Numerical model usage has substantially increased in many industries. It is the aerospace industry that numerical models play possibly the most important role for development of optimum design. However, numerical models need experimental verification. This experimental verification is used not only for validation, but also updating numerical model parameters. Verified and updated models are used to analyze a vast amount of cases that structure is anticipated to face in real life. In this thesis, structural finite element model updating of a utility helicopter fuselage was performed as a case study. Initially, experimental modal analyses were performed using modal shakers. Modal analysis of test results was carried out using LMS Test.lab software. At the same time, finite element analysis of the helicopter fuselage was performed by MSC.Patran &amp / Nastran software. v Initial updating was processed first for the whole helicopter fuselage then, tail of the helicopter was tried to be updated. Furthermore, a new method was proposed for the optimum node removal location for getting better Modal Assurance Criterion (MAC) matrix. This routine was tried on the helicopter case study and it showed better performance than the Coordinate Modal Assurance Criterion (coMAC) that is often used in such analyses.

Two subjects are included in this thesis; one is to construct the Coffin-Manson equation of the unleaded SnAgCu solder according to the experimental results provided by the Metal Research Laboratory (MRL) of Industrial Technologies Research Institute (ITRI). The results of CSP thermal cycle fatigue and SOJ pull tests and the corresponding stress and strain distributions solved from FEM analyses have been used to derive the Coffin-Manson equation for the SnAgCu solder. The other subject is to investigate the effect of CTE mismatch on the fatigue life of solder balls in the opto-electronic packaging. The solidified shapes of the different solder balls after undergoing the re-flow process are predicted by employing the Surface Evolver package program. The FEA meshes of the solidified solder balls in opto-electronic packaging are built according to the output results of the Surface Evolver program. The maximum equivalent plastic shear strain range of the solder after under one thermal cycle process is calculated by employing the MARC finite element package. The fatigue lives of solder balls under different arrangements are estimated according to the proposed Coffin-Manson equation. The effect of solder ball parameters, i.e. solder volume, solder offset distance, solder DNP and solder material on the reliability of different solder balls has also been explored in this thesis.

A new scratch test methodology is proposed. The new test methodology is developed based on the principles of materials science and solid mechanics, which include the consideration of material parameters, use of microscopy for image analysis and the finite element method (FEM). The consistency and reproducibility of test results are shown using a new scratch test device on two sets of neat and talcfilled polypropylene (PP) systems. Three different test conditions, i.e., linear load increase under constant rate, constant load under constant rate, and linear rate increase under constant load, have been conducted to determine the most effective, informative test conditions for evaluation of scratch resistance of polymers. Experimental observations and FEM results show a good qualitative correlation. The unique advantages of the new scratch test method for evaluating scratch resistance of polymers are discussed. A systematic study of surface damage effected by a progressive scratching load is performed on model polypropylene (PP) systems. Mar-scratch and stress -whitening transitions can be readily observed, and the corresponding critical loads determined. Distinctive scratch hardnesses and surface damage features are found for different material systems. Visibility of scratched surface is quantified using gray level analysis via a flatbed scanner and a commercial image analysis tool. It is found that the onset of scratch visibility can be determined accurately and reproducibly using the custom -built scratcher under progressive loading condition. Talc particles are found to be responsible for the increased light scattering, leading to greatly increased visibility. The observed scratch visibility is also found to be related to the measured frictional force profiles. Approaches for producing scratch resistant PP are discussed.

The analysis of wave propagation in solids with complex microstructures, and local heterogeneities finds extensive applications in areas such as material characterization, structural health monitoring (SHM), and metamaterial design. Within continuum mechanics, sources of heterogeneities are typically associated to localized defects in structural components, or to periodic microstructures in phononic crystals and acoustic metamaterials. Numerical analysis often requires computational meshes which are refined enough to resolve the wavelengths of deformation and to properly capture the fine geometrical features of the heterogeneities. It is common for the size of the microstructure to be small compared to the dimensions of the structural component under investigation, which suggests multiscale analysis as an effective approach to minimize computational costs while retaining predictive accuracy. This research proposes a multiscale framework for the efficient analysis of the dynamic behavior of heterogeneous solids. The developed methodology, called Geometric Multiscale Finite Element Method (GMsFEM), is based on the formulation of multi-node elements with numerically computed shape functions. Such shape functions are capable to explicitly model the geometry of heterogeneities at sub-elemental length scales, and are computed to automatically satisfy compatibility of the solution across the boundaries of adjacent elements. Numerical examples illustrate the approach and validate it through comparison with available analytical and numerical solutions. The developed methodology is then applied to the analysis of periodic media, structural lattices, and phononic crystal structures. Finally, GMsFEM is exploited to study the interaction of guided elastic waves and defects in plate structures.

