To meet the need of lightweight chassis in the near future, a technological step of introducing anisotropic materials like Carbon Fibre Reinforced Plastics (CFRP) in structural parts of cars is a possible way ahead. Though there are commercially available tools to find suitability of Fibre Reinforced Plastics (FRPs) and their orientations, they depend on numerical optimization and complexity increases with the size of the model. Nevertheless, the user has a very limited control of intermediate steps. To understand the type of material system that can be used in different regions for a lightweight chassis, especially during the initial concept phase, a more simplified, yet reliable tool is desirable.The thesis aims to provide a framework for determining fibre orientations according to the most-ideal loading path to achieve maximum advantage from FRP-materials. This has been achieved by developing algorithms to find best-fit material orientations analytically, which uses principal stresses and their orientations in a finite element originating from multiple load cases. This thesis takes inspiration from the Durst criteria (2008) which upon implementation provides information on how individual elements must be modelled in a component subjected to multiple load cases. This analysis pre-evaluates the potential of FRP-suitable parts. Few modifications have been made to the existing formulations by the authors which have been explained in relevant sections.The study has been extended to develop additional MATLAB subroutines which finds the type of laminate design (uni-directional, bi-axial or quasi-isotropic) that is suitable for individual elements.Several test cases have been run to check the validity of the developed algorithm. Finally, the algorithm has been implemented on a Body-In-White subjected to two load cases. The thesis gives an idea of how to divide the structure into sub-components along with the local fibre directions based on the fibre orientations and an appropriate laminate design based on classical laminate theory.

<p>  </p> <p>This thesis is motivated by the author’s observation that no systematic methodology is available to characterize and model mechanical behaviors of 3D printed parts in terms of their elastic modulus and critical loading capacities. Note that the more controlled and steadier printing process is, the easier the mechanical properties parts can be predicted. This research focuses on the methods for the prediction and validation of mechanical properties of 3D printed parts, and the focus is the responses of the printed parts subjected to tensile loads. The mathematic models are derived to characterize the mechanical properties of a part along three principal directions, and the models are validated experimentally by following the American Society for Testing and Materials (ASTM) D638 testing standards. It is assumed that a unidirectional plane stress occurs to each lamina to (1) simplify a compliance matrix with a size 3 by 3 and (2) characterize the mechanical properties by the elastic modules and strengths in three principal directions. Two mathematical models are developed using the experimental data from the classical laminate theory and finite element analysis (FEA) by the SolidWorks. Both of the developed models are used to predict the ultimate tensile strength and Young’s modulus of the specimens that are printed by setting different raster angles on different layers. This thesis work aims to (1) gain a better understanding of the impact of printing parameters on the strengths of printed parts and (2) explore the feasibility of using the classical laminate theory to predict the mechanical properties of the parts printed with different raster angles and patterns. To validate the proposed mathematic models, parts by FDM are tested by following the ASTM testing standards; moreover, it testifies if the selected ASTM-D638 is suitable to test 3D printed parts by FDM. </p>

