I skolämnet matematik och centralt innehåll problemlösning har en kvalitativ observation har genomförts i en årskurs fem. Syftet med studien har varit att utöka kunskaper om hur undervisningen kan synliggöra elevernas förståelse för matematiken i problemlösningsuppgifter med hjälp av muntlig kommunikation i mindre grupper. Datainsamlingen har skett genom ljudinspelning av elevsamtalen. Denna studie syftar identifiera en instrumentell eller relationell förståelse hos eleverna som synliggör vid en muntlig kommunikation. Detta har gjort genom att granska de argument som eleverna delger i sina samtal med varandra. Analysen har visat att elevernas förståelse synliggörs när undervisningen erbjuder de förutsättningar som krävs för att muntlig kommunikation ska vara givande. / <p>Matematik</p>

Den här rapporten handlar om ett maskintekniskt konstruktionsprojekt som framtagits av Christian Wikman och Oliver Öhman. Det är ett uppdrag som givits av EcoistVehicleTM för att slutföra högskoleingenjörsexamen inom maskinteknik vid Högskolan i Halmstad. Princip- och Primärkonstruktion (Olsson, 1995), Fundamentals of Vehicle Dynamics (Gillespie, 1992) och en stor mängd egen sökning har använts som grund till metoden som använts under projektets gång.   EcoistVehicleTM är ett fordonsprojekt som startats av Thomas Koch. Det är en eldriven, singelsits och trehjulig bil med ett drivande bakhjul. Idén bakom bilen är att transportera föraren till sin destination på ett miljövänligt sätt. Bilen är lämpad till landsbygd och pendling med en räckvidd på 40-50km. Syftet med uppdraget som gavs våren 2017 var att hitta snabbare metoder att konstruera och tillverka en svingarm till fordonet.   Uppdraget som gavs var att konstruera och möjligtvis tillverka en svingarm för det drivande bakhjulet som skall passa in på bilens dimensioner samt ha en relativt snabb tillverkningsprocess för en produktionsserie på 10-20 bilar. Uppdragsgivarens önskemål var att 3D-printa ut de större delarna av svingarmen och sedan efterbearbeta monteringsdelar och passytor med fräsning. Flera tillverkningsprocesser som används inom fordonsindustrin för framtagning av motorcykelsvingarmar har setts över och jämföras för att få fram den metod som passar detta projekt.   Det som författarna bidragit med till projeketet är en högre kunskap om 3D-printning av metall, då specifikt aluminium, olika koncept för tillverkning samt analyser av konstruktionen för att testa hållfasthet till den slutgiltiga produkten. / This report will be about a mechanical design project that has been developed by Christian Wikman and Oliver Öhman. The assignment was given by EcoistVehicleTM to complete a bachelor’s degree in mechanical engineering at Halmstad University. Princip- och Primärkonstruktion (Olsson, 1995), Fundamentals of Vehicle Dynamics (Gillespie, 1992) and a large amount of research on the web has been used as the foundation for the method that’s been used all through this project.   EcoistVehicleTM is a vehicle project started by Thomas Koch. It is an electrically powered, single seat, three wheeled vehicle that's driven by a single rear wheel. The idea behind the car is to transport the driver to his destination in an environmentally friendly way. The car is suited for commuting in the countryside with a range of 40-50km. The purpose of the assignment that was given in the spring of 2017 was to look into faster methods of designing and manufacturing a swingarm for the vehicle.   Our assignment was to design and possibly manufacture a swingarm for the driving rear wheel that should fit the specifications of the car and have a relatively fast manufacturing process for a series of 10-20 cars. Our mentor and taskmaster has a request to 3D-print the larger parts of the swingarm then after work the mounting surfaces and mating surfaces with milling. Several manufacturing processes used in the automotive industry for the production of motorcycle swingarms will be screened and compared to get the method that will fit this project.   The authors have contributed with a higher knowledge of 3D-printing, specifically aluminum, different design concepts together with analysis of the design to test the solidity of the final product.

A 3D nonlinear finite element analysis was developed for simulating the behavior of skewed concrete slabs and to identify the response of the slab with different angles and element sizes. The purpose of this research is helping the engineering and construction industry to utilize the FEM study and results more in different structural applications.Simulations performed in ABAQUS for skewed slabs are also compared to straight and skewed slabs according to the analytical formulation by Timoshenko.The result showed that when the distance increases, the load capacity measured by reaction forces decreases for all different skew angles except angle 0° and 15° which show a stable reaction force along the entire path. .The study reveals that depending on the skew angle and the element size, the stress distribution and vertical displacements in the slab vary significantly from those in a straight slab. It is shown that the displacement decreases with the increase of the skew angle while the stresses increase with the decrease of the skew angle.There are small differences in the vertical displacements and stress distribution between the results obtained by this study and the results obtained by Timoshenko regarding the plates with skews of 0°, 30° and 45°.

