This master thesis studied the possibilities of implementing new handbook methodologies for sizing of corner and bathtub attachments with respect to static strength.  Parametric studies of corner and bathtub attachments were performed in order to examine the effect of boundary conditions and vital dimensions with respect to static strength. The parametric studies were performed by solving FE-models of attachments with different dimensions. Variables such as flange thickness, end-plate thickness, end-plate length and total attachment width were varied in order to identify geometric trends for prediction of cross-sectional loads.  The FE-models consisted of a bolt, washer and attachment assembly. The bolt was subjected to pre-tension and contact conditions were applied in between each part. The parametric study examined the cross-sectional loads of critical cross sections of the end-plate, bolt, flanges and back.  The parametric study of the bathtub attachment resulted in verification of critical failure modes from earlier handbook methodology, as well as a foundation for a new handbook methodology for sizing with respect to static strength. The parametric study of the corner attachment resulted in an identification of critical failure modes. The non-symmetric configuration of a corner attachment was found to result in larger load distribution in the bolt shank cross section.

Arbetet som presenteras i rapporten omfattar en undersökning av en grundkurs i hållfasthetslära, en kurs som över tid haft en relativt låg genomströmning, och uppdraget avser att förstå kursens kontext samt presentera sammanställningar av problemområden och förbättringsförslag. Först presenteras en förstudie med syfte att förstå kursens kontext och utmaningar. För detta syfte har intervjuer genomförts med lärare, studenter, assistenter och programansvariga, vidare har kursdokument och kurslitteratur studerats. Utöver förstudiens insamlade material och dess resultat behövdes ytterligare data samlas in för en djupare ämnesdidaktisk undersökning. Denna djupare analys har inspirerats av en diskursiv ansats där kursen i hållfasthetslära ses som en diskurs. Resultatet av denna ämnesdidaktiska undersökning och dess diskursanalys presenteras som en uppdelning utifrån didaktikens grundfrågor; Vad, Hur, Varför och Vem. Analysen av detta resultat stärks genom diskussioner kopplat till viss tidigare forskning. Avslutningsvis presenteras förbättringsförslag utifrån funna problemområden och en diskussion. Funna problem inom kursen inkluderar att höga krav ställs på studenterna och vidare att kursen utgör en utmaning för såväl lärare i sin undervisning som för studenter i sitt lärande. Till detta framkommer ett behov av att hos kurslärare och assistenter utveckla sin syn på det specifika ämnets didaktik d.v.s. hur hållfasthetslära bör undervisas för att uppnå kursens syften och mål. Det finns behov av att aktivera och engagera studenterna tillsammans med fler aktiva initiativ för att motverka den låga genomströmningen. Kursens projektuppgift och somliga assistenter utgör påtagliga problemområde inom kursen särskilt kopplat till kommunikation mellan lärare och assistenter, undervisning och återigen förståelse för ämnesdidaktik. Kursens lärandemål behöver utvärderas och arbetas med tillsammans med det funna problemet kring kursens bredd kopplat till vad som faktiskt testas vid tentamen. Presenterade förbättringsförslag behandlar kurs-, tentamen- och lärandemålutformning, projektuppgiften och övningarna. Vidare presenteras förslag för att förbättra den sociala biten i undervisning och inlärning inom kursen m.a.p. den kunskap som görs viktig inom diskursen. Till detta föreslås bl.a. metoden SCALE-UP. Den didaktiska utvecklingen diskuteras även och bättre genomtänkta undervisningsmetoder med hjälp av ämnesdidaktiska perspektiv föreslås. / The work presented in the report includes an investigation of a basic course in solid mechanics, a course that over time has had a relatively low student completion, and the assignment aims to understand the context of the course and present a summary of problem areas and suggestions for improvement. First, a pre-study is presented with the aim of understanding the context and challenges of the course. To this end, interviews have been conducted with teachers, students, assistants and program managers, and course documents and course literature have been studied. In addition to the pre-study collected material and its results, additional data needed to be collected for a more profound subject didactic investigation. This deeper analysis has been inspired by a discursive approach where the course in solid mechanics is seen as a discourse. The results of this subject didactic investigation and its discourse analysis are presented through the fundamental questions of didactics; What, How, Why and Who. Within this result, the analysis is strengthened through discussions linked to previous research. Lastly, improvement proposals are presented based on problem areas found followed by a discussion. Found problems within the course include high demands placed on the students in relation to the fact that this course constitutes a challenge both for teachers in their teaching and for students in their learning. In addition to this, there is a need for course teachers and assistants to develop their view of the specific subject's didactics, i.e., how solid mechanics should be taught to achieve the aims and objectives of the course. There is a need to activate and engage the students through more active initiatives to counteract the low student completion. The course's project assignment and certain assistants constitute tangible problem areas within the course, particularly linked to communication between teachers and assistants, teaching in itself and, again, understanding of subject didactics. The learning objectives of the course need to be evaluated and worked on together with the problem found regarding the scope of the course linked to what is actually tested on the exam. Presented improvement proposals deal with the design of the course, exam and learning objectives, the project task and the tutorials. Furthermore, proposals are presented to improve the social part of teaching and learning within the course with respect to the knowledge that is made important within the discourse. For this, among other things, the SCALE-UP method is proposed. The didactic development is also discussed and better thought-out teaching methods using subject didactic perspectives are suggested.

