Goal oriented error estimation in multi-scale shell element finite element problems

Abstract A major challenge with modern aircraft design is the occurrence of structural features varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as onset failure may require information on more refined scale for both metallic and composite components. This work considers errors encountered in coarse global models due to mesh size how these are propagated into detailed local sub-models. The error calculated by a goal oriented estimator, formulated solving dual problems Zienkiewicz-Zhu smooth field recovery. Specifically, novel concept this applying estimator shell elements propagating continuum sub-model. methodology tested simplified aluminium beam section four different feature designs, thereby illustrating sensitivity various common setting. simulations show that when only contained holes flange section, there was little von Mises stress modifications. However, were added webbing large concentrations predicted yielding. Despite increase nominal stress, maximum does not significantly change. change near holes. Monte Carlo simulation utilising marginal distributions performed robustness multi-scale analysis uncertainty estimation would expected experimental measurements. shows trade-off between Saint-Venant’s principle applied loading model investigating response variance.