Military aircraft have strict requirements to show a low radar signature within different aspect angels and frequency bands. The Finite Difference method and Finite Element method are used by Saab to determine the radar signature from different objects, but the methods  suffer from a few limitations. In this master thesis, the Discontinuous Galerkin Finite Element method is implemented to compute the radar signature. The method is implemented in Matlab and is used to discretize Maxwell's Equations in one dimension. The implementation includes dispersive media and absorbing boundary conditions. Performance comparisons between the Finite Element method and the Discontinuous Galerkin Finite Element method are carried out. The results show that the Finite Element method perform better in one dimension, however the results also suggests that the Discontinuous Galerkin Finite Element method will perform better in higher dimensions.

Knee joint kinematics is the result of a complex roto-translation movementcharacteristic of the tibio-femoral (TF) and patello-femoral (PF) articulations.This movement depends on the shape of the femur, the tibial plateau andthe patella. Moreover, it depends also on the morphological and mechanicalproperties of the soft tissues of the knee joint. In fact, the knee is characterizedby an extrinsic stability due to the active constraints (muscles and tendons)and passive soft tissues (menisci, retinaculum and ligaments) that surround it.As a result, knee kinematics and kinetics are different in each human being, andsometimes, even in the same person, with the right knee behaving differentlycompared to the left one.The ideal total knee arthroplasty TKA, used to correct pathologies that couldaffect the knee joint, should enable the restoration of the patient’s functionalknee kinematics and kinetics, so that the patient does not normally notice theTKA implant.Nowadays, TKA surgery is a well-established procedure and surgeons maychoose from among the broad range of TKA solutions available on the marketto meet the patient’s request. Prostheses may differ because of shape, materials,and mechanical constraints of their components. Consequently, the restorationof the knee joint biomechanics is limited by the degrees of freedom guaranteedby the adopted design solution.Despite the success of TKAs, pain and limited motor skills are reportedto still affect the clinical outcomes and not all patients are shown to be happyafter a TKA.Current complaints regarding post-TKA surgery might be related to the absenceof a proven tool that enables predicting patient-specific outcomes based ondifferent TKA solutions and providing guidelines to surgeons. In fact, surgicalpre-planning is usually based on a patient’s evaluation that the clinician canmake also based on medical images, and clinical experience. Data reported inthe literature can help in guiding the surgeon to a final decision regarding thebest subject-specific solution.Numerical methods, able to simulate knee biomechanics for various configurations,can be fundamental for the development of the appropriate reliableand effective tools to support clinically-tailored responses to a question.In particular, they can be used for subject-specific analyses on the intact kneeand for supporting the surgical pre-planning phase by comparing the effect ofdifferent solutions.When developing a subject-specific knee model, different kinds of datainputsare needed, such as the knee shapes and alignment information, softtissuesbehavior and boundary conditions describing the investigated motortasks. Often, most of this requested data are unlikely to be available (e.g.subject-specific soft-tissues material properties). Consequently, it is a commonoperating procedure to integrate literature data with subject-specific informationin order to develop knee models for collecting personalized outputsthat could be used to address research and clinical questions.However, up to now, the resulting effect of different generalized sources, asa mix of subject-specific and literature data, still needs to be evaluated for itsimpact on personalized outputs concerning knee behaviour.Furthermore, clinical questions are often focused on specific requests thatpartially use features of more complex knee models that could require too muchtime to be efficiently incorporated into daily clinical evaluations.For these reasons, the principal aims of this research have been to assess,first, the impact of differently derived generalized sources on the developmentof an intact subject-specific knee model or after a TKA; second,to provide guidelines to identify efficient clinically-tailored data sourcesused in and for knee modeling.To accomplish these tasks, a numerical knee model of an intact knee wasdeveloped based on both subject-specific and literature data sources. Theinfluence of different approaches to deal with a subject’s information, such asthe reconstruction of the knee geometries from different imaging sources, hasiiibeen evaluated. Moreover, a sensitivity analysis was performed to understandthe