<p>Under vår utbildning på högskolan i Skövde har vi stött på Skolverkets Diagnostiska uppgifter i matematik - för användning i de tidiga skolåren. Genom användandet av materialet tror vi att elevernas inlärningsprocess blir synlig. Men hur ser lärarna på materialet? För att få svar på frågor om detta har vi intervjuat fem lärare i grundskolans tidigare årskurser. Den empiriska studien har en kvalitativ ansats där vi genom intervjuer försöker ta reda på lärarnas åsikter och uppfattningar om materialet. Vi tolkar utifrån vår teoretiska bakgrund samt vårt resultat att materialet används på olika sätt. Det kan sättas ihop till ett arbetshäfte, vilket används under en längre period. Det kan användas som ett summerande prov av elevernas kunskapsnivå i slutet av årskurs två. Enligt vår tolkning är det hur de alltid gjort på skolan som styr förfarandet. Det är oklart om lärarna ser nyttan med materialet, eftersom de uttrycker att de har goda kunskaper om elevernas kunskapsnivå även utan att använda det. När lärarna använder materialet som ett prov, uttrycker de att de får resurser utefter resultatet som meddelas till rektor, vilken i sin tur anmäler resultatet till kommunens kvalitetsredovisning. Vi har genom vår undersökning funnit att lärarna är fokuserade på mål att uppnå för årskurs fem. Vi tror att om lärarna arbetade med materialet så som författarna av det avser, underlättar det för läraren att nå målen.</p>

<p>The following report contains an evaluation of the use of mathematical simulation programs at the company Isaberg Rapid AB. The work includes booth FE and motion simulations where the results are compared with real life test data.</p><p>The goal of the report is to evaluate the accuracy of simulations which can be performed by engineers as a part of the design process. By using mathematical simulation tools it is possible to find a good design solution early in the development phase and thereby shorten lead time and reduce costs.</p>

Die vorliegende Arbeit umfasst die Entwicklung, Implementierung und Anwendung von Verfahren zur Parameteridentifikation schädigungsmechanischer Materialgesetze. Die duktile Schädigung wird auf kontinuumsmechanischer Basis durch Erweiterung der von Mises Fließbedingung mit dem Gurson-Tvergaard-Needleman sowie mit dem Rousselier Modell beschrieben. Das klassische Rousselier Modell wird dabei für beschleunigtes Porenwachstum und Porennukleation ergänzt. Das nichtlineare Rand- und Anfangswertproblem wird mit dem finite Elemente System SPC-PMHP berechnet, welches im Rahmen des Sonderforschungsbereichs (SFB) 393 für Parallelrechner entwickelt wurde. Im Zusammenhang mit der Entfestigung des Materials wird ein Lokalisierungskriterium für die Dehnungen im geometrisch nichtlinearen Fall angegeben. Die Identifikation der Materialparameter erfolgt über gemessene Kraft-Verschiebungskurven, lokale Verschiebungsfelder und über den Zeitpunkt der Lokalisierung. Dazu wird ein nichtlinearer Optimierungsalgorithmus verwendet, der mittels Gradientenverfahren die Zielfunktion in das nächste Minimum überführt. Eine semianalytische Sensitivitätsanalyse liefert die Ableitungen der Verschiebungen und Kräfte nach den Parametern. Verschiedene numerische Untersuchungen geben Aufschluss über die anzuwendende Optimierungsstrategie. Abschließend werden die lokalen Verschiebungsfelder mit dem Objektrasterverfahren sowie die Kraft-Verschiebungskurven an gekerbten Flachzugproben aus StE 690 ermittelt und die Parameter des Materials identifiziert.

