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UBC Theses and Dissertations

Asymptotic solutions of steadily spinning shallow shells of revolution under uniform pressure Lin, Yi Han


The problem of a steadily spinning shallow elastic shell of revolution under a uniform pressure distribution is investigated by perturbation and asymptotic methods. Accurate numerical solutions are also obtained to confirm the adequacy of perturbation and asymptotic solutions. The limiting case of a flat plate is first solved for the entire range of values of the two load parameters. The results provide a different interpretation of the existing nonlinear membrane solution for the same problem. Depending on the particular geometric and load configuration, the boundary value problem for the shell case is reduced either to the solution of a sequence of linear problems or to the solution of a previously solved nonlinear problem (including one for a flat plate) modified by the solutions of a sequence of linear problems. The analysis for the shell problem under a combined centrifugal and pressure loading shows a complex interplay among the load and geometric parameters. It also enables us to consider a number of previously investigated problems as special cases of our problem and offers a unified treatment of these problems.

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