potential changes on kinetics and kinematics outcomes due to differentlyderived literature inputs, such as models and the properties that characterizethe joint materials and ligaments description. The outputs collected after finiteelement analyses were analyzed and compared with already published experimentaloutcomes for the same analyzed specimen and replicated boundaryconditions.Additionally, the effects on knee joint contact forces and kinematics afterTKA surgery and due to the mis-alignment of implant components or misidentificationsof ligament insertions were evaluated in another sensitivityanalysis performed with a rigid body analysis for four different TKA designsimplanted in a subject-specific knee model. As for the intact knee model, theanalyzed configurations were compared against already published experimentaloutputs or literature data replicating similar boundary conditions.Moreover, several dedicated knee models were developed to address specificclinical questions, such as the lack of biomechanical explanations for certainbehaviours of TKA designs.Once compared to already published experimental or literature data, the resultsof the developed models agree.The main results from the numerical simulations performed show that, changingthe values of some of the parameters used as inputs, the knee model kinematicsis less influenced than the contact forces and stresses outputs.In particular, in developing an intact knee model, the main effecting parameteris the material properties selection for the knee cartilage layers. Among theconfigurations analyzed using subject-specific knee models with TKAs, theposition of the tibial component and the height of the patellar buttonare the most effecting inputs.Exploring the different chapters of this research thesis, several specific resultsare shown regarding each main step followed in developing a knee numericalmodel. For example, new approaches based on MRIs have been suggested andtested proving that they are suitable for collecting subject-specific informationregarding geometrical shapes and landmark definitions. Moreover, a newgraphical method was proposed resulting more effective and immediate thanconventional representations in reporting huge amount of data. In particular,the method is the favourite to show complex biomechanical analyses especiallyfor the clinical audience that replied to a survey. Furthermore, the differentmodels tailored to address specific clinical questions collected useful biomechanicalresults, to provide clinical advice or industrial guidelines, and can beconsidered as examples of what should be included in a knee model for similarscenarios.The results of this thesis offer several contributions. Generally, these findingscould provide useful guidelines for knee-model developers to achievea more balanced approach to subject-specific intact knee models based upongeneral sources in order to improve the understanding of personalized kneebiomechanics.To address a general comment to the title of this thesis, there is no singleanswer. In fact, the selection of data sources is case-dependent using, forexample, the subject’s or literature available data to describe material’s behavioror the boundary conditions of a specific motor task. Moreover, differentclinical questions can be addressed with different numerical approaches, e.g.finite element analysis is necessary especially in the case that stress outputs arerequested, but can be too time-consuming for addressing complex sensitivityanalyses.Once the knee model developer has identified the necessary data sources andthe approaches to be implemented, the question-tailored knee models can thusbe used for several applications such as predicting subject-specific abnormalknee kinematics and kinetics for different TKA designs, polyethylene wear,patellofemoral dislocation and bone remodeling, choosing the best fitting TKAdesign for a specific patient, and developing a procedure to optimize TKAimplant designs. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Abstract The main objective of this thesis was to use and combine Finite Element Method (FEM) and small signal equivalent circuit models in actuator and energy harvesting design and to study the dynamics of the said designs. The work is divided into four different sections. In the first section, the small signal parameters are derived for a pre-stressed piezoelectric actuator using a series of measurements. In addition, the tunability of the resonance frequency using mass and series capacitors is investigated. In the second section, a piezoelectric Fabry Perot Interferometer actuator is simulated using FEM and the small signal parameters are derived using FEM simulations. The modelled results are compared with the actual measurements and the resonance frequency is found to differ by only 0.8 percent from the measured values when the mirror is attached to the actuator. In the third section a piezoelectric wide band energy harvester is developed with multiple beam topology. Two different designs are compared, one produced using the