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DESIGNING AND DETAILING OF BUILDING SYSTEMS.MECHANICS IN CIVIL ENGINEERING

BILATERAL ESTIMATES IN ELASTIC ROD STABILITY PROBLEMS FORMULATED THROUGH BENDING MOMENTS

Vestnik MGSU 2/2013
  • Kupavtsev Vladimir Vladimirovich - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associated Professor, Department of Theoretical Mechanics and Aerodynamics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Мoscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 47-54

In the article, the author proposes an original method of identification of upper and lower bounds of critical values of loading parameters in respect of three stability problems for a non-uniformly compressed rectilinear one-span elastic rod with a varying longitudinal bending stiffness value.Initial variational formulations of stability problems under consideration are presented through internal bending moments that emerge at the moment of the rod stability loss and that satisfy uniform boundary conditions rather than additional integral conditions. The author has obtained forms of the bending moment and respective loading parameter values in case of the rod equilibrium bifurcation in the basic problem of stability of an elastic rectilinear rod with a constant cross section, compressed by longitudinal forces at the rod ends.The calculation of the lower bound is reduced to determination of the greatest eigenvalues for the matrices presented in the form of modular matrices of the second order with the elements expressed through the integrals of available forms of bending moments. The calculation of the upper bound is reduced to determination of the greatest eigenvalue for the matrix that almost coincides with one of modular matrices.

DOI: 10.22227/1997-0935.2013.2.47-54

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  7. Chanyshev A.I., Igonina E.A. O potere ustoychivosti beskonechno dlinnoy polosy za predelom uprugosti pri szhatii [On the Loss of Stability of an Indefinitely Long Strip beyond the Elasticity in Compression]. Fizicheskaya mezomekhanika [Physical Mesomechanics]. 2010, vol. 13, no. 51, pp. 89—95.
  8. Paymushin V.N., Gyunal I.Sh., Lukankin S.A. Issledovanie kachestva nelineynykh uravneniy teorii uprugosti na zadachakh ustoychivosti ploskikh krivolineynykh sterzhney sloistoy struktury (postanovka zadachi) [Research into the Quality of Non-linear Equations of the Theory of Elasticity Exemplified by the Problems of Stability of Flat Curvilinear Rods That Have a Layered Structure (Problem Definition)]. Izvestiya vuzov. Aviatsionnaya tekhnika. [News of Institutions of Higher Education. Aeronautical Engineering]. 2010, no. 2, pp. 34—37.
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