UBC Theses and Dissertations
Bending of spherical shells Gurel, Ahmet Okan
This study of the bending of a spherical shell of constant thickness consists of five chapters. In the first chapter, general differential equations of the problem are derived and presented with the variables in dimensionless form. The second chapter deals with the solution of the two second order differential equations in terms of Bessel Functions. The solution is applicable for shells with a colatitude of about 25 degrees or less. Expressions are given for the internal stresses and displacements in terms of these values at the boundary. The third chapter gives a numerical solution of the problem. Solutions are found for three cases of radius to thickness ratio, namely 30, 100 and 500, and for colatitudes from 8 to 90 degrees. In the preparation of tables the Alwac III-E Electronic Digital Computer was used. The flow diagram and programme for the Alwac III-E are given. The fourth chapter compares the numerical method with one of Timoshenko's approximate solutions. The wave lengths, deflections, rotations and moments are calculated by two methods and compared. As the conclusion to these comparisons a graph is given, which shows the approximate error in the damped harmonic solution. In the last chapter, a numerical example is solved using tables from the digital computer. The ratio of radius to thickness is 500; radius being 125 feet and the colatitude 30 degrees. The edges are considered as being on rollers.
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