CORRECTORS IN A BEAM MODEL FOR UNIDIRECTIONAL COMPOSITES

Homogenization theory is applied to the elastic analysis of beams comp osed of many fibers parallel to the beam ark. We first analyze the mic rostructure of the beam to define the local perturbation of a global m ean behavior, due to nonhomogeneity. We describe this perturbation usi ng first-and second-order terms in the asymptotic expansion of displac ements in the power series of the small parameter. As an example of ap plication, we use this description in the derivation of a beam-type el ement for the analysis of beams with multiple parallel fibers. Indepen dent shear relations are included in the kinematics defining the globa l behavior of the beam. We quote the formula for the stiffness matrix of an equivalent homogeneous, Hermitian beam element, in which effecti ve coefficients and local perturbations appear. The computational proc ess is then illustrated on an example of a superconducting coil for a nuclear fusion device.