A semi-analytical method is proposed for investigating the stability of planar equilibrium configurations of an inextensible elastic rod under end-loading conditions. The method is based on representing the second variation of the constrained strain energy of the rod as a diagonal quadratic form using the eigensolutions of an auxiliary Sturm–Liouville problem. The coefficients of the resulting form which determine the sign of the second variation are analyzed by numerically solving an initial-value problem. Examples of curvilinear configurations of rods and a circular ring under point loads are considered and their stability is analyzed using the proposed method.
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