From the nano scale to the macro scale, large models are used to simulate and predict the responses of dynamic systems. The construction and evaluation of such models, often in the form of finite element models, require tremendous computational resources and time. Due to this large computational endeavor, it is paramount to learn as much as possible from the models and their solutions. In this work, analyses and methods for efficiently deriving significant knowledge of damped systems from models and their solutions are presented. Of primary interest to this work is the analysis of damped structures. Damping, the means by which energy is dissipated, often adds an additional layer of complexity to finite element models and any subsequent analyses. This added complexity is due to the relative complexity of many damping models and their accompanying computational burden. Furthermore, on the micro and nano scale, a variety of damping mechanisms, each with their own unique set of physics, may be present. The research presented in this work is organized in two parts. The first part presents methods for deriving knowledge from models and their solutions. Here, the developed methods perform approximate yet highly efficient analysis on the matrices and solution vectors of finite element models. In this work, methods utilizing the Neumann series approximation are presented. These methods efficiently predict how the response of a structure depends on its damping or any other input model parameter. Additionally, a method for analyzing the spatial dependence of damping with the use of loss factor images is presented. Research presented in the second part derives knowledge solely from solutions of models. In this part, it is assumed that the matrices of the models are not available, and therefore analysis is restricted to the solution itself. Here, research is focused on the analyses of structures on the micro and nano scale. Specifically, micro and nano beams surrounded by a viscous compressible fluid are analyzed. The dynamic responses of the structure and the surrounding fluid are analyzed to determine the prominent damping mechanisms. Here, results from 2--Dimensional analytical models and 3--Dimensional finite element models are complemented by experimental measurements to analyze damping due to viscous dissipation and acoustic radiation.

Modelling and simulation of the human body during an impact situation such as a car accident, can lead to better designed safety features on vehicles. In order to achieve this, investigation into the material properties and the creation of a numerical model of cortical bone is needed. One approach to creating a material model of cortical bone suitable for these situations is to describe the material model as visco-elastic, as reported by Shim et al. [1], Bekker et al. [2] and Cloete et al. [3]. The work by Shim et al. and Bekker et al. developed three-dimensional models, but do not accurately capture the transition in behaviour in the intermediate strain rate region, while Cloete et al. developed a phenomenological model which captures the intermediate strain rate behaviour in one dimension. This work aims to verify and extend these models. The intermediate strain rate regime (1 s−1 to 100 s−1 ) is of particular interest because it is a key characteristic of the behaviour of cortical bone and several studies have been conducted to gather experimental data in this region [3, 4, 5, 6]. The behaviour can be captured using non-linear viscoelastic models. This dissertation focuses on the development and implementation of a material model of cortical bone based on non-linear visco-elastic models to capture the intermediate strain rate regime behaviour. The material model was developed using uni-axial test results from cortical bone. The model by Cloete et al. has been improved and extended, and issues of local and global strain rate with regards to the viscosity have been clarified. A hereditary integral approach was taken in the analysis and implementation of discrete models and was found to be consistent with mathematical models. The model developed was extended to three dimensions in a manner similar to that of Shim et al. and Bekker et al. for implementation in commercial finite element software (LS-Dyna and Abaqus).

