Homogenization of very thin elastic reticulated structures

Abstract

This work is devoted to the homogenization of the anisotropic, linearized elasticity system posed on thin reticulated structures involving several parameters. We show that the result depends on the relative size of the parameters. In every case, we obtain a limit problem where both the microscopic and macroscopic scales appear together. From this problem, we get an asymptotic development which gives an approximation in L2 of the displacements and the linearized strain tensor.