The theory of Kirchhoff rods as an exact consequence of three-dimensional elasticity

✍ Scribed by Fabrizio Davì

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 742 KB
• Volume: 29
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041205

✦ Synopsis

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 in the cross-sectional coordinates. A constitutive relation that exhibits the maximal symmetry compatible with the assumed constraints is chosen and the equilibrium equations in terms of displacements are obtained.