Homogenization and optimal design of an elastic material reinforced by means of quasi-periodic fibres of higher rigidity
We consider an elastic material reinforced by means of identical fibres of size r(epsilon), which are built with another material, which are epsilon-periodically distributed in the plane {x(3) = 0}, but which make a variable angle with respect to this plane. We describe the asymptotic behaviour of this material when epsilon goes to 0. We exhibit the limit law of the material using the Gamma-convergence method. Depending indeed on the size of r(epsilon) and of the Lame coefficients of the elastic material building the fibres, we exhibit different limit functionals. We finally study an optimal design problem with respect to the angle. (c) 2007 Elsevier Ltd. All rights reserved.
homogenization reinforcement quasi-periodic fibres gamma-convergence optimal design problem two-scale convergence