Outlooks in Saint Venant theory I. Formal expansions for torsion of Bredt-like sections

Francesco Dell'Isola (1, 2) , Giuseppe C. Ruta (1)

1 Dipartimento di Ingegneria Strutturale e Geotecnica
2 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita

Starting from a regular curve (middle line), we define a section of a Saint Venant cylinder transporting the curve along its normal; this we call a Bredt-like section. A formal series expansion for Prandtl stress flow function valid for these sections is given. Starting from it, and using standard relationships, formal expansions for warping, shear stress vector field and torsional stiffness are obtained. Although the expansions are affected by degenaration in regularity, at least where curvature of the middle line is not smooth or at its ends, we obtain all traditional results of the theory of strengh of materials and are able to give an estimate of the error associated with them. Moreover, some interesting open problems are formulated, concerning both the problems of regularizing the expansions and of generalizing them for sections with variable thickness.

Domains: Mechanics [physics.med-ph]

Francesco Dell'Isola, Giuseppe C. Ruta. Outlooks in Saint Venant theory I. Formal expansions for torsion of Bredt-like sections. Archives of Mechanics, 1994, pp.23. ⟨hal-00502394⟩