Engineering Journal: Science and InnovationELECTRONIC SCIENCE AND ENGINEERING PUBLICATION
Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский
Article

Straining an axially loaded slender column

Published: 12.04.2018

Authors: Egorov A.V.

Published in issue: #4(76)/2018

DOI: 10.18698/2308-6033-2018-4-1750

Category: Mechanics | Chapter: Mechanics of Deformable Solid Body

The article considers processes of straining rectilinear ideal and nonideal (inhomogeneous) bars with the flexibility parameter λ = 867 caused by an axial compressive force, and these processes are compared. A bar is assumed to be inhomogeneous when a liner of small volume and reduced stiffness is located asymmetrically in the center of the bar. Steel bars are articulated on the ends. The analysis of the mechanical behavior of the bars is carried out using volumetric finite elements in the program complex LS-DYNA in a dynamic formulation. The design model takes into account geometric and physical nonlinearity, plasticity, isotropy, the real diagram of material deformation. The results of analysis are in the function of time, which makes it possible to observe the deformation process in the running time mode.A video illustrating this process is given. It is shown that the deformations of an ideal bar are due to the Poisson effect, there are no bending deformations. It is found that for a nonideal bar there is a critical force at which buckling of bar occurs, which is associated with significant transverse displacements (deflections). The value of the obtained critical force agrees with the well-known Euler's solution.


References
[1] Feodosyev V.I. Soprotivlenie materialov [Strength of materials]. Moscow, BMSTU Publ., 2016, 543 p.
[2] Feodosyev V.I. Izbrannye zadachi i voprosy po soprotivleniu materialov [Selected tasks and questions on the strength of materials]. Moscow, Nauka. Fizmatlit Publ., 1996, 368 p.
[3] Bolotin V.V. Nekonservativnye zadachi teorii uprugoy ustoychivosti [Nonconservative problems of the theory of elastic stability]. Moscow, Fizmatlit Publ., 1961, 340 p.
[4] Timoshenko S.P. Ustoychivost sterzhney,plastin i obolochek [Stability of bars, plates and shells]. Moscow, Nauka Publ., 1971, 808 p.
[5] Volmir A.S. Ustoychivost deformiruemykh system [Stability of deformable systems]. Moscow, Nauka. Fizmatlit Publ., 1967, 984 p.
[6] Alfutov N.A. Osnovy rascheta na ustoychivost uprugikh system [Basics of calculating the stability of elastic systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
[7] Svetlitsky V.A. Stroitelnaya mekhanika mashin. Mekhanika sterzhney. V 2 to-makh. Tom 1. Statika [Structural mechanics of machines. Mechanics of rods. In 2 volumes. Vol. 1. Statics]. Moscow, Fizmatlit Publ., 2009, 408 p.
[8] Lagozinsky S.A., Sokolov A.I. Ustoychivost pryamolineynykh sterzhney, nagruzhennykh sledyashchimi silami [Stability of rectilinear rods loaded with tracking force]. Sbornik statey “Problemy prikladnoy mekhaniki, dinamikii prochnosti mashin” [Collection of articles “Problems of applied mechanics, dynamics and strength of machines”]. Svetlitsky V.A., Naraykin O.S., eds. Moscow, BMSTU Publ., 2005, pp. 244–259.
[9] Seyranian A.P., Elishakoff I., eds. Modern Problems of Structural Stability. Wien, Springer-Verlag, 2002, 398 p. ISBN 3211836977. URL: http://www.springer.com/us/book/9783211836972# (дата обращения 07.03.2018).
[10] Ferretti M., Luongo A. Flexural-Torsional Flutter and Buckling of Braced Foil Beams under a Follower Force. Mathematical Problems in Engineering,2017 (2):1–10. DOI: 10.1155/2017/2691963
[11] Di Egidio A., Luongo A., Paolone A. Linear and nonlinear interactions between static and dynamic bifurcations of damped planar beams. International Journal of Non-Linear Mechanics, 2007, vol. 42 (1), pp. 88–98. DOI: 10.1016/j.ijnonlinmec.2006.12.010