Gegenstand dieser Arbeit ist die Forschungsdisziplin, welche in der Strukturmechanik als Modellordnungsreduktion bekannt ist. Im Mittelpunkt stehen Kopplungsprozesse von starren und elastischen Mehrkörpersystemen - sowohl in theoretischer Hinsicht als auch bezüglich der praktischen Realisation im Rahmen des Finite-Elemente-Programms ANSYS und des Mehrkörpersimulationsprogramms SIMPACK. Eine Vielfalt von strukturerhaltendenMOR-Methoden wurde zum Zwecke des Überblicks dargestellt. Darüber hinaus findet sich eine Kategorisierungsmethodik in Hinsicht auf den später beschriebenen FEM-MKS-Kopplungsprozess. Die Effizienz der MOR-Methoden wird sowohl hinsichtlich der Qualität der ROM als auch bezogen auf die hierfür benötigte Rechenzeit bemessen. Aus diesem Grunde wurden etliche MOR Schemata dargelegt, mit dem Ziel, den Effizienzfaktor während der Berechnung eines ROMs zu maximieren, das heißt maximale Qualität und minimale Rechenzeit zu erzielen. Die Validierung der dynamischen ROM-Eigenschaften basiert auf der Anwendung der sogenannten Modellkorrelationskriterien. Dies wurde an vier Anwendungsbeispielen aus dem Feld der Strukturmechanik getestet: der 3D-Balkenstruktur, der UIC60-Schiene, dem Pleuel und der Kurbelwelle. Die Anwendung der diagonal perturbation-Methodik verbessert die Kondition der Steifigkeitsmatrix eines Modells, von beiden Arten von Lösungsprozeduren, d.h. direkte und iterative Verfahren, betroffen sind. Die dynamische Bewegung mechanischer MKS wird als ein Index-3-DAE-Systemformuliert und die Information über die elastischen Körper wird in Form der sogenannten Standard Input Datei in einen MKS-Code transferriert. Die Einführung des Back-projection-Ansatzes ermöglicht die weitere Verwendung bestimmter ROM-Typen, derren assoziierten physikalische Eigenschaften unangemessen definiert wurden. Zum Abschluss werden die theoretischen, modellierenden und numerischen Fortschritte der Arbeit resümiert und kombiniert im Sinne der Model Order Reduction Package Toolbox (MORPACK). Die Matlab-basierte MORPACK-Toolbox ermöglicht den FEM-MKS-Kopplungsprozess für die Verwendung von ANSYS und SIMPACK. Hierin sind ein Großteil der zuvor erläuterten Erweiterungen eingeschlossen. Mit Hilfe der zwei integrierten inneren MOR- und SID-Schnittstellen als auch der vier Anwendungsebenen wird der Import von freien oder eingespannten ROM in SIMPACK ermöglicht. / The research discipline referred to as the Model Order Reduction in structural mechanics is the topic of this Thesis. Special emphasis is given to the coupling process of rigid and elastic Multi Body Dynamics in terms of both the theoretical aspects and the practical realization within the environment of the commercial Finite Element and the Multi Body Systems software packages, ANSYS and SIMPACK respectively. In this regard, a variety of structure preserving Model Order Reduction methods is presented and a categorization methodology is provided in view of the later FEM-MBS coupling process. The algorithmic scheme of several of the MOR methods indicates the capability of generating qualitatively better Reduced Order Models than the standardized Guyan and Component Mode Synthesis approaches. The efficiency of a MOR method is measured in terms of both the quality of the ROM and the associated time required for the .computation Based on the application of the, so called, Model Correlation Criteria the efficiency of the MOR schemes is tested on four application examples originating from the area of structural mechanics, i.e. the 3D elastic solid bar structure, the UIC60 elastic rail, the elastic piston rod, and the elastic crankshaft model. Herewith, the superiority of alternative MOR schemes in comparison to Guyan or CMS methods is demonstrated in terms of the ROM?s quality and the computation time by the use of either the one-step or the two-step MOR algorithms. Numerous of the FE discretized structures suffer from the, so called, ill-conditioned properties regarding the associated stiffness matrix. On one hand, the direct solution of a MOR method might produce erroneous ROMs due to the associated truncation phenomenon and on the other hand, any kind of iterative approach suffers from vast computation times. The application of the diagonal perturbation methodology improves the condition properties of the model?s stiffness matrix and thus, both kinds of the aforementioned solution procedures are affected. The back-projection approach is introduced, which projects the ROM belonging to the Non physical subspace reduction-expansion methods category back onto the physical configuration space and thus, enabling its further usage in a MBS code, e.g. SIMPACK. Finally, the theoretical, modelling, and numerical advancements are combined in terms of the Model Order Reduction Package. The Matlab-based MORPACK toolbox enables the FEM-MBS coupling process for the ANSYS-SIMPACK utilization and herewith, several of the aforementioned enhancements are included. With the help of the two integrated inner interfaces, i.e. MOR and SID, as well as four application levels, the import into SIMPACK of alternatively free or fixed ROMs is enabled. The functionality of MORPACK is demonstrated based on two application examples, namely, the 3D elastic solid bar and the UIC60 elastic rail, the dynamic properties of which are validated prior to their import into SIMPACK.

