Calculation of microstrains and microstresses in a thick non‐symmetric heterogeneous plate by homogenization

摘要

AbstractWe consider the thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use theReissner‐Mindlinthermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non‐uniformly and rapidly oscillating functions of the space variable.Two‐scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution ofmicrostrainsandmicrostressesinside the plate when a macroscopic behaviour is