The topic of this thesis is the numerical simulation of transversely isotropic 3D structures and laminates by means of the adaptive finite element method. To achieve this goal, the theoretical background of elastic deformation problems, transverse isotropy, plate theory, and the classical laminate theory is recapitulated. The classical laminate theory implies a combination of the membrane problem and the plate problem with additional coupling terms. The focus of this work is the adjustment of two integral parts of the adaptive FE algorithm according to the classical laminate theory.
One of these parts is the solution of the FE system; a good preconditioner is needed in order to use the conjugate gradient method efficiently. It is shown via a spectral equivalence bound that the combination of existing preconditioners for the membrane and plate problems poses a capable preconditioner for the combined laminate problem.
The other part is the error estimation process; the error estimator determines where the current mesh has to be refined for the next step. Existing results on residual error estimators for the elasticity problem, the biharmonic problem, and the plate problem are combined and extended to obtain a posteriori local residual error indicators for the classical laminate theory problem.
The effectiveness of both results is demonstrated by numerical examples.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-150439 |
| Date | 18 August 2014 |
| Creators | Weise, Michael |
| Contributors | Technische Universität Chemnitz, Mathematik, Prof. Dr. rer. nat. habil Arnd Meyer, Univ.Prof. Dipl.-Ing. Dr. techn. Joachim Schöberl |
| 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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