NEW APPROACH TO DETERMINING AXIAL CRITICAL LOADS SHELLS, PLATES AND RODS

Authors

  • Volodymyr Todchuk Ivan Kozhedub Kharkov University of Air Force

DOI:

https://doi.org/10.18372/2306-1472.79.13833

Keywords:

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

Abstract

Purpose: To show that one of the reasons for the large difference between the calculated and experimental critical loads is the incorrect interpretation of the buckling process. Methods: The energy criterion of stability and the relation of the general linear theory of thin-walled structures are used. Results: New formulas for critical loads of shells and plates have been obtained. Discussion: To estimate the bearing capacity of engineering structures, precise formulas are needed to calculate the critical loads under axial compression. Such formulas have not yet been obtained. The reason for the large discrepancies between the theoretical and experimental values of the axial critical loads of cylindrical shells was not found. In this paper, an attempt was made to solve this problem. In contrast to the usual approach, it is assumed here that when the structure is buckled, the distance between the loaded ends does not change. This allowed us to obtain new formulas for axial critical loads. The values of critical loads calculated by these formulas are close to the experimental data. Based on this, it was concluded that the formulas obtained can be used for real calculations of the critical loads of cylindrical shells and plates, and the proposed approach can be used to continue studies of the stability of thin-walled structures.

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.

References

Bryan G. H. (1891) Proc. London Math. Soc., vol. 22, pp. 54.

Vol'mir A. S. (1976) Ustoychivost' deformiruyemykh system [Stability of deformable systems]. M., Science, 984p. (In Russian)

Grekov V. F.,P'yankov A.A.,Todchuk V. A. (2013) Opredeleniye kriticheskikh osevykh szhimayushchikh usiliy izotropnykh tsilindrov [Determination of the critical axial compressive forces of isotropic cylinders]. Compressor and power engineering No 1 (31), pp.28-32. (In Russian)

Grekov V. F., P'yankov A.A., Todchuk V. A. (2014) Ob ustoychivosti obolochek, plastin i sterzhney [On the stability of shells, plates and rods]. Compressor and power engineering, vol. 3(37), pp.33-37. (In Russian)

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

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

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

Novozhilov V., Sudpromgiz L. (1962) Teoriya tonkikh obolochek [The theory of thin shells].– 431p. (In Russian)

Sausvell R. V. (1948) Vvedeniye v teoriyu uprugosti. [Introduction to the theory of elasticity]. M. Gosizdat, ,674 p. (In Russian)

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

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

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

Todchuk V. A. (2012) Ob odnom podkhode k resheniyu zadachi ustoychivosti tsilindra pri osevom szhatii. [On one approach to the solution of the stability problem of a cylinder under axial compression]. Bulletin of the Petrine Academy vol. 2-3 (27-28), pp. 3-7 St. Petersburg. (In Russian)

Todchuk V. A. (2017) Ob odnom podkhode k opredeleniyu kriticheskikh nagruzok obolochek, plastin i sterzhney. [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

Published

13-08-2019

How to Cite

Todchuk, V. (2019). NEW APPROACH TO DETERMINING AXIAL CRITICAL LOADS SHELLS, PLATES AND RODS. Proceedings of National Aviation University, 79(2), 62–70. https://doi.org/10.18372/2306-1472.79.13833

Issue

Section

AIRPORTS AND THEIR INFRASTRUCTURE