Effiziente Dreieckselemente fuer Flaechentragwerke

This thesis deals with the efficient formulation of triangular plate, membrane and shell finite elements in the linear elastic range. The aim of this study is the development of low order elements that achieve high convergence rates and a stable solution without any locking defects. For an efficient formulation of shear - deformable plate elements with Reissner - Mindlin kinematics, the problem of shear locking needs to be completely resolved. In order to avoid locking, different methods, like the assumed natural strain method (ANS), mixed functionals, the Kirchhoff - mode concept or enhanced rotations are adapted to the special needs of triangular geometry. To improve the convergence of triangular membrane elements, drilling rotations are introduced using Allmann - interpolation or the Free Formulation by Bergan. These elements can be further improved with the enhanced assumed strain method (EAS). By combining the most powerful plate and membrane elements, efficient facet elements for the analysis of shell structures can be constructed. Besides the mathematical conditions for stable and convergent finite element formulations, an understanding of the mechanical aspects of the applied methods is of primary interest. The performance of the different element formulations is tested by numerous numerical examples. (orig.)Available from TIB Hannover: RN 3694(21) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman