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R. Lackner, H.A. Mang:
"A posteriori Error Estimation in Nonlinear FE Analyses of Shell Structures";
International Journal for Numerical Methods in Engineering, 53 (2002), 10; 2329 - 2355.

During the last decade, significant scientific efforts were made in the area of quality assurance of numerical results obtained by means of the finite element method (FEM). These efforts were based on adaptive remeshing controlled by an estimated error. This paper reports on the extension of error estimation to nonlinear shell analysis involving strain-hardening and softening plasticity. In the context of incremental-iterative analysis, an incremental error estimator is introduced. It is based on the rate of work. The stress recovery technique proposed by Zienkiewicz and Zhu (1992) is modified to allow for discontinuities of certain stress components in case of localization such as, e.g., cracking of concrete. The developed error estimator is part of a calculation scheme for adaptive nonlinear FE analysis. If the estimated error exceeds a prespecified threshold value in the course of an adaptive analysis, a new mesh is generated. After mesh refinement 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 influence of the user-prescribed error threshold on the numerical results is investigated.

Keywords: cooling tower, reinforced concrete, adaptivity, error estimation, retrofitting, ultimate load, stress recovery, adaptive mesh refinement, uniform mesh refinement, layer concept

http://dx.doi.org/10.1002/nme.381