Numerical Simulation of Short Fibre Reinforced Composites

Dipl.-Math. Rolf Springer

AutorIn

Dipl.-Math. Rolf Springer

Titel

Numerical Simulation of Short Fibre Reinforced Composites

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-872702

Datum der Einreichung

22.12.2022

Datum der Verteidigung

25.08.2023

Abstract (EN)

Lightweight structures became more and more important over the last years. One special class of such structures are short fibre reinforced composites, produced by injection moulding. To avoid expensive experiments for testing the mechanical behaviour of these composites proper material models are needed. Thereby, the stochastic nature of the fibre orientation is the main problem. In this thesis it is looked onto the simulation of such materials in a linear thermoelastic setting. This means the material is described by its heat conduction tensor κ(p), its thermal expansion tensor T(p), and its stiffness tensor C(p). Due to the production process the internal fibre orientation p has to been understood as random variable. As a consequence the previously mentioned material quantities also become random. The classical approach is to average these quantities and solve the linear hermoelastic deformation problem with the averaged expressions. Within this thesis the incorpora- tion of this approach in a time and memory efficient manner in an existing finite element software is shown. Especially for the time and memory efficient improvement several implementation aspects of the underlying software are highlighted. For both - the classical material simulation as well as the time efficient improvement of the software - numerical results are shown. Furthermore, the aforementioned classical approach is extended within this thesis for the simulation of the thermal stresses by using the stochastic nature of the heat conduc tion. This is done by developing it into a series w.r.t. the underlying stochastic. For this series known results from uncertainty quantification are applied. With the help of these results the temperature is developed in a Taylor series. For this Taylor series a suitable expansion point is chosen. Afterwards, this series is incorporated into the computation of the thermal stresses. The advantage of this approach is shown in numerical experiments.

Freie Schlagwörter (EN)

linear thermoelasticity, finite element method, numerical analysis, uncertainty quantification, scientific computing

Klassifikation (DDC)

518

519

Normschlagwörter (GND)

Lineare Elastizitätstheorie, Thermoelastizität, Finite-Elemente-Methode, Numerische Mathematik, Unsicherheitsquantifizierung, Wissenschaftliches Rechnen

GutachterIn