A posteriori error estimation in non‐linear FE analyses of shell structures

Abstract

SUMMARYDuring the last decade, signiÿcant scientiÿc e orts were made in the area of quality assurance of numerical results obtained by means of the ÿnite element method (FEM). These e orts were based on adaptive remeshing controlled by an estimated error. This paper reports on the extension of error estimation to non-linear shell analysis involving strain-hardening and softening plasticity. In the context of incremental-iterative analyses, an incremental error estimator is introduced. It is based on the rate of work. The stress recovery technique proposed by Zienkiewicz and Zhu (Int. J. Numer. Meth. Engng 1992; 33:1331) is modiÿed to allow for discontinuities of certain stress components in case of localization arising from, e.g. cracking of concrete. The developed error estimator is part of a calculation scheme for adaptive non-linear FE analysis. If the estimated error exceeds a prespeciÿed threshold value in the course of an adaptive analysis, a new mesh is generated. After mesh reÿnement the state variables are transferred from the old to the new mesh and the calculation is restarted at the load level which was attained with the old mesh. The performance of the proposed error estimator is demonstrated by means of adaptive calculations of a reinforced concrete (RC) cooling tower. The in uence of the userprescribed error threshold on the numerical results is investigated.