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/ε where ε is the diameter of the cell of the periodic structure.

Formal asymptotic expansions give “homogenized” equations with coefficients independant of ε corresponding to an equivalent homogeneous plate.

Solution of these homogenized equations is proved to be (in a weak sense) the limit, when ε 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.

Additional information

Notes on contributors

R. P. Gilbert

Alain Bourgeat

Roland Tapiero