Journal
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Volume 50, Issue 8, Pages 1316-1325Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmecsci.2008.05.001
Keywords
buckling; non-uniform rods; geometric/material non-linearity; regular perturbation; finite elasticity; Galerkin's method
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The post-buckling solutions of non-uniform linearly and non-linearly elastic rods are constructed via a higher-order perturbation approach. For rods with continuously varying flexural stiffness, the onset of buckling and the post-buckling branches are determined employing a suitable set of admissible functions within the context of Galerkin's method combined with a regular perturbation approach. On the other hand, for piece-wise continuous rods, closed-form eigenvalue solutions are exploited as a basis for the non-linear post-buckling description. Closed-form conditions on the non-linearly elastic constitutive function for the bending moment are obtained ensuring supercritical or subcritical divergence bifurcations. Several illustrative examples are discussed highlighting the effects of the stiffness non-uniformity on the onset of buckling and the post-buckling non-linear regime as well as the influence of the non-linear elasticity on the latter. (C) 2008 Elsevier Ltd. All rights reserved.
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