• Volodymyr Todchuk Ivan Kozhedub Kharkov University of Air Force



bending, critical load, displacement, stability, experiment, energy


Purpose: To show that within the framework of the linear theory, it was possible to obtain formulas for axial critical loads, the calculation results for which are in good agreement with experimental data. Method: An energetic solution method using the general linear theory of thin-walled shells. Results: New formulas for the critical loads of cylindrical shells are obtained. The analysis of the obtained results is carried out. Recommendations for their use are given. Discussion: Difficulties in theoretical determination of the critical loads of cylindrical shells under axial compression, which are close to the experimental data, forced researchers to seek empirical solutions. Many empirical relationships have been obtained that give different results and describe known experiments. However, there remains a need to theoretically find formulas that allow calculating the critical loads of cylindrical shells of any geometric parameters. Such formulas have been obtained. A comparison of the critical loads calculated using these formulas with empirical and experimental critical loads is carried out. The differences between them are minor.

Author Biography

Volodymyr Todchuk, Ivan Kozhedub Kharkov University of Air Force

Candidate of Technical Sciences, Associate Professor. Department of Aircraft, Kharkov Higher Command-Engineering School, Ukraine. Education: Kharkov Higher Command-Engineering School, Ukraine (1967). Research area: the design and strength of aircraft.


Euler l. (1744). Methodus inveniendi lineas curvas…, Lausanne et Geneve, Additamentum 1: De cursives elasticis, 267 p.(In English)

Bryan G. H. (1891). Proc. London Math. Soc., vol. 22, 54 p. (In English)

Lorenz R. (1911). Die nicht assensymmetrische Knickung dunnwandiger Hohlzulinder. Zeitschrift, Bd 12, Nr. 7, pp. 241-260. (In German)

Timoshenko S. P. (1914). K voprosu o deformatsii i ustoichivosti tsilindricheskoi obolochki.[ On the Deformation and Stability of a Cylindrical Shell]. Vestn. Technology Island, vol. 21, from 785 to 792; Izv. Petrograd. elekrotekhn. inta, 1914, vol. 11, pp. 267 – 287. (In Russian)

Timoshenko S. P. (1971). Ustoichivost' sterzhnei, plastin i obolochek. [Stability of rods, plates and shells.] M., Science, 807 p. (In Russian)

Todchuk V. A. (2017). Ob odnom podkhode k opredeleniyu kriticheskikh nagruzok obolochek, plastin i sterzhnei [On one approach to the determination of critical loads of shells, plates and rods.] Materials of the 18nd International Scientific and Technical Conference, Kiev, pp. 49-51. (In Russian)

Todchuk V. A. (2018). Stability of cylindrical shells. Proceedings of the NAU, no 3, pp. 56-61.

Todchuk V. A. (2019). New approach to determining axial critical loads shells, plates and rods. Proceedings of the NAU, no 2, pp. 62-70.

Vol'mir A. S. (1976). Ustoichivost' deformiruemykh sistem. [ Stability of deformable systems] M., Science, 984p. (In Russian)

Timoshenko S. P. (1946). Ustoichivost' uprugikh sistem. [Stability of elastic systems.] OGIZ - Gostehizdat, 532p. (In Russian)

Grigolyuk E. I., Kabanov V. V. (1978). Ustoichivost' obolochek. [Stability of shells.] M., Nauka, 359p. (In Russian)

Weingarteb V. I., Morgan E. J., Seide P. (1965). Elastic stability of thin- walled cylindrical and conical shells under axial compression. AIAA Journal, vol. 3, no 3, pp.500 -505.



How to Cite

Todchuk, V. (2020). NEW FORMULAS FOR THE CRITICAL FORCES OF CYLINDRICAL SHELLS CALCULATION. Proceedings of National Aviation University, 84(3), 50–56.