Statics of curved rods on account of torsion and flexion

We adress the problem of a thin curved rod in linear elasticity for small d isplacements. We use an asymptotic two-scale method based on the small para meter epsilon, ratio of the thickness to the overall lengths. The two leadi ng order terms have the Bernoulli's structure and the corresponding displac ement is inextensional. The constitutive law involve torsion effects at the same order as flexion effects, so that the description of the kinematics i nvolve an angle theta which is the rotation of the sections. The Lagrange m ultiplier, associated with the constraint of inextensibility, is discussed. The variational formulation of the problem in the subspace of the inextens ional displacements is given, as well as the equations involving the Lagran ge multiplier. (C) Elsevier, Paris.