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An exact solution in a nonlinear theory of rods

✍ Scribed by A. B. Whitman; C. N. DeSilva

Publisher
Springer Netherlands
Year
1974
Tongue
English
Weight
760 KB
Volume
4
Category
Article
ISSN
0374-3535

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✦ Synopsis

A three dimensional nonlinear equilibrium theory of elastic rods, applicable to large displacements and small strains, and accounting for extensibility and shear deformation is developed. Integrals of the governing equations are determined for the case of specified end force and moment. A class of solutions is obtained for an initially straight, untwisted rod and compared to the classical solution. The effects of extensibility and shear deformation are discussed.

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A one-dimensional model of a linearly elastic thin rod is deduced from threedimensional elasticity by regarding the Kirchhoff hypotheses as internal constraints prevailing in a three-dimensional tubular region. It follows from such an assumption that the displacement and the strain fields are linear