conventional PZT-steel structure and one with a PZT-LTCC structure. The final section presents an FEM model for a shoe mounted energy harvester and concentrates on the modelling of walking dynamics in FEM. The simulation results are compared to actual measurements and the simulated power values are found to differ by only 7% when the cymbal stroke is below 1.3 mm. The generated model is also expandable to other types of energy harvesters and the methods developed can be used in a variety of different energy harvesting simulations and harvester development. The results show that the equivalent circuit approach together with FEM modelling is a powerful tool in the dynamics design of piezoelectric actuators and energy harvesters. / Tiivistelmä Väitöstyön päätavoitteena oli yhdistää elementtimenetelmät (FEM) ja piensignaalimallit aktuaattorien ja energiankorjuukomponenttien suunnittelussa ja tutkia niiden dynamiikkaa. Työ on jaettu neljään eri osaan. Ensimmäisessä osassa piensignaalimallit johdettiin pietsosähköisestä aktuaattorista mittausten avulla. Lisäksi resonanssitaajuuden muuttamista tutkitaan massan ja sarjaan kytketyn kapasitanssin avulla. Toisessa osassa simuloidaan pietsosähköistä Fabry Perot interferometria käyttäen elementtimenetelmää. Lisäksi komponentin piensignaalimalli luodaan käyttäen simulointimallia. Lopuksi piensignaalimallin ja prototyypin mittaustuloksia verrataan. Mallin resonanssitaajuus poikkeaa mitatusta vain 0.8 %, kun aktuaattoriin on kiinnitetty peili. Kolmannessa osassa kehitetään ja verrataan toisiinsa kahta erilaista laajakaistaista monipalkkista pietsosähköistä energian korjuukomponenttia. Toinen komponenteista on toteutettu perinteisellä PZT-teräs rakenteella ja toinen yhteissintratulla PZT-LTCC rakenteella. Viimeisessä osassa luodaan simulaatio malli kenkään asennetulle cymbal tyyppiselle pietsosähköiselle energian korjuukomponentille ja kävelyn dynamiikkaa tutkitaan. Luotua mallia verrataan prototyypin mittaustuloksiin ja simuloitu energian tuotto poikkeaa vain 7 % alle 1.3 mm puristusliikkeellä. Tulokset osoittivat, että piensignaalimallin ja elementtimenetelmän yhdistäminen on tehokas apu pietsosähköisten aktuaattorien ja energiankorjuukomponenttien dynamiikan suunnittelussa.

Electrical connectors are widely utilized for signal communications in automotive electronic systems whose performance is related to the reliability of the entire system. Electrical connectors are frequently affected by the engine vibration, resulting in fretting damages on electrical connector. In this thesis, the main propose is to find a signal analysis method to predict the fretting damages on fuel pump connector induced by engine vibration. The data of the fuel pump connector is studied from a vibration test of the four-cylinder engine and the dominating frequencies are used in the fretting test to verify the analysis method. The fretting damage is identified through visual inspection by microscope. The model of the connector is built in COMSOL to explain the fretting on the contact surfaces. The results present the signal analysis method can be directly used to predict the risk of fretting damages during the engine vibration. Some significant frequencies are pointed out as guidelines for future tests and optimization.

As cities are densified and as the housing shortage iscontinuously high, the need to utilize height in new constructionsincreases, and with it, also the need to quickly make preliminaryassessments when designing structural components in higherbuildings. The question of whether calculations made using handmethods and calculations made using computerized methods yieldsresults of the same order of magnitude, when analyzing structures,is therefore of interest. The question investigated in this work is whether calculationsmade by hand and calculations made with FEM-design 3D Structure,with respect to stresses in a single structural component, yieldresults of the same order of magnitude. A 16 storey building withconcrete walls and floors was the basis for the calculations. Thecalculations were made for two load cases for both handcalculations and calculations made with FEM-design 3D Structure;one case where vertical forces are considered to have a beneficialeffect on the stability of the building and one case wherevertical forces are considered to have an adverse effect on thestability of the building. The survey shows that there are major differences in resultsbetween the two methods for each load case respectively. Theexplanation for this is believed to depend upon thecharacteristics of the two calculation methods. The recommendation given in this essay is that hand calculationsshould be used when the accuracy is of less important for theapplication of the results, when there is no access tocomputerized calculation programs, or when the time required tomake more accurate calculations is limited. FEM design 3DStructure 16 should be used when accuracy is of greater importanceand complexity is high. The work was carried out in collaboration with Knut JönsonIngenjörsbyrå i Uppsala AB.

