Analytical Calculation of Cylindrical Shells in the Form of Second-Order Algebraic Surfaces

When choosing the shape of a shell, one should strive for the boundary conditions to ensure momentless behavior of the shell. Second-order algebraic surfaces include three degenerate surfaces: parabolic, elliptic, and hyperbolic cylindrical surfaces, and two surfaces derived from them: circular cylindrical surface and cylindrical surface with incomplete ellipse in cross-section. These five surfaces are the objects of this research. For the first time, comparative static analysis of the five shells under a load of self-weight type is performed using the momentless shell theory. The explicit formulae for the determination of three internal membrane forces are obtained. It is shown that the parabolic cylindrical shell and the cylindrical shell with incomplete ellipse in cross-section perform better within the momentless shell theory. The constraints for the application of the momentless theory obtained earlier by other authors are confirmed. For the first time, a system of three partial differential equations with respect to the displacements of middle surfaces of the five cylindrical shells given in previously unused curvilinear coordinates is derived. It is established that no studies dealt with the calculation of hyberbolic cylindrical shells so far. A brief review of publications on the analysis of strength, stability, dynamics, and application of the five considered cylindrical shells is given to clarify the directions of investigation of these five cylindrical shells.