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Calculation of microstrains and microstresses in a thick non‐symmetric heterogeneous plate by homogenization
Author(s) -
Tapiéro Roland
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180906
Subject(s) - homogenization (climate) , thermoelastic damping , mathematics , mathematical analysis , geometry , transverse plane , thermal , physics , thermodynamics , biodiversity , ecology , structural engineering , engineering , biology
We 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 the Reissner‐Mindlin thermoelastic 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 of microstrains and microstresses inside the plate when a macroscopic behaviour is given.