The human body consists of a number of very complex, highly specialised organs which perform a variety of functions that are essential to life and health. One of the main functions of the skin, the largest of the human organs, is to maintain the integrity of the body. It does this by acting as a physical barrier, preventing micro-organisms and other potentially harmful substances from entering the body. When the integrity of the skin is damaged through injury, a self-protective mechanism is triggered and the reparative wound healing process begins. Under normal circumstances the wound healing process culminates in the skin recuperating its normal characteristics and functions at the site of the injury, with only a small visible mark being left behind. However, in some cases the wound healing process may become altered leading to the production of abnormal scars, such as keloids. Keloid scars are formed from scar tissue at the site of an injury, as a result of excessive tissue repair that extends beyond the boundaries of the original wound. These scars are characterised by excess collagen deposition produced during the wound healing process. It is estimated that as many as 20% of the black and Hispanic population are affected by keloid scarring. In addition to the aesthetic aspect, keloid scars can also be painful, itchy and prone to become infected. Keloid scar formation can be triggered by skin injuries caused by, for example, acne, wounds, shaving, burns, and surgical incisions. The mechanism by which keloid scars form is currently not well understood and consequently no effective treatments exist to date.This thesis describes an investigation into the mechanical properties of single keloid and normal skin fibroblast cells for the purpose of establishing if there is a quantitative difference between the two types of cells. This information will be of benefit to researchers looking for a better understanding of the keloid formation mechanism and for those seeking improved treatments. An atomic force microscope (AFM) was employed to indent single Keloid and normal skin fibroblast cells taken from five patients. Values for the apparent Young's modulus of the cells were then calculated by fitting the experimental data using Hertz's model. Apparent Young's modulus values were then compared. The findings of the analysis indicate that statistically, there is a significant difference in the Young's modulus values of normal and keloid cells, with keloid cells exhibiting substantially greater stiffness than normal skin fibroblast cells. To enable the keloid and normal skin fibroblast cells to be studied in as close to their natural, physiological environment as is possible the AFM experiments described in this thesis were undertaken in a phosphate buffered saline (PBS) solution. In such cases the use of a fluid medium presents additional complexities, not least of which is the introduction of a hydrodynamic drag force due to viscous friction of the cantilever with the liquid which can affect the experimental data obtained and consequently any material properties calculated as a result of using these data. In order to investigate the effect of dragging force on the experimental data obtained from the AFM a novel integrated finite element based model was developed. The model, described in this thesis, provides quantification of the drag force in AFM measurements of soft specimens in fluids, consequently enabling more accurate interpretation of the data obtained from AFM experimentation. The model is validated using extensive data obtained from AFM experimentation undertaken in a number of fluids of different viscosities, at a variety of tip velocities and platform-tip separations and by comparison with an existing analytical model. The novel model is shown to accurately account for drag forces in AFM in fluid media without the need for extrapolation of experimental data and can be employed over the range of tip geometries and velocities typically utilised in AFM experimentation.The work described in this thesis demonstrates that the AFM is a valuable tool that can be used to successfully investigate the mechanical properties of biological samples in fluids. It was shown that increased accuracy in the interpretation of data obtained from AFM experimentation can be obtained by taking into account the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. The investigation into the mechanical behaviour of keloid cells described in this thesis significantly adds to the yet small body of research undertaken on keloid cells to date. The findings of the investigation will provide valuable information that will be of benefit in the future to researchers looking to develop effective treatments for the prevention, reduction or removal of keloid scars.

