S. Perrin et P. Boisse, ERROR CALCULATION IN THE CONSTITUTIVE RELATION FOR MINDLIN PLATE FINITE-ELEMENT ANALYSES, Engineering computations, 15(6-7), 1998, pp. 837
An extension of the concept of error on constitutive relation is propo
sed to the case of Mindlin plate finite element computations. The erro
r of the performed analysis is estimated from the incompatibility in r
elation with the constitutive equation of admissible fields calculated
from the finite element results. In a first stage, loads and moments
densities leading to the equilibrium of each element are computed on t
he element edges as the sums of densities derived from the finite elem
ent solution and of densities with a resultant equal to zero on each e
lement edge. Then strictly statically admissible stress resultants are
calculated within each element. Both of the two stages allow an optim
ization for the statically admissible field in order to get a more acc
urate error. The calculations are local which is very interesting espe
cially in case of complex structure analyses with a large number of de
grees of freedom for which adaptivity is an important feature. A set o
f examples shows the efficiency of the proposed estimator and the good
adaptation of the error on constitutive law method to Mindlin plate a
nalysis.