On the optimal design of the shape of a buckled elastic beam |
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Authors: | SV Sorokin AV Terentiev |
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Affiliation: | Department of Engineering Mechanics, Stare Marine Technical University of St. Petersburg, Lotsmanskaya str. 3, St. Petersburg, 190008, Russia?e-mail: sorokins@mail.ru, RU
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Abstract: | Analysis of stability, post-buckling bending and vibrations is performed for a beam (a spring element) having an optimal shape.
A buckled pin-jointed spring element of a constant thickness and variable width is considered. The optimal shape of this beam
is suggested to provide a uniform distribution of maximum bending stresses in its buckled equilibrium configuration for a
given value of a supercritical axial force. Sensitivities of a critical force and a buckling mode to variations of the shape
of a beam are calculated. A dependence of the static lateral deflection upon an axial force is analysed. Nonlinear equations
of large-amplitude oscillations are derived by a use of the Hamilton principle. The natural frequencies of a spring element,
compressed by a supercritical force are calculated.
Received April 29, 1999 |
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Keywords: | : stability vibrations beams post-buckling behaviour optimal shape |
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