Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability
We deduce a one-dimensional model of elastic planar rods starting from the Föppl–von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the two-dimensional parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells.