R. Lackner:
"Adaptive finite element analysis of reinforced concrete plates and shells";
Supervisor, Reviewer: H.A. Mang, G. Hofstetter; Institute for Strength of Materials, TU Wien, Vienna, Austria, 1999.
The continuous increase of computer power allows simulations of the mechanical behavior of complex engineering structures by means of numerical analysis tools, such as the finite element method (FEM). Because of its general applicability and the availability of user-friendly computer software, the FEM has become equally popular in research and engineering design. However, the enthusiasm resulting from attractive new possibilities for engineering analysis and design has reduced the awareness about the FEM being a numerical approach and, hence, about the approximate character of the obtained results.The adaptive FEM represents an attempt to estimate the accuracy of the FE solution a posteriori. If the user-specified accuracy is either not reached or if it is exceeded the mechanical model will be adapted automatically. Apart from the underlying FE program, the basic ingredients of adaptive FE-analysis are an estimator of the error of the FE solution ("estimation" is required since analytical solutions are not available) and a mesh generator for changes of the mechanical model characterized by the FE mesh.
In this thesis, a tool for adaptive analysis in the context of numerical simulations of the mechanical behavior of reinforced concrete (RC) structures is presented. For this purpose, an estimator of the discretization error for the case of elastoplastic material behavior is proposed. It is based on a smoothening algorithm applied to the discontinuous distribution of the stresses obtained from FE analysis. For the application of error estimation to problems with localization such as cracking of concrete, the aforementioned smoothening algorithm is modified.
For the generation of the mesh, the "advancing front method" is employed. This technique is extended to permit an alignment of the mesh on the basis of the "localization tensor". The use of non-aligned element configurations for discretization in case of localization would increase the tendency of element "locking".
After mesh refinement, the calculation is continued at the load level which was attained by the old mesh. Consequently, the state variables from the old mesh must be transferred to the new mesh. Contrary to commonly used transfer schemes, both the displacements and the stresses are transferred. The distribution of the history variables for the new mesh is obtained from the constitutive law and the yield criterion, respectively.
The performance of the proposed adaptive calculation tool is demonstrated by means of an extensive numerical study. First, two benchmark problems are solved in order to provide insight into the performance of the error estimator and the calculation strategy. Thereafter, results from a number of examples of concrete and reinforced concrete structures are presented. The final example is concerned with adaptive analyses of an RC cooling tower. As regards adaptive analyses, intelligent remeshing leads to a considerable reduction of the number of finite elements for results of comparable quality as the ones obtained from uniform mesh refinement. The transfer of variables which is required for the developed calculation scheme does not yield a decrease of the quality of the results in comparison to the ones obtained from the by far more expensive strategy of consideration of the entire load history after each mesh refinement.
Keywords: cooling tower, reinforced concrete, adaptivity, error estimation, finite element method, mesh generation, fem, @dissertation, @adaptivity, ultimate load