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Buckling and post-buckling of non-uniform non-linearly elastic rods
- Source :
-
International Journal of Mechanical Sciences . Aug2008, Vol. 50 Issue 8, p1316-1325. 10p. - Publication Year :
- 2008
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00207403
- Volume :
- 50
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Mechanical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 33529887
- Full Text :
- https://doi.org/10.1016/j.ijmecsci.2008.05.001