Determination of Optimal Cylindrical Shells in the Form of Second-Order Surfaces

Thin shells with cylindrical and conical middle surfaces are most popular. Many shell-type structures have been built in the form of rotational and translational surfaces, for which there are several dozen optimality criteria. Hyperbolic, parabolic, elliptic, and circular cylindrical roofs with rectangular base are considered, for which, as evidenced by thorough literature review, there is no comparative analysis of strength, stability, and dynamics. Nevertheless, architects are already trying to expand the classification range of ruled middle surfaces of zero Gaussian curvature with a rectangular base by including torse surfaces. Five thin cylindrical shells outlined by second-order algebraic surfaces with different generating plane curves are studied. The stress-strain state of hyperbolic, parabolic, elliptic and circular cylindrical roofs with rectangular base subjected to static load of self-weight type is investigated. The roofs have the same dimensions of the base, the same height, thickness and structural material, that is, a comparative calculation is performed. It is established that the smallest (maximum) membrane stresses occur in the ellipsoidal shell with an incomplete half-ellipse, and the smallest (maximum) bending and equivalent stresses occur in the parabolic cylindrical shell, which is confirmed by the results of previously performed calculations using the analytical momentless theory. Therefore, it is recommended to use ellipsoidal cylindrical shells with an incomplete half-ellipse in cross-section for building structures. Currently, almost all problems of structural mechanics of shells are solved by numerical methods, therefore, the displacement-based finite element method was chosen to solve this problem.