Composite monocoque frames are becoming increasingly more popular inperformance cars. Compared to their steel and aluminum counterparts theyprovide additional torsional stiffness at the cost of less weight. This thesiscovers the complex optimization process of a monocoque applied within theregulations of a Formula Student competition. It aims to give the reader a goodunderstanding of the rules and how they affect the optimization process whilegenerating an optimized design used in the competition of Formula StudentGermany -21 by KTH Formula Student. The rules of Formula Student dictate the structural requirements on themonocoque based on a steel space frame. All materials except low carbon steelused in the structure require proof of equivalence through regulated testingmethods. However, this thesis shows that the regulated setup can severelyaffect results through a deep analysis of the testing methodology.The torsional stiffness of the monocoque is analyzed and optimized accordingto the results of a free-size optimization. Both through slight adjustmentsin chassis geometry and the laminate, resulting in a theoretical torsionalstiffness of 9.9 kNm/deg, more than five times as much as the old space frame.Weighing in at 20 kg, a significant weight reduction of about 10 kg, eventhough it was larger, with a surface area of about 4.2 m2. This design will be the first monocoque manufactured within KTH FormulaStudent since 2010. Therefore, a lot of focus was put on analyzing the rulesand lay the ground for future development by conducting tests on optimizedpanels. These results have the potential to further reduce the weight of a futuremonocoque with a different geometry. / Allt fler sportbilar använder självbärande karosser i komposit. Till skillnadfrån deras stål och aluminium motsvarighet så tillåter kompositkonstruktionenen styvare konstruktion för samma vikt. Denna rapport går igenom denkomplicerade optimeringsprocessen för en självbärande kaross i kolfiber appliceratinom tävlingen Formula Student. Målet med rapporten är att läsaren ska fåen bättre förståelse av reglerna och dess påverkan på optimeringsprocessensamtidigt som en optimerad design presenteras för användandet i “FormulaStudent Germany -21” åt KTH Formula Student. Reglerna inom Formula Student ställer strukturella krav på den självbärandekarossen baserat på en standard för stålrörsramar. Alla material förutomlåg kols stål som används i strukturen kräver att ekvivalens bevisas genomspecifika tester. Denna rapport visar att dessa tester kan generera olika resultatgenom en djup analys av metodiken. Torsions styvheten av karossen analyseras och optimeras enligt reglernagenom en så kallad free-size optimization". Genom att variera geometri ochkomposit utvecklades en kaross som var mer än 5 gånger så styv som dentidigare stålrörsramen med en teoretisk torsions styvhet på 9.9kNm/deg. Meden vikt på 20 kg reducerades även vikten 10 kg, även om den var större, ochhade en area på cirka 4.2m2. Denna design kommer att vara den första självbärande komposit karossentillverkad inom KTH Formula Student sedan 2010. Efter den djupa analysen avreglerna, testas då de optimerade panelerna, vilket lägger grunden för framtidautvecklingen. Dessa resultat har potential att reducera vikten ytterligare av enframtida kaross, genom ändringar i geometrin.

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.

The main objective of this work was to design a suitable composition of a protective coatings, made of several different layers of specific materials - with respect to residual stress, induced due to a mismatch in thermal expansion coefficients of each layer. Protective coating in this work means both the thermal and the environmental barrier. These coatings protect components against high temperatures and harsh environment. In this work, necessary theoretical background in the field of the thermal and environmental barrier coatings is introduced. There are mentioned some basic design approaches, commonly used materials and processing methods for the coating structure. The literature review gives an overview of modeling of such coated structures, in particular it is devoted to the thermal barrier coatings deposited by air plasma spray process. The next chapter closely describes classical laminate theory used for calculation of residual stresses in the coating. One of the assumptions of this theory is homogenous temperature field through the coating’s thickness. However, in this work was revealed a way to extend the classical lamination theory of such cases, in which the temperatures vary along the thickness of the coating. In the practical part, the analytical model was used for designing suitable properties of some coatings, which were consists of two, three and four layers. The calculations were performed both for constant temperature and for the temperature gradient. All results obtained from analytical approach were verified by numerical calculations.