Considering the unlikely core melt down scenario for a light water reactor (LWR) a possible failure mode of the reactor pressure vessel (RPV) and its failure time has to be investigated for a determination of the loadings on the containment. Worldwide several experiments have been performed accompanied with material properties evaluation, theoretical, and numerical work. At the Institute of Safety Research of the FZR a finite element model has been de-veloped simulating the thermal processes and the viscoplastic behaviour of the ves-sel wall. An advanced model for creep and material damage has been established and has been validated using experimental data. The thermal and the mechanical calculations are sequentially and recursively coupled. The model is capable of evalu-ating fracture time and fracture position of a vessel with an internally heated melt pool. The model was applied to pre- and post test calculations for the FOREVER test se-ries representing the lower head RPV of a PWR in the geometrical scale of 1:10. These experiments were performed at the Royal Institute of Technology in Stock-holm. The results of the calculations can be summarised as follows: # The creeping process is caused by the simultaneous presence of high tem-perature (>600 °C) and pressure (>1 MPa) # The hot focus region is the most endangered zone exhibiting the highest creep strain rates. # The exact level of temperature and pressure has an influence on the vessel failure time but not on the failure position # The failure time can be predicted with an uncertainty of 20 to 25%. This uncer-tainty is caused by the large scatter and the high temperature sensitivity of the viscoplastic properties of the RPV steel. # Contrary to the hot focus region, the lower centre of the vessel head exhibits a higher strength because of the lower temperatures in this zone. The lower part moves down without significant deformation. Therefore it can be assumed, that the vessel failure can be retarded or prevented by supporting this range. # The development of a gap between melt crust and vessel wall could not be proofed. First calculations for a PWR geometry were performed to work out differences and commonalities between prototypic scenarios and scaled experiments. The results of the FOREVER-experiments cannot be transferred directly to PWR geometry. The geometrical, mechanical and thermal relations cannot be scaled in the same way. Because of the significantly higher temperature level, a partial ablation of the vessel wall has to be to expected in the PWR scenario, which is not the case in the FOREVER tests. But nevertheless the FOREVER tests are the only integral in-vessel retention experiments up to now and they led to a number of important insights about the behaviour of a vessel under the loading of a melt pool and pressure.

<p>Paper A: In this paper, the development and implementation of a contact algorithm based on C2-continuous surface representations is discussed. In 3D contact simulations involving models with arbitrarily curved surfaces (as in the case of vessel walls), the discretization of the contact surfaces by means of facet-based techniques could lead to numerical instabilities and finally loss of quadratic convergence. These instabilities arise mainly due to the sliding of contractor (slave) nodes over the boundaries of target (master) contact facets, where jumps of the normal vector are experienced. The paper addresses successfully this problem, by discretization of the target surfaces by means of C2-continuous parameterization schemes. Initially, the uniform cubic B-spline surfaces are introduced. Next, in an attempt for more accurate representations of the geometric models of the contact surfaces, a new parameterization based on the expression of cubic B-splines is developed. The two approaches are implemented into a finite element framework and more specifically, into the multipurpose finite element analysis program FEAP. The special merits of the developed algorithms and the advantages of the smooth surfaces over facet-based approaches are exhibited through a classical contact mechanics problem, considering incompressibility, finite deformations and large slidings. Next, a simulation of balloon angioplasty with stenting is presented, where the contact between both medical devices (balloon and stent) with the arterial wall is modeled. The arterial wall is modeled in this first approach, as hyperelastic, homogeneous, isotropic, while a cylindrically orthotropic model is developed to capture the nonlinear, anisotropic behavior of the balloon catheter under pressure. Two stents with the same geometry but different strut thickness, are studied. Both are considered elasto-plastic. The performed simulations point out the outcome of the balloon angioplasty and stenting in terms of luminal gain and mechanical strains. Finally, a comparison between the two stent configurations is presented.</p><p>Paper B: The second paper makes use of the contact tool developed in Paper A and focuses on the changes of the mechanical environment of the arterial wall due to stenting, as a function of a set of stent design parameters. In particular, Paper B presents a detailed geometric and material model of a postmortem human iliac artery, composed by distinct tissue components, each associated with specific mechanical properties. The constitutive formulation for the artery considers anisotropic, highly nonlinear mechanical characteristics under supraphysiological loadings. The material and structural parameters of the arterial model are obtained through uniaxial tensile tests on stripes extracted from the several arterial tissues that form the stenosis, axially and circumferentially oriented. Through cooperation with a well-established stent manufacturing company, an iliac stent was acquired. The dimensions of the stent are measured under a reflected-light microscope, while it is parameterized in such a way as to enable new designs to be simply generated through variations of its geometric parameters. The 3D balloon-stent-artery interaction is simulated by making use of the smooth contact surfaces with C2-continuity, as previously mentioned. Next, scalar quantities attempt to characterize the arterial wall changes after stenting, in form of contact forces induced by the stent struts, stresses within the individual components and luminal change. These numerically derived quantities allow the determination of the most appropriate stent configuration for an individual stenosis. Therefore, the proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures, stent material and geometries on a patient-specific level.</p>