Thanks to advancements in the polymer industry, metal replacement with high performance polymers has become a growing practice in many industries due to the economical, lead time and weight advantages. Getinge AB was interested in introducing metal replacement to the medical technology industry by launching a thesis project to replace the die-cast aluminium in a key structural component of their ventilator products. The ultimate goal of the project was to provide enough information to decide if going to a prototype stage is an investment worthwhile. In order to provide the necessary data, the project was conducted in the following manner: an evaluation of the current aluminium design was done using finite element method (FEM) simulations, followed by a thorough material choice and design adjustments in order to enhance strength and manufacturability. Finally another set of FEM simulations were conducted for the new plastic design, that was compared to the performance of the originaldesign, in order to confirm the validity of the updated structure. The results from the project show that metal replacement might be a sound choice for the structure, considering the mechanical performance, potential cost reduction and reduced lead time. However the part strength is a liability and require thorough physical testing. / Utveckling inom polymerteknik har lett till att metallersättning har blivit ett vanligare tillvägagångssätt för att spara pengar, ledtid och vikt i produkter inom olika industrier. Getinge AB var intresserade av att introducera metallersättning i den medicinsktekniska branchen genom att starta detta examensarbete som går ut på att ersätta pressgjutet aluminium i en viktig strukturell komponent i deras ventilatorer. Slutmålet med projektet var att erhålla erforderligt beslutsunderlag för att bestämma om det är värt att gå vidare till tillverkning av en prototyp. För att bidra med nödvändig data har projektet genomförts enligt följande:den befintliga aluminiumkonstruktionen utvärderades med hjälp av finitaelementmetoden (FEM), därefter genomfördes ett noggrannt materialval samt designanpassningar för att förbättra hållfasthet och tillverkningsbarhet. Till sist utfördes ytterligare en uppsättning av FEM-simuleringar för att validera den nya konstruktionen mot datan erhållen från FEM-simuleringar av den ursprungliga konstruktionen. Projektets resultat visar att metallersättning kan anses ett godtagbart alternativ för strukturen med avseende på den mekaniska prestandan, reducerat pris och reduktion av ledtid. Konstruktionens hållfasthet är en riskfaktor och djupgående fysisk provning krävs.

<p>  </p> <p>Many engineering structures are designed to withstand a critical mechanical load before failure. When a load greater than the critical load is encountered, the manner of structural failure is important. Nature has been a source of technical inspiration for centuries, and the power of modern scientific investigative techniques has enhanced engineers’ abilities to learn from millennia of evolutionary mechanical refinement. </p> <p>Chitons, a family of marine mollusks, feed on algae attached to rocky substrates, and parts of their feeding organs are subjected to varied loads in the process. In this work, the manner of failure of a chiton’s tooth and supporting structure is investigated, and it is suggested that mechanical details of the structure enable load-limiting and fail-safe performance that protects the animal from potentially dangerous overloading.</p>

