Przypadek Obrotowej Symetrii Powłok o Małej Wyniosłości - Pietraszkiewicz, W. (Engineering Transactions, 1966)
The object of the considerations are equations of shells or revolution on the grounds of the linear theory of shallow shells. The case of rotational symmetry is studied in detail. The possibility of using membrane solutions for particular solutions is analysed, some conditions for this being derived. Some cases of shells and loads for which a membrane solution coincides with the accurate particular integral of the equations are indicated. Accurate solutions are obtained for uniformly loaded paraboloidal and logarithmic shells. As an example the axially symmetric problem of a uniformly loaded single column shell roof of the paraboloidal and logarithmical type and negative Gauss curvature is solved. The above conditions for the numerical values are not fulfilled in this example. The differences between the accurate results and the solution obtained by using the membrane theory solution as a particular integral are greater than the accuracy of the linear theory of shallow shells.