I skolämnet matematik och centralt innehåll problemlösning har en kvalitativ observation har genomförts i en årskurs fem. Syftet med studien har varit att utöka kunskaper om hur undervisningen kan synliggöra elevernas förståelse för matematiken i problemlösningsuppgifter med hjälp av muntlig kommunikation i mindre grupper. Datainsamlingen har skett genom ljudinspelning av elevsamtalen. Denna studie syftar identifiera en instrumentell eller relationell förståelse hos eleverna som synliggör vid en muntlig kommunikation. Detta har gjort genom att granska de argument som eleverna delger i sina samtal med varandra. Analysen har visat att elevernas förståelse synliggörs när undervisningen erbjuder de förutsättningar som krävs för att muntlig kommunikation ska vara givande. / <p>matematik</p>

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En av dagens vanligaste maskiner för att underlätta hanteringen av tungt gods är gaffeltrucken. Denna tillverkas i industriell produktion där konkurrensen är hård. Den hårda konkurrensen bland tillverkningsföretagen på den globala marknaden ökar strävan att tillverka produkter till ett så kostnadseffektivt pris som möjligt. Syftet med det här arbetet är att utreda huruvida det går att optimera en befintlig drivlinsupphängning med avseende på tillverkningskostnad och vikt. Genom en produktutveckling skall ett koncept för en optimerad lösning tas fram gällande konstruktion, materialval och tillverkningsmetod. För att skapa ett underlag till denna produktutvecklingsprocess har väsentliga teorier tagits fram och presenterats i arbetet. Produktutvecklingen kommer generera ett nytt koncept. I produktutvecklingen utförs även materialval, val av tillverkningsmetod, beräkningar, FEM-simuleringar, designoptimering och utvärdering angående kostnaderna. Detta resulterade slutligen i en möjlig kostnadsreducering. Vikten kan dessutom reduceras utan att försämra hållfastheten.

Alumina is one of the most commonly used engineering ceramics for a variety of applications ranging from microelectronics to prosthetics due to its desirable properties. Unfortunately, conventional machining techniques generally lead to fracture, tool failure, low surface integrity, high energy consumption, low material removal rate, and high tool wear during machining due to high hardness and brittleness of the ceramic material. Laser machining offers an alternative for rapid processing of brittle and hard engineering ceramics. However, the material properties, especially the high thermal expansion coefficient and low thermal conductivity, may cause ceramic fracture due to thermal damage. Striation formation is another defect in laser cutting. These drawbacks limit advanced ceramics in engineering applications. In this work, various lasers and machining techniques are investigated to explore the feasibility of high-quality laser machining different thicknesses of alumina. The main contributions include: (i) Fibre laser crack-free cutting of thick-section alumina (up to 6-mm-thickness). A three-dimensional numerical model considering the material removal was developed to study the effects of process parameters on temperature, thermal-stress distribution, fracture initiation and propagation in laser cutting. A rapid parameters optimisation procedure for crack-free cutting of thick-section ceramics was proposed. (ii) Low power CW CO2 laser underwater machining of closed cavities (up to 2-mm depth) in alumina was demonstrated with high-quality in terms of surface finish and integrity. A three-dimensional thermal-stress model and a two-dimensional fluid smooth particle hydrodynamic model (SPH) were developed to investigate the physical processes during CO2 laser underwater machining. SPH modelling has been applied for the first time to studying laser processing of ceramics. (iii) Striation-free cutting of alumina sheets (1-mm thickness) is realised using a nano-second pulsed DPSS Nd: YAG laser, which demonstrates the capability of high average power short pulsed lasers in high-quality macro-machining. A mechanism of pulsed laser striation-free cutting was also proposed. The present work opens up new opportunities for applying lasers for high-quality machining of engineering ceramics.

