Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa-121275
Rückert, Jens
Jung, Michael (Prof. Dr. rer. nat. habil.) (Gutachter)
Kirchhoff Plates and Large Deformations - Modelling and C^1-continuous Discretization
Kurzfassung in englisch
In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Wissenschaftliches Rechnen | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Meyer, Arnd (Prof. Dr. rer. nat. habil.) | |
| URL/URN: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-121275 | |
| SWD-Schlagwörter: | Schale , Platte , Deformation | |
| Freie Schlagwörter (Deutsch): | Schalen , Platten , große Deformationen , große Verzerrungen , C^1-stetige FEM , shells , plates , large deformation , finite strain , C^1-continuous FEM | |
| DDC-Sachgruppe: | Numerische Analysis | |
| Tag der mündlichen Prüfung | 26.08.2013 |
