Homogenization of a Thick Plate Model with Inclusions or Openings Periodically Distributed in the Thickness

Abstract

AMS (MOS): 65 M-N Using Hencky-Mindlin thermoelastic linear model for plates with a large number of small identical inclusions or openings in their thickness, we obtain equilibrium equations in which coefficients depend on x and periodically on x/e where e is the diameter of the cell of the periodic structure. Formal asymptotic expansions give “homogenized” equations with coefficients independant of e corresponding to an equivalent homogeneous plate. Solution of these homogenized equations is proved to be (in a weak sense) the limit, when e tends to zero, of original equations solution. Moreover this result leads to a method giving explicit computation of thermal and elastic coefficients of the equivalent homogeneous plate in the case of right cylindrical openings. Numerical results for different shapes of openings are given.