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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-121275 |
| Date | 16 September 2013 |
| Creators | Rückert, Jens |
| Contributors | TU Chemnitz, Fakultät für Mathematik, Prof. Dr. rer. nat. habil. Arnd Meyer, Prof. Dr. rer. nat. habil. Michael Jung |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
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