Coercivity is a characteristic property of the bilinear term in a weak form of a partial differential equation in both infinite space and the corresponding finite space utilized by a numerical scheme. This concept implies \textit{stability} and \textit{well-posedness} of the weak form in both the exact solution and the numerical solution. In fact, the loss of this property especially in finite dimension cases leads to instability of the numerical scheme. This phenomenon occurs in three major families of problems consisting of advection-diffusion equation with dominant advection term, elastic analysis of very thin beams, and associated plasticity and non-associated plasticity problems. There are two main paths to overcome the loss of coercivity, first manipulating and stabilizing a weak form to ensure that the discrete weak form is coercive, second using an automatically stable method to estimate the solution space such as the Discontinuous Petrov Galerkin (DPG) method in which the optimal test space is attained during the design of the method in such a way that the scheme keeps the coercivity inherently. In this dissertation, A stable numerical method for the aforementioned problems is proposed. A stabilized finite element method for the problem of migration risk problem which belongs to the family of the advection-diffusion problems is designed and thoroughly analyzed. Moreover, DPG method is exploited for a wide range of valuing option problems under the black-Scholes model including vanilla options, American options, Asian options, double knock barrier options where they all belong to family of advection-diffusion problem, and elastic analysis of Timoshenko beam theory. Besides, The problem of American option pricing, migration risk, and plasticity problems can be categorized as a free boundary value problem which has their extra complexity, and optimization theory and variational inequality are the main tools to study these families of the problems. Thus, an overview of the classic definition of variational inequalities and different tools and methods to study analytically and numerically this family of problems is provided and a novel adjoint sensitivity analysis of variational inequalities is proposed.

Low-density armour often uses ceramic materials, as their high compressive strength and relatively low weight make the material ideal for moving in the field. The ballistic protection works by redirecting the plastic flow of the projectile radially, which reduces penetration. The main drawback of using ceramics is their brittle behaviour, causing rapid crack propagation. When subjected to ballistic impacts, the ceramic fails catastrophically by spalling and cracking. The fracture behaviour is essential to model correctly to predict the effectiveness of armor systems. In this experiment, a notched specimen was used to investigate mode I fracture. The setup is similar to an open edge on impact experiment where the fracture propagation is initiated by the impact of a projectile fired by an air pressure gun. To avoid spallation, the projectile velocities were kept low to only initiate crack development from bending. For velocities below 15 m/s, a single crack develops across the specimen. For higher velocities between 15-75 m/s, the behaviour is different for short and long projectiles. For short projectiles, a straight crack develops before bifurcating when the projectile and ceramic lose contact. For longer projectiles, the crack bifurcates at the initiation. It forms a pointed ellipse up to the point when the projectile and ceramic lose contact, at which point it behaves the same as for shorter projectiles. Simulations were conducted using LS-Dyna and Impetus AFEA with four different material models. Two different fracture formulations were also used. Erosion was used in LS-Dyna, while erosion and node-splitting were used in Impetus AFEA. Simulations in both LS-Dyna and Impetus AFEA could reproduce experimental results. Simulations show that bifurcation highly depends on the materials' tensile strength. The transition from straight to bifurcating cracks emerges in a small velocity range, allowing for the possibility of calibrating the simulations to experiments. A possibility for comparing the crack development in simulations and the experimental setup besides crack patterns is the crack mouth opening displacement (CMOD). Measurements of CMOD with photon doppler velocimetry (PDV) correlated well with the simulations. / Komplexa skydd använder sig ofta av keramiska material då keramer har stark kompressionsstyrka och relativt låg vikt, vilket gör dem idealiska för att röra sig i fält. Ballistiskt skygg verkar genom att omdirigera projektilens plastiska flöde radiellt, vilket reducerar risk för penetration. Största nackdelen med keramiska material är deras spröda beteende. På grund av materialets tidsberoende beteende är materialegenskaperna svåra att bestämma. När materialet utsätts för ballistisk belastning orsakar det ofta katastrofartad sprickbildning. Sprickbeteendet är därför ett viktigt fenomen att bestämma för att förutsäga effektiviteten hos skyddsmaterialet. I detta experiment används en uppställning med ett skårad provkropp för att studera sprickutvecklingen av mod I sprickor. Uppställningen har likheter med kant anslags experiment där sprickutbredningen initieras med hjälp en cylindrisk projektil. För att begränsa brottbeteendet till mod I använder sig uppställningen av låga projektilhastigheter mellan 15 och 75 m/s för att initiera sprickor genom böjning. För hastigheter under 15 m/s utvecklades endast raka sprickor som propagerade över hela provkroppen. För hastigheter mellan 15 och 75 m/s skiljer sig beteendet mellan långa och korta projektiler. För korta projektiler delar sig sprickan när projektilen studsar mot provkroppen. För långa projektiler delar sig sprickan i två redan vid initiering och bildar en spolform upp till den punkt då projektilen tappar kontakt med provkroppen varefter beteendet mellan kort och lång projektil är likartat. Simuleringar utfördes med LS-Dyna och Impetus AFEA med fyra olika materialmodeller. Två olika brottformuleringar användes. Erosion användes i LS-Dyna, medan erosion och node-splitting användes i Impetus AFEA. Simuleringar i både LS-Dyna och Impetus AFEA kunde återskapa de experimentella resultaten. Simuleringarna visar att delningen av sprickan vid avlastning i hög grad beror på materialens draghållfasthet. Övergången från rak spricka till sprickdelningen uppstår i ett snävt hastighetetsfönster vilket ger möjlighet att kalibrera simuleringar mot experimentella resultat. En möjlighet jämföra sprickutvecklingen i simuleringar och experiment förutom sprickmönster är sprick öppnings förskjutning (CMOD). Mätningar av CMOD med fotondopplerhastighetsmätningar (PDV) överensstämmer väl med simuleringarna.

