T. Huemer, R. Lackner, H.A. Mang:
"Implementation and Application of an Algorithm for Incremental Adaptive Finite Element Analysis of Concrete Plates";
in: "Proceedings of the Workshop on Mechanics of Quasi-Brittle Materials and Structures", G. Pijaudier-Cabot, Z. Bittnar, B. Gérard (ed.); Hermes, Prague, 1999, 331 - 352.
Adaptive Finite Element (FE) analyses permit control of the discretization error. As regards adaptive nonlinear FE-analysis, the error is estimated after each load or displacement step of an incremental calculation. Based on the result of the error estimation an improved FE-mesh is generated. Re-calculations are performed until the error no longer exceeds a userdefined tolerance.Based on the advancing front method, an automatic mesh generation algorithm for quadrilateral elements is developed. A given mesh density function is used for the mesh generation. Even if the current mesh density function is strongly graded, geometrically well-shaped elements are generated. The developed error estimator is based on the rate of the mechanical work. It permits consideration of elasto-plastic material behavior in conjunction with softening because of cracking of concrete.
A new algorithm for incremental analyses of materially nonlinear problems is presented. It is based on a technique for estimating the incremental error. The algorithm does not require re-calculations of the structural answer from load steps preceding the current load step. Thus, the proposed procedure can be used effectively for the analysis of complicated structures with a large number of degrees of freedom.
The usefulness of this procedure is demonstrated by means of the investigation of an unreinforced concrete plate. A comparison of the obtained results with results from computations based on regularly refined FE-meshes shows that the adaptive procedure enables a significant improvement of the quality of the localized (crack) zone.
Keywords: FEM, error estimation, finite element method, mesh generation, adaptivity, fictitious crack concept, non-linear