Corrector in a beam model for unidirectional composites

Homogenization theory is applied to the elastic analysis of beams composed of many fibers parallel to the beam axis. We first analyze the microstructure of the beam to define the local perturbation of a global mean behavior, due to nonhomogeneity. We describe this perturbation using first- and second-order terms in the asymptotic expansion of displacements in the power series of the small parameter. As an example of application, we use this description in the derivation of a beam-type element for the analysis of beams with multiple parallelfibers. Independent shear rotations are included in the kinematics defining the global behavior of the beam. We quote the formula for the stiffness matrix of an equivalent homogeneous, Hermitian beam element, in which effective coefficients and local perturbations appear. The computational process is then illustrated on an example of a superconducting coil for a nuclear fusion device.