V současnosti je velmi aktuálním tématem generování elektrické energie z alternativních zdrojů, zejména z vibrací. Zařízení, která přeměňují mechanickou energii na elektrickou, využívají často ke své činnosti piezoelektrický jev. Pro optimální nastavení takového elektromechanického měniče pro danou aplikaci je třeba mít k dispozici výpočtový model, který bude schopný postihnout všechny klíčové aspekty jeho provozu. Tato práce se tedy zabývá vytvořením takovéhoto nástroje, který je schopen komplexně popsat elektromechanickou odezvu studovaného piezoelektrického měniče energie v podobě vetknutého, vícevrstvého keramického nosníku s piezoelektrickými vrstvami. Uvažovaná vícevrstvá konstrukce je během své činnosti vystavena kinematickému buzení a je rovněž zatížena tepelnou zbytkovou napjatostí vznikající při její výrobě. Vytvořený výpočtový model využívá klasickou laminátovou teorii k určení statické elektromechanické odezvy dané konstrukce. Elektromechanická odezva při kmitání uvažované konstrukce v ustáleném stavu je získána s využitím Hamiltonova variačního principu a teorie kmitání prutů. Vytvořený výpočtový model je dále schopen odhadnout zdánlivou lomovou houževnatost dané vícevrstvé konstrukce pomocí metody váhových funkcí. Výstupy vytvořeného výpočtového modelu jsou ověřeny s využitím numerických simulací na bázi MKP a dostupných experimentálních výsledků. V diplomové práci je následně vytvořený výpočtový model aplikován při hledání optimálního rozložení jednotlivých vrstev konkrétního vícevrstvého nosníku s cílem maximalizovat jeho elektrický výkon a odolnost vůči šíření povrchových trhlin, resp. vzniku křehkého lomu. Tohoto cíle je dosaženo pomocí vhodného rozložení tepelných zbytkových napětí v jednotlivých vrstvách uvažované konstrukce (řízeného použitými materiály a tloušťkami jednotlivých vrstev).

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.:1 Introduction 1.1 Motivation 1.2 Organisation of this work 1.3 Notation and basic definitions 2 Basic theory of 3D simulation 2.1 Differential geometry 2.1.1 Initial and deformed domain 2.1.2 Strain tensor 2.2 Energy functional 2.2.1 Linearly elastic material law 2.2.2 Equilibrium of forces 2.2.3 Large deformations 2.2.4 Small deformations 2.3 Voigt notation and elasticity matrix 3 Transversely isotropic material law 3.1 Elasticity tensor 3.2 Conversion of the material constants 3.3 Elasticity matrix 3.4 Eigenvalues 3.5 State of plane strain 3.6 State of plane stress 4 Plate theory and classical laminate theory 4.1 The Kirchhoff–Love hypothesis 4.2 Constitutive law and bilinear form of the laminated plate 4.3 Definition of resultants 4.4 Boundary conditions 4.5 From the equilibrium conditions to the weak formulation 4.5.1 Membrane equilibrium 4.5.2 Plate equilibrium 4.5.3 Combined weak formulation 4.5.4 The CLT problem in Voigt notation 5 Discretisation 5.1 Short introduction to FEM 5.2 Adaptive FEM 5.3 Finite elements for 3D elasticity problems 5.4 Finite elements for plates 5.4 Finite elements for plates 5.4.1 BFS rectangles 5.4.2 rHCT triangles 5.5 CLT elements 5.5.1 Rectangles 5.5.2 Triangles 6 Solver and preconditioner 6.1 The preconditioned conjugate gradient method 6.2 Hierarchical basis and BPX preconditioners 6.3 Preconditioning of CLT problems 6.3.1 General laminates 6.3.2 Some special cases and examples 7 A posteriori residual error estimation 7.1 Residual error estimator for 3D elements 7.2 Residual error estimator for plate and CLT elements 7.2.1 Auxiliary definitions and assumptions on the mesh 7.2.2 Interpolation operators 7.2.3 Important inequalities 7.2.4 Cut-off functions 7.2.5 Definition of the error 7.2.6 Reliability inequality 7.2.7 Efficiency inequality 8 Some details of the implementation 8.1 The adaptive FE package SPC-PM 8.2 Remarks on some added features 8.2.1 Capability of the current code 8.2.2 Cuntze’s failure mode concept 8.3 Coordinate transformation of higher-order derivatives 8.3.1 Mapping of coordinates 8.3.2 Transformation of derivatives of up to the third-order 8.3.3 Recursive construction of transformation matrices 8.3.4 Simplification for axis-parallel rectangles 9 Numerical examples 9.1 A three-dimensional example from eniPROD 9.2 Example problems for laminates 9.2.1 Rectangular plate under in-plane load 9.2.2 Rectangular plate under vertical load 9.2.3 L-shaped plate with inhomogeneous natural boundary conditions 10 Conclusion and outlook Bibliography Acknowledgements List of main symbols Theses