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier–Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Fackverksmodellering (eng. strut-tie modeling) är en accepterad och rationell beräkningsmetod för betongkonstruktioner där vanlig balkteori inte kan appliceras. Det gäller områden för s.k. diskontinuitetsregioner (D-regioner). Den komplexa spännings- och kraftfördelningen som uppstår i D-regioner substitueras till fackverkskomponenter i form av trycksträvor, dragstag och noder. Lastfallen omvandlas, under förenklade villkor, med andra ord till ett lösbart fackverksfall. Metodiken för tillgångasättet har länge ansetts som iterativ och långdragen process, där ett fackverk antas samt optimeras tills ett godtyckligt och rimligt fackverk har uppnåtts. Erfarenhet har betydelse för hur fackverksutformningen kommer att se ut. Oerfarna ingenjörer kan till en början ha svårt att se hur spännings- och kraftfördelningen i en betongkonstruktion sprider ut sig. Med hjälp av FEM kan fackverksmodelleringens process effektiviseras. Spänningsoch kraftfördelningen kan tas fram i belastande betongkonstruktioner i form av finita elementmodeller. Därmed kan konstruktörerna visuellt utforma fackverket efter fördelningen. I studien har ett verkligt fall tillhandahållits från företaget WSP. Konstruktionsdelen som ska dimensioneras är en väggskiva från ett flerbostadshus i Stockholm. Med FEM-design har väggskivan rekonstruerats till en finita elementmodell med en framtagen spännings- och kraftfördelning. Fördelningen har använts som ett underlag för vidare dimensionering för hand efter Svenska Standard, Eurokod 2. Resultaten visar att det är möjligt att utforma ett fackverk med FEM-design som underlag. Även framtagna stångkrafter och upplagskrafter har jämförts mellan handberäkning och FEM, som visar att skillnader mellan beräkningsmetoderna är mellan ungefär 5,1-7,7 %, dock bara för studiens fall. Rapporten visar att en påskyndning i processen kan göras om man använder FEM. Metoden möjliggör en förenkling i processen som kan nyttjas av oerfarna konstruktörer. Detta kan bidra till en bättre slutprodukt och gynna utvecklingen för byggbranschen i slutändan. / Strut-tie modeling is an accepted and rational calculation method for regions in concrete structures where Berouille-theorem can’t be applied. These regions are so called discontinuity regions (D.regions). The stress and force distribution is substituted for strut, ties and nodes much like the members of a truss. Complex load-bearing cases can be transformed, under simplified conditions, to solvable cases. The strut-tie modeling can be seen as an iterative process. At the start of the process the form of the truss is assumed and optimized through trial and error. Experience in the field is therefore of big significance, where unexperienced designers can have a hard time to visualize the stress and force distribution through the concrete structure. The purpose of the study is to use the strut-tie method on a concrete structure. The study will investigate if the strut-tie method can be simplified and if the assumed truss is reasonable. The stress and force distribution is going to be visualized through a finite element model, and hence try to eliminate the iterative modelling phase. In the study, a real load-bearing case will be examined. The concrete structure is a deep beam in an apartment block in Stockholm, Sweden. The designs of the apartment have been provided from the multinational company WSP. The deep beam have been reconstructed to a finite element model through the program FEMdesign 17 3D Structure. The visualized results from the stress and force distribution have been used as a base for further calculations, with the strut-tie method, in accordance to Eurocode 2. The result from the study shows that it’s possible to create a truss from FEM-designs visualized stress- and force distribution. In the study a comparison have also been made between truss member forces calculated by strut-tie and the forces calculated by FEM-design. It shows a difference between 5,1-7,7%. The study shows through the program FEM-design 17 that strut-tie method can be improved, and help unexperienced designers during the truss modeling phase.

Geomagnetically Induced Currents (GIC) have been a growing concern within power system operators and researchers as they have been widely reported to lead to power system related issues and material damage to system components like power transformers. In power transformers, GIC impacts are evidenced by part-wave saturation, resulting in transformers experiencing increased presence of odd and even harmonics. The three-phase three-limb (3p3L) transformer has been found to be the most tolerant to high dc values compared to other core types. The research was based on a hypothesis which reads “transformer laboratory testing results can be used as a guide towards developing suitable Finite Element Matrix (FEM) models to be used for conducting GIC/DC experiments”. This study thus investigates the response of a 15 kVA 3p3L laboratory transformer to dc current, emulating the effects of GICs. GIC and dc current are the same under steady state conditions, and hence mentioned interchangeably. Laboratory tests conducted identified two critical saturation points when the transformer is exposed to dc. The early saturation point was identified to be at around 1.8 A/phase of dc (18% of rated current), while the deep saturation point was at around 15 to 20 A/phase of dc (about 72% of rated current). Further analysis showed that holes drilled on the transformer can lower the transformer knee-point by about 26%, depending on the size and location of the holes. The holes hence end up affecting the operating point of the transformer due to losses occurring around the holes. A transformer FEM model was developed following the laboratory exercise, where it was concluded that a 2D model leads to grossly erroneous results, distorting the magnetizing current by about 60% compared to the laboratory results. A solid 3D model improved performance by about 30% as it took the transformer's topological structure into consideration. The 3D model was then refined further to include joints and laminations. It was discovered that laminations on the transformer need to be introduced as stacks of the core, with each core step split into two, allocating a 4% air gap space between stacks. Refinement of the T-joints proved that the joints have a relatively high influence on the transformer behaviour, with their detailed refinement improving the transformer behaviour by about 60%. The final FEM model was used for dc experiments. The results of such experiments showed close resemblance to the laboratory results, with saturation points identified in FEM lying within 10% of the laboratory identified saturation points. Overall, the various investigation methods explored showed that the hypothesis was satisfactorily proven true. Laboratory results functioned as a guide in developing the model, offering a reference case.