Abstract
We consider the problem of determining the stability boundary of an elastic rod clamped at both ends and loaded by a compressive force and a couple. The constitutive equations of the rod are such that both shear of the cross section and compressibility of the rod axis are considered. The stability boundary is given by the bifurcation points of a system of eight nonlinear first-order differential equations, obtained by using the first integrals. Depending on the parameter values the type of bifurcation is determined. The post-critical shape of the rod is obtained by the numerical integration of a system of 12 nonlinear first-order differential equations.
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Glavardanov, V.B., Maretic, R.B. Stability of a twisted and compressed clamped rod. Acta Mech 202, 17–33 (2009). https://doi.org/10.1007/s00707-008-0043-5
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DOI: https://doi.org/10.1007/s00707-008-0043-5