Analysis of Geometry and Strength of Shells with Middle Surfaces Defined by Two Superellipses and a Circle

In this study, thin shells in the form of algebraic surfaces defined by a geometric frame of three plane superellipses lying respectively in three coordinate planes are considered. As the main focus of the study, the case when the horizontal superellipse is a circle is examined. It is shown that depending on the type of the other two superellipses, it is possible to obtain a conical surface, or a surface of negative Gaussian curvature, including conoids, or surfaces of positive Gaussian curvature. The construction of 12 particular cases of such surfaces with a circular base is illustrated. Six of them are investigated in detail using the methods of differential geometry, i.e. expressions of the fundamental quadratic forms are obtained, for the first time. Out of the 12 presented shell shapes, two ruled shells of zero and negative Gaussian curvature (conical and cylindroidal respectively) with the same geometric frame were selected for comparative static analysis. The two shells were analyzed for uniform distributed load using displacement-based FEM implemented in the SCAD software. It is shown that despite the two shells having identical geometric frames, the conical shell demonstrated better performance over the most strength parameters.