Error calculation in the constitutive relation for Mindlin plate finite element analyses

An extension of the concept of error on constitutive relation is proposed to the case of Mindlin plate finite element computations. The error of the performed analysis is estimated from the incompatibility in relation 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 the element edges as the sums of densities derived from the finite element solution and of densities with a resultant equal to zero on each element edge. Then strictly statically admissible stress resultants are calculated within each element. Both of the two stages allow an optimization for the statically admissible field in order to get a more accurate error. The calculations are local which is very interesting especially in case of complex structure analyses with a large number of degrees of freedom for which adaptivity is an important feature. A set of examples shows the efficiency of the proposed estimator and the good adaptation of the error on constitutive law method to Mindlin place analysis.