a partial substantiation of theoretical analyses and it is concluded that the apparent disparity may be due to the uncertain character of the displacement dependent boundary restraints employed. In chapter II, the essential equivalence of the governing differential equations adopted by many nuthors is demonstrated for the first time in an integrated manner. The solutions of these equations: equations is discussed with special reference to an criginal analysis of the case of a pressure loaded, freely supported shell. Alternative solutions by direct integration and the Calerkin method are discussed but these are shown to lead to excessive computational difficulties. The effect of various boundary conditions is than examined and their influence on critical load values is shown to be significant. In the research undertaken, displacement dependent boundary conditions were avoided by using only force dependent conditions in the experimental work. The simplest of these conditions are those corresponding to a free support. In chapter III, the requirements of experimental techniques necessary to obtain the equilibrium path in both the stable and unstable states of equilibrium are discussed. This has led to the development of new techniques of preparation of accurate, stress free specimens and the adoption of a new, controlled deflection loading technique. the experimental investigation also presents, for the first time, the measurement of surface strains throughout the loading history of the shells. The results of the experimental investigations are discussed and compared with theory in Chapter IV. A critical comparison with the published experimental work of previous investigators is included where relevant. Chapter V summarises the main findings of the investigation regarding the basic aspects and shows that good agreement with theory is obtained by the refinement of experimental techniques introduced so as to approach as closely as possible, the assumptions of the theoretical analysis. Thus, for the first time to the author's knowledge, experimental results which are both consistent in them selves and in agreement with theory have been obtained. The application of the results of the investigation to practical engineering problems is considered. A Bibliography and Author's Index is provided in Chapter VI, followed in Chapter VII by Appendices giving details of analyses considered in the thesis, together with a full presentation of the results of the experimental investigation.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: R M Kenedi
• Keywords: Mechanical engineering
• Date of Award: 1965
• Depositing User: Enlighten Team
• Unique ID: glathesis:1965-73848
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:56
• Last Modified: 14 Jun 2019 08:56
• URI: https://theses.gla.ac.uk/id/eprint/73848