Thermal stresses in spherical shells

Barrowman, E. M (1970) Thermal stresses in spherical shells. PhD thesis, University of Glasgow.

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The subject matter of this thesis concerns the analytical and experimental investigation of the stress distributions caused by the steady state temperature distributions in spherical shells with various boundary conditions. After a short critical review of the relevant literature, consideration is given in Chapter 1 to the analytic expressions for the temperature distributions in spherical shells exposed to ambient temperature and subject to the conductive, convective and radiant modes of heat transfer. In Chapter 2 the equations for the stress resultants in a spherical shell as presented by Flugge are modified to include thermal effects. A particular solution of the shell equation is presented using the derived analytic temperature distributions. This solution, along with an asymptotic complementary function solution derived by Leckie, gives a general solution for the thermal stresses in spherical shells due to axisymmetric temperature distributions. The problem of a heated opening in a spherical shell is considered and results are presented for the stresses for selected values of the shell parameters. In Chapter 3 consideration is given to that region of the shell with large meridional angle whereas the region of shell appropriate to the shallow shell theory is considered in Chapter 4. In both these regions appropriate simplifications can be made to the complicated general solution for the spherical shell and somewhat simpler expressions for the stress resultants are obtained. It is shown that the shallow shell theory is suitable for the evaluation of the thermal stresses in that region of the sphere which can be appropriately described as shallow. Thermal stresses in cylindrical skirts are considered and comparisons are made with analytic work which has already been presented. In Chapter 5 the stress concentrations at the junction of a uniformly heated cylindrical shell and a shallow spherical shell are investigated and computed results are presented for various cylinder to sphere thickness ratios. Asymmetric temperature distributions on spherical shells are considered in Chapter 6 and methods of solution for the resulting stress distributions are discussed. An analytic solution is presented for a slowly varying line of temperature on a spherical shell. The experimental investigations are described in Chapter 7 which also includes an examination of the problem of measuring thermal strains by the use of strain gauges. Temperature distributions into three thicknesses of spherical shell from small uniformly heated circular openings are measured and agree favourably with the theoretical predictions. The stress distribution into a 1/2 inch spherical shell from a uniformly heated opening is measured using temperature compensated strain gauges and agreement is found between the experimental results and the analytic predictions. In Appendix 1 the computational procedures associated with the numerical evaluation of the analytic expressions developed in the thesis are considered. The circular disc is considered in Appendix 2, while in Appendix 3 the convective and radiant modes of heat transfer are examined. Appendix 4 gives the results obtained for the author by Babcock and Wilcox from a computer analysis, using the finite element technique, of a particular temperature distribution on a spherical shell. These results are compared with the equivalent theoretical predictions derived in the thesis.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: A S Tooth
Keywords: Mechanical engineering, Thermodynamics
Date of Award: 1970
Depositing User: Enlighten Team
Unique ID: glathesis:1970-72427
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 24 May 2019 15:12
Last Modified: 24 May 2019 15:12

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