Surface loading of a thin-walled toroidal shell.

Abstract

The present study is concerned with the series solution based on the Sanders shell theory for the linear elastic problems of the surface loading of thin-walled toroidal shells. The Sanders theory is considered to be one of the most accurate first order theories. For toroidal shells, series solutions have been given by several authors, using other theories and furthermore using a stress approach. In the present study a displacement approach is taken. The governing equations are first developed in toroidal coordinates. The loading case of a pad of uniform normal pressure is then considered in detail, and series expansions are written for the load, displacement and stress terms. Results are computed using the shell theory for sample problems. To check the accuracy of the theory, the results are compared with numerical results obtained using the Finite Element Method (FEM), the Mushtari-Vlasov-Donnel (MVD) and Flugge shell theories. There is a close agreement in the results. The Sanders shell theory is then applied to the problem of local loads on sectorial toroidal shells. The results are compared with results for corresponding cylindrical shells. Three tables are given summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters. The results given provide practical information for structural analysts and designers of piping and vessels, and furthermore give information about the Sanders shell theory and FEM solution characteristics.