Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Large deformations of a heavy cantilever


Author: Chang Yi Wang
Journal: Quart. Appl. Math. 39 (1981), 261-273
MSC: Primary 73H99
DOI: https://doi.org/10.1090/qam/625473
MathSciNet review: 625473
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Abstract: A cantilever of uniform cross-section and density is held at an angle $ \alpha $ at one end. The shape of the cantilever depends heavily on $ \alpha $ and a nondimensional parameter $ K$ which represents the relative importance of density and length so that of flexural rigidity. Perturbations on the elastica equations for small and large $ K$ show good agreement with exact numerical integration. It is found that whenever $ K$ reaches a critical value, bifurcations of the solutions occur. This nonuniqueness can be observed by the flipping phenomena as $ \alpha $ is increased.


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DOI: https://doi.org/10.1090/qam/625473
Article copyright: © Copyright 1981 American Mathematical Society


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