In this thesis work a literature survey is done to collect published data for T-welded joints with a thickness of 5-12 mm, produced in high strength steel and treated with HFMI. In addition to this, large structures are researched. The data was evaluated in nominal stress and effective notch stress and compared with the recommended FAT value from the International Institute of Welding (IIW) for post-weld improved joints. It was concluded that not sufficient data exist for T-joints in high strength steel, especially steels of grades with yield strength greater than 450 MPa, and thicknesses of 5-12mm, neither does enough data exist for large structures. The recommended fatigue strength values from the IIW were compared. / I detta arbete så kommer en litteraturstudie att genomföras för att samla data om svetsade t- balkar med en tjocklek på 5-12 mm, av materialet höghållfasta stål och behandlade med HFMI. Stora strukturer kommer även att undersökas. Den samlade datan är utvärderad i nominell spänning och effective notch stress och jämförd med International Institute (IIW) of Welding för efterbehandlade svetsar. En slutsats är att det inte finns tillräckligt med data för svetsade t-balkar i höghållfasta stål med en tjocklek mellan 5-12 mm. Data om stora strukturer bör också utvecklas. De rekommenderade utmattningshållfasthets värden från IIW jämfördes.

The aim of this master thesis was to investigate the mechanical properties of ExpandedPolystyrene (EPS) through experimental testing. The strain was measured on thespecimen’s surface with Digital Image Correlation (DIC), in order to investigate howthe first principal strain at fracture initiation depends on the loading of the material.To impose different loading conditions various tests were performed, such as biaxialtension-compression, uniaxial tension and bending tests. The study was done withfour densities of EPS, 35, 50, 75 and 100 g/L. To investigate how strain and stressat fracture initiation depend on temperature, the bending tests were performed atthree different temperatures, -20, 20 and 50 °C. All tests were performed in the SolidMechanics lab at KTH, Stockholm. For every experiment, five repetitions were madeto reduce the influence of the inhomogeneous microstructure of EPS and the stochasticbehaviour of fracture mechanics. The results indicate that the fracture initiation straindecreases with increasing density of EPS, while the fracture strength increases withincreasing density of EPS. Further, the results indicate that the loading conditions havean influence on the fracture initiation strain. / Målet med detta examensarbete var att undersöka materialegenskaper för EPS genomatt utföra experimentell testning. Töjningen mättes på provbitarnas yta med hjälp avDIC-teknik, för att undersöka hur första huvudtöjningen vid sprickinitiering beror påbelastningen av materialet. För att belasta material på olika sätt utfördes olika tester,såsom enaxligt drag, biaxiellt drag och tryck samt böjtester. Testerna gjordes med fyradensiteter av EPS, 35, 50, 75 and 100 g/L. För att undersöka hur töjning och kraft vidsprickinitiering beror på temperatur utfördes böjtesterna vid tre temperaturer, -20,20 and 50 °C. Alla tester utfördes på institutionen för hållfasthetslära vid KungligaTekniska högskolan. Varje experiment repeterades fem gånger för att minimerainverkan av den inhomogena mikrostrukturen hos EPS. Resultaten tyder på attbrottinitieringstöjningen minskar med ökande densitet av EPS, medan brottlastenökar med ökande densitet av EPS. Vidare indikerar resultaten att belastningen har eninverkan på brottinitieringstöjningen.

