Error estimation through the constitutive relation for Reissner-Mindlin plate bending finite elements

摘要

This paper deals with the so-called `error estimation through the constitutive relation' for Reissner-Mindlin plate bending finite element analysis, which is based on the calculation of statically admissible stress resultant fields. Further an energy norm through the constitutive relation is introduced to quantify the difference between the calculated statically admissible stress resultant fields and the stress resultants given by the finite element analysis. The statically admissible stress resultant fields are obtained by local calculations at the node or at the element level. The procedures involve an optimization for estimating the statically admissible quantities as close as possible to the finite element result, and thus lead to a more accurate error estimation, considering the Pragger-Synge theorem. The set of examples shows the good agreement between the proposed indicator and the error obtained from the analytical solution. It is concluded that plate bending analysis is a field of application which is well fitted for error estimation through the constitutive relation.