Summary
Nonlinear elastic constitutive laws for slender rods are derived from three-dimensional elasticity, using an asymptotic analysis in appropriate scaled material coordinates. Although the strain is everywhere small, displacements and rotations may be large and the elastic behaviour is nonlinear. In the lowest-order rod theory, the couple-resultant and tensile load are expressed as derivatives of a cross-sectional energy. The equations of this theory are similar to those in a director theory of Green and Laws. An iterative procedure for the generation of higher order rod theories is outlined.
Sommario
A partire dell'elasticità tridimensionale, si dedottono le leggi costituive non-lineare elastiche per verghe sottile, utilizzando un metodo asintotico in coordinate materiau delle scale opportune. Benchè la deformazione sia piccolò, i dislocamenti e le rotazioni possono essere grandi ed il comportamento elastico è non-lineare. Nella teoria delle verghe del ordine molto basso, la coppiarisultanta ed il carico tensile si esprimono come derivate di una energia trasversale. Le equazioni di questa teoria sono analoghe di quelle nella teoria direttiva di Green & Laws. Un procedimento iterativo è delineato per la generazione delle teorie delle verghe di ordini superiori.
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Parker, D.F. On the derivation of nonlinear rod theories from three-dimensional elasticity. Z. angew. Math. Phys. 35, 833–847 (1984). https://doi.org/10.1007/BF00945447
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DOI: https://doi.org/10.1007/BF00945447