On the Calculation of Nonlinear Buckling of a Bar

— The classical problem of nonlinear buckling of a bar caused by a compressive longitudinal force is considered. Calculated dependences in elementary functions are obtained for the direct analytical determination of the main parameters of a bent bar, such as the coordinates of the outline of the bar...

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Bibliographic Details
Published in:Mechanics of solids 2021-09, Vol.56 (5), p.684-689
Main Author: Anakhaev, K. N.
Format: Article
Language:English
Subjects:
Bending
Buckling
Classical Mechanics
Cross-sections
Helicopters
Inverse method
Mathematical analysis
Modulus of elasticity
Physics
Physics and Astronomy
Protective structures
Stiffness
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Summary:— The classical problem of nonlinear buckling of a bar caused by a compressive longitudinal force is considered. Calculated dependences in elementary functions are obtained for the direct analytical determination of the main parameters of a bent bar, such as the coordinates of the outline of the bar, bending angles along the length of the bar, diagrams of moments of force and internal bending energy. Comparison of the calculated values obtained with the results of known (basic) solutions (Sikorsky Yu.S., Popov E.P., Zakharov Yu.V. – Okhotkin K.G.) gave, in general, a fairly close convergence of the results (~1–2%), examples of calculation are given, including comparison with the data of linear calculation. The results obtained can be used both for theoretical research and for engineering calculations in practice, in particular, when determining (by the inverse method) the stiffness of rods of an arbitrary cross-section, or the elastic modulus of various materials (composite) with known cross-sections of the rod, including when designing protective structures from dangerous slope geophysical processes, etc.
ISSN:0025-6544
1934-7936
DOI:10.3103/S002565442105006X