The thesis presents the structural behaviour of fibre reinforced polymer (FRP) laminated composites based on 3D elasticity formulation and finite element modeling using Abaqus. This investigation into the performance of the laminate included subjecting it to various parameters i.e. different boundary conditions, material properties and loading conditions to examine the structural responses of deformation and stress. Both analytical and numerical investigations were performed to determine the stress and displacement distributions at any point of the laminates. Other investigative work undertaken in this study includes the numerical analysis of the effect of flexural deformation of the FRP strengthened RC slab. The formulation of 3D elasticity and enforced boundary conditions were applied to establish the state equation of the laminated composites. Transfer matrix and recursive solutions were then used to produce analytical solutions which satisfied all the boundary conditions throughout all the layers of the composites. These analytical solutions were then compared with numerical analysis through one of the commercial finite element analysis programs, Abaqus. Out of wide variety of element types available in the Abaqus element library, shells and solids elements are chosen to model the composites. From these FEM results, comparison can be made to the solution obtained from the analytical. The novel work and results presented in this thesis are the analysis of fully clamped laminated composite plates. The breakthrough results of fully clamped laminated composite plate can be used as a benchmark for further investigation. These analytical solutions were verified with FEM solutions which showed that only the solid element (C3D20) exhibited close results to the exact solutions. However, FEM gave poor results on the transverse shear stresses particularly at the boundary edges. As an application of the work above, it is noticed that the FEM results for the FRP strengthened RC slab, agreed well with the experimental work conducted in the laboratory. The flexural capacity of the RC slab showed significant increase, both at service and ultimate limit states, after FRP sheets were applied at the bottom surface of the slab. Given the established and developed programming codes, exact solutions of deflection and stresses can be determined for any reduced material properties, boundary and loading conditions, using Mathematica.

Hög lärarkompetens inom formativa arbetssätt gynnar elevers lärande i matematiska problemlösningsuppgifter. Ett formativt arbetssätt synliggör elevers kunskapsutveckling. Dessutom ställer dagens teknik höga krav på elevers matematikkunskaper. Syftet med studien är att undersöka vad forskning säger om hur lärare kan använda de fem nyckelstrategierna för planering och genomförande av problemlösningsuppgifter i matematik. Frågeställningarna är: På vilka sätt kan lärare utforma lektionsplanering för formativt lärande? Vilka formativa återkopplingsstrategier är användbara för lärare? Efter insamling, analys och sammanställning av vetenskapliga studier visar resultatet att undervisning som genomförs utifrån fem nyckelstrategier bidrar till elevers lärande. Resultatet visar även att bland annat kamratbedömning, självbedömning samt ett kollaborativt arbete är gynnsamma arbetssätt. Uppdelning av problemlösningsuppgifter visar att lärare får syn på elevers kunskaper. Det är däremot mer utmanande för elever att själva välja metoder, vilket inte möjliggörs vid uppdelning av problemlösningsuppgifter. Lärare behöver samla in information om elevers kunskaper för att kunna ge återkoppling och anpassa kommande undervisning. Ett systematiskt tillvägagångssätt är avgörande för elevers lärande. Kamrat- och självbedömningbidrar till ökat lärande eftersom återkoppling mellan elever är för dem enklare att förstå. Av den anledningen är det viktigt att lärare anpassar återkoppling till elevers nivå. Det är också viktigt att elever får kunskap om hur återkopplingen kan användas. Ett formativt arbetssätt är tidskrävande till en början och både elever och lärare behöver kunskap om hur det används. Ett förslag till vidare forskning är om digital teknik kan vara ett tidssparande hjälpmedel vid ett formativt arbetssätt.

