Analytical and numerical stress state analysis of a shell with tangential developable middle surface

• Published in: AIP Conference Proceedings 2022-08, Vol.2559 (1)
• Main Authors: Aleshina, O., Cajamarca-Zuniga, D., Ivanov, V., Rekach, F., Alborova, L.
• Format: Article
• Language: English
• Subjects: Differential equations; External pressure; Finite element method; Internal forces; Mathematical analysis; Numerical methods; Shells (structural forms); Structural design
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0099513

Nowadays, diverse calculation methods are available for structural design. Because of the wide use of thin-shell structures in architecture, engineering, aircraft industry and other fields, it is necessary to understand and know the possibilities of different calculation methods, including the analytical ones. Works on the study of the stress-strain state of the shell of an equal slope with an ellipse at the base have not been widely performed. The article presents the derivation of the differential equations of equilibrium of the Momentless Theory of shells for determining internal forces arising in the torse of an equal slope with a directrix ellipse under the action of external pressure. The results of the internal forces by the Finite Element Method and the Variational Difference Method have been obtained too. In this research, we used the FEM-based SCAD computer program and the VDM-based "SHELLVRM" program. According to the results, we have determined the advantages and disadvantages of three calculation methods, including two numerical and one analytical. VDM results are more accurate compared to FEM, but the FEM-based program is the simplest and most versatile to solve the set task.