Adaptive FE Analysis of RC Shells. I: Theory

This paper contains the description of an adaptive calculation scheme for nonlinear (elastoplastic) finite element (FE) analysis. The underlying error estimator accounts for the error in the elastic regime as well as for the one arising from plastic loading. It is based on the stress recovery scheme proposed by Zienkiewicz and Zhu in 1992. The adaptation of the FE mesh is performed by means of the h-version of mesh refinement. The advancing front method is employed for remeshing. Before restart of the analysis after mesh refinement, the transfer of variables from the old to the new mesh must be performed. Unlike as for commonly used transfer schemes, the presented mode of transfer employs stresses and displacements for the evaluation of the state variables for the new mesh. All ingredients of the adaptive calculation scheme (i.e., error estimation, mesh generation, and the transfer of variables) are extended for application to the layer concept and to curved surfaces. Both extensions are necessary for adaptive analyses of reinforced concrete (RC) shells (see companion paper).