Företaget Uniper som är en elproducent och äger vattenkraftverk över hela Sverige har upptäckt nya sorter av skador i kammaren till en av av deras Kaplanturbiner. Skador förekommer i form av sprickbildningar i ett område som kallas för sugröret. Röret består av rostfritt stål och är omgivet av förankringsstag, armeringsjärn och betong. Företaget anlitade konsultbolaget Sweco som analyserade det utsatta området med FEM-beräkningar. Konsultbolagets slutsatser kring sprickbildningen var att de ansågs bero på en fel utförd svets eller dåliga förhållanden vid utförandet av tidigare reparationer. Sweco upptäckte även att konstruktionen vid stora tryckdifferenser, mer specifikt vid driftstopp, skapar utåtriktade momentana krafter mot betongen, vilket kan med stor sannolikhet orsaka utmattningsbrott. Utifrån de framtagna data om rörets beteende valde bolaget att förnya den kringgjutna betongen att samt svetsa ihop områdena som hade bildat sprickor för att minimera spridningen. Reparationen eliminerade inte  sprickbildningen då det fortsätter ännu idag att förekomma små sprickor i kammaren.    I detta projektarbete analyserades sugrörskonans beståndsdelar med andra metoder som tidigare inte har använts av företaget Sweco. Detta i syfte att få en helhetsbild av orsakerna till det som har skapat sprickor i kammaren. De genomförda simuleringarna i konan delades upp i fall A – F för att identifiera de mest utsatta områdena.   Det framkom att svetsförbandet mellan sugrörskonan och nedre löphjulskammaren var de svagaste punkterna i konstruktionen. Utsatta området förstärktes med förstärkningsring runt röret som visade 45 % minskning av spänningsvärdet i jämförelse med tidigare fall som hade samma förutsättningar. Med en kompletterande detalj i sugröret som föreslås av detta projektarbete anses rörelsen minska vilket även minimerar risken till sprickbildningar.

Heat treatment processes are used to develop the desired mechanical properties for steels. Unfortunately, heat treatment, especially quenching, can cause distortion. Failure to meet geometry specifications can result in extensive rework or rejection of the parts. A series of quenching simulations, using DANTE, have been conducted on an AISI 4140 steel Navy C-ring distortion coupon and a WPI designed plate with a hole to determine the effects of quenching process parameters including part geometry, agitation during quenching, and quench start temperatures on distortion. The heat transfer coefficients (HTC) of the quenchant with selected pump speeds were measured by CHTE quench probe system, which is the key input for heat treatment simulation. The maximum HTC of the quenching oil was increased from 2350 W/m2K to 2666 W/m2K with higher pump speed. Quenching experiments were also conducted. It was found that the experimental measured gap opening of the standard Navy C-rings increased from 0.307mm without agitation to 0.536mm at a high agitation. Quench start temperature does not have a significant effect on the gap opening. The experimental results showed good agreement with simulation results. The important processing parameter identification was conducted using design of experiments (DoE) coupled with analysis of variance (ANOVA). The effect of processing parameters in decreasing order of importance were determined to be: quenchant type, part geometry, agitation speed, quenching orientation, quenchant temperature, immersion rates, and quench starts temperature. Based on the simulation and experimental results, it was found that the two most import parameters are: 1. The part geometry and size (product design) 2. The temperature dependent heat transfer coefficients between the part and the quenchant (process design) The coupling of these product and process parameters is necessary to apply the systems analysis that must be accomplished to understand the interaction between the part design and process design parameters. This coupling can be accomplished by locally applying the well-known Biot number. Bi (T) = h(T) * L / k(T) Where h(T) = film coefficient or convective heat transfer coefficient [W/m2*K]. LC = characteristic length, which is generally described as the volume of the body divided by the surface area of the body [m]. k(T) = thermal conductivity of the body [W/m*k] The concept of a local Biot number is introduced to quantify the local variations of part size, geometry and heat transfer coefficient. First, a large Bi indicates large temperature gradients within the part. Second, large local (geometry dependent) variations in Bi number will lead to large lateral temperature gradients. Therefore, variations in local Bi can lead to large temperature gradients and therefore high stress during quenching and finally distortion. This local Bi concept can be used in a systems approach to designing a part and the quenching system. This systems approach can be designated as design for heat treating.