Freie SchlagwГ¶rter (DE) adaptive FEM, Plattentheorie, klassische Laminattheorie, Faserverbundwerkstoff, transversale Isotropie, numerische Simulation Freie SchlagwГ¶rter (EN) adaptive FEM, plate theory, classical laminate theory, fibre-reinforced material, transverse isotropy, numerical simulation Klassifikation (DDC) 518 NormschlagwГ¶rter (GND) Finite-Elemente-Methode, Laminat, Plattentheorie, Faserverbundwerkstoff GutachterIn The effectiveness of both results is demonstrated by numerical examples. 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 other part is the error estimation process the error estimator determines where the current mesh has to be refined for the next step. 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. 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. The focus of this work is the adjustment of two integral parts of the adaptive FE algorithm according to the classical laminate theory. The classical laminate theory implies a combination of the membrane problem and the plate problem with additional coupling terms. To achieve this goal, the theoretical background of elastic deformation problems, transverse isotropy, plate theory, and the classical laminate theory is recapitulated. AutorIn Michael Weise Titel Adaptive FEM for fibre-reinforced 3D structures and laminates ZitierfГ¤hige Url: Гњbersetzter Titel (DE) Adaptive FEM fГјr faserverstГ¤rkte 3D-Strukturen und Laminate Datum der Einreichung Datum der Verteidigung Abstract (EN) The topic of this thesis is the numerical simulation of transversely isotropic 3D structures and laminates by means of the adaptive finite element method.

Classical laminate plate theory