Abstract
Previously derived results for the mentioned canonical load cases for pretwisted rectangular plates (or shallow helicoidal shells) of rectangular cross section are generalized so as to include arbitrarily prescribed cross wise thickness variations. The present method of derivation is simpler than the earlier one in terms of Marguerre's equations for transverse deflection and Airy stress function, and consists in applying a semi-inverse solution procedure to the system of equilibrium and compatibility equations of shallow shell theory. A particular case of the results of this paper concerns the problem of pure bending of a pretwisted plate with elliptical thickness variation. The results for this case coincide with recent results obtained by Goodier and Griffin through use of three-dimensional elasticity theory.
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