On shear and torsion factors in the theory of linearly elastic rods - Mathematical PhysicsReport as inadecuate




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Abstract: Lower bounds for the factors entering the standard notions of shear andtorsion stiffness for a linearly elastic rod are established in a new andsimple way. The proofs are based on the following criterion to identify thestiffness parameters entering rod theory: the rod-s stored-energy density perunit length expressed in terms of force and moment resultants should equal thestored-energy density per unit length expressed in terms of stress componentsof a Saint-Venant cylinder subject to either flexure or torsion, according tothe case. It is shown that the shear factor is always greater than one,whatever the cross section, a fact that is customarily stated without proof intextbooks of structure mechanics; and that the torsion factor is also greaterthan one, except when the cross section is a circle or a circular annulus, afact that is usually proved making use of Saint-Venant-s solution in terms ofdisplacement components.



Author: Antonino Favata, Andrea Micheletti, Paolo Podio-Guidugli

Source: https://arxiv.org/







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