No description available.

<p>The rapid growth of fields such as metamaterials, composites, architected materials, porous solids, and micro/nano materials, along with the continuing advancements in design and fabrication procedures have led to the synthesis of complex structures having intricate material distributions and non-trivial geometries. These materials find important applications including biomedical implants and devices, aerospace and naval structures, and micro/nano-electromechanical devices. Theoretical and experimental evidences have shown that these structures exhibit size-dependent (or, nonlocal) effects. This implies that the response of a point within the solid is affected by a collection of points; ultimately a manifestation of the multiscale deformation process. Broadly speaking, at a continuum level, the mathematical description of these multiscale phenomena leads to integral constitutive models, that account for the long-range interactions via nonlocal kernels. </p> <p><br></p> <p>Despite receiving considerable attention, the existing class of approaches to nonlocal elasticity are predominantly phenomenological in nature, following from their definition of the material parameters of the nonlocal kernel based on 'representative volume element' (RVE)-based statistical homogenization of the heterogeneous microstructure. The size of the RVE required for practical simulation, does not achieve a full-resolution of the intricate heterogeneous microstructure, and also implicitly enforces the use of symmetric nonlocal kernels to achieve thermodynamic consistency and mathematically well-posedness. The latter restriction directly limits the application of existing approaches only to the linear deformation analysis of either periodic or isotropic nonlocal structures. Additionally, the lack of a consistent characterization of the nonlocal effects, often results in inconsistent (also labeled as 'paradoxical') predictions depending on the nature of the external loading. In order to address these fundamental theoretical gaps, this dissertation develops a fractional-order kinematic approach to nonlocal elasticity by leveraging cutting-edge mathematical operators derived from the field of fractional calculus.</p> <p><br></p> <p>In contrast to the class of existing class of approaches that adopt an integral stress-strain constitutive relation derived from the equilibrium of the RVE, the fractional-order approach is predicated on a differ-integral (fractional-order) strain-displacement relation. The latter relation is derived from a fractional-order deformation-gradient mapping between deformed and undeformed configurations, and this approach naturally localizes and captures the effect of nonlocality at the root of the deformation phenomena. The most remarkable consequence of this reformulation consists in its ability to achieve thermodynamic and mathematical consistency, irrespective of the nature of the nonlocal kernel. The convex and positive-definite nature of the formulation enabled the use of variational principles to formulate well-posed governing equations, the incorporation of nonlinear effects, and enabled the development of accurate finite element simulation methods. The aforementioned features, when combined with a variable-order extension of the fractional-order continuum theory, enabled the physically consistent application of the nonlocal formulation to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Indeed, a rigorous theoretical analysis was conducted to demonstrate the natural ability of the variable-order in capturing the role of microstructure in the deformation of heterogeneous porous solids. These advantages allowed the application of the fractional-order kinematic approach to accurately and efficiently model the response of porous beams and plates, with random microstructural descriptions. Results derived from multiphysical loading conditions, as well as nonlinear deformation regimes, are used to demonstrate the causal relation between the kinematics-based fractional-order characterization of nonlocal effects and the natural role of microstructure in determining the macroscopic response of heterogeneous solids. The potential implications of the developed formalism on scientific discovery of material laws are examined in-depth, and different areas for further research are identified.</p>