Abstract
A variational theorem of three-dimensional linear elasticity, for which the comparison functions satisfy all the differential equations of the problem, and all boundary conditions are Euler equations of the variational equation, is reformulated so as to apply to the two-dimensional theory of thin shallow shells of revolution. This variational equation is then applied to the problem of the approximate determination of the interior solution state of a shallow spherical shell, without consideration of the associated edge zone solution state. Explicit results are obtained for the stress boundary value problem and the displacement boundary value problem, and a proceedure, involving an infinite linear system of ordinary equations, is indicated for a mixed problem with different boundary conditions being prescribed along different portions of the edge of the shell. Additionally, possible further developments of a similar nature are discussed.
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