[Back]

R. Lackner, H.A. Mang:
"Error Estimation in Ultimate Load Analysis of Reinforced Concrete Structures";
in: "CD-ROM Proceedings of the 1st European Conference on Computational Mechanics (ECCM '99)", W. Wunderlich (ed.); Lehrstuhl für Statik, TU München, Germany, 1999, 23 pages.

Approximately twenty years ago the first reports on ultimate load analysis of reinforced concrete (RC) surface structures by the Finite Element Method (FEM) appeared in the open literature. During the eighties significant progress was made in the field of constitutive modelling both in the precracking and the postcracking material domain as well as in the area of structural analysis of real-life civil engineering structures such as cooling towers. At this time, systematic investigations of the error of such ultimate load analyses were unfeasible. At the best, the rate of convergence of the obtained results was estimated by means of uniform mesh refinement. Early studies of discretization errors were restricted to linear elasticity. During the last decade, significant scientific efforts were made in the area of quality assurance of numerical results. Primarily restricted to the linear range, these efforts were based on adaptive remesh ing controlled by error analysis. The aim of the calculation scheme presented in this paper is a synthesis of both realistic modelling of the material behavior and an adaptive procedure suitable for the solution of nonlinear problems 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 is modified to allow for discontinuities of certain stress components in case of localization such as cracking of concrete. If the estimated error exceeds a prespecified threshold value, 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 by the old mesh. The usefulness of the developed adaptive analysis scheme is demonstrated by a comprehensive numerical study of an RC cooling tower.

Keywords: reinforced concrete, FEM, adaptivity, error estimation, mesh refinement, shells, stress recovery