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When a building is exposed to fire, it is required to remain structurally stable for a period of time. The regulations do however allow some types of localised failures within this time frame. The damage area of these failures must be contained and remain proportional to the initial triggering action and not continue into a widespread collapse, commonly referred to as a progressive collapse. In order to prevent progressive collapses, it is necessary to first identify which types of failures that could result in a progressive collapse. In a recent study (Iqbal N., Ph.D. thesis, Luleå University of Technology, 2016), single-storey steel frame buildings affected by localised fires were analysed. In the study it was identified that an initial failure in the truss’ top chord could potentially result in a progressive collapse. The reason for this is because when the top chord fails, the truss and its roof sheeting deflect and transitions into only handling catenary forces. The catenary forces present in the roof sheeting are then transferred to the adjacent trusses which therefore risks collapsing. The analysis could however not determine the possibility of progressive collapses and how factors such as truss span length affect the possibility of progressive collapses. The purpose of this thesis therefore became to analyse how span length affect the roof sheeting’s catenary forces and try to determine if a failure in the top chord could result in a progressive collapse. To answer this, finite element analyses where conducted on two different truss models with varying span lengths, i.e. 18- and 36-meter. Each model consisted of three trusses along with columns, bracings, and roof sheeting. Additionally, a hand calculation model was adopted to determine the strength of the catenary forces. From the finite element analysis, it could be seen that the adjacent trusses of the 36-meter truss model became grossly deformed. Hence indicating that a longer span length would increase the possibility of a progressive collapse. However, the hand calculation model used to calculate the strength of the catenary forces indicated that catenary forces present in the roof sheeting of the longer truss model, was relatively weak compared to the shorter truss model. The reason for this could not be determined, but some adjustments to the hand calculation model might be necessary to make it compatible with the analysed truss model. Consequently, it was impossible to determine the possibility of a progressive collapse. Additionally, during this work it was identified that other factors, such as truss model, bay length and roof sheeting thickness, could affect the possibility of progressive collapses. Hence, further work is necessary to determine the possibility of a progressive collapse. / När en byggnad utsätts för brandpåverkan ska den förbli strukturellt stabil under en viss tidsperiod. Regelverken tillåter dock att vissa typer av lokala skador inträffar redan under denna tidsperiod. Dessa skador måste begränsas till en viss area och förbli proportionerliga mot den initiala skadan och inte resultera i utbredda kollapser, det vill säga fortskridande ras. För att kunna förhindra fortskridande ras är det nödvändigt att först identifiera vilka typer av skador som skulle kunna resultera i fortskridande ras.  I en relativt ny analys (Iqbal N., Doktorsavhandling, Luleå tekniska universitet, 2016) analyserades den bärande konstruktionen i enplans stålhallar då konstruktionen utsattes för lokala bränder. Där det identifierades att ett brott i balkens överram eventuellt skulle kunna resultera i ett fortskridande ras. Brottet i överramen medförde nämligen att balken och dess takplåt sjönk ihop och övergick till att endast hantera linkrafter. Takplåtens linkrafter fördelades ut till de angränsade balkarna som därmed riskerade att kollapsa. Analysen kunde dock inte verifiera att ett fortskridande ras var möjligt eller avgöra hur faktorer såsom balkspännvidd påverkade sannolikheten för ett fortskridande ras. Syftet med detta arbete blev därför att analysera om balkspännvidd påverkade takplåtens linkrafter samt att försöka avgöra om ett brott i överramen kan resultera i ett fortskridande ras eller inte. För att besvara detta genomfördes finita elementanalyser på en 18- och en 36-meter lång balk. Varje modell bestod av tre balkar med tillhörande pelare och takplåt. För att sedan kunna uppskatta styrkan av linkrafterna i takplåten tillämpades en handberäkningsmodell.  Resultatet från finita elementanalyserna visade att den längre balkmodellen utsattes för högre påkänningar i jämförelse med den kortare balkmodellen. Detta indikerar att en längre spännvidd ökar sannolikheten för fortskridande ras. Handberäkningsmodellen som användes för att beräkna styrkan av linkrafterna gav dock generellt mindre linkrafter för den längre balkmodellen jämfört med den kortare balkmodellen. Anledningen till detta gick inte att fastställa men det skulle kunna vara så att handberäkningsmodellen behöver justeras för att kunna tillämpas på den undersökta balkmodellen. I och med detta var det omöjligt att avgöra sannolikheten för ett fortskridande ras. Under detta arbete identifierades det även att andra faktorer så som balkmodell, centrumavstånd mellan fackverk och plåttakstjocklek skulle kunna påverka linkrafternas styrka. På grund av detta är fortsatt arbete nödvändigt för att kunna avgöra möjligheten och sannolikheten för ett fortskridande ras.

The Accelerated bridge construction (ABC) techniques are gaining popularity among the departments of transportation (DOTs) due to their reductions of on-site construction time and traffic delays. One ABC technique that utilizes precast deck panels has demonstrated some advantages over normal cast-in-place construction, but has also demonstrated some serviceability issues such as cracks and water leakage to the transverse joints. Some of these problems are addressed by applying longitudinal prestressing. This thesis evaluates the service and ultimate capacities in both flexure and shear, of the finite element models of the post-tensioned system currently used by Utah Department of Transportation (UDOT) and a proposed curved-bolt system to confirm the experimental results. The panels were built and tested under negative moment in order to investigate a known problem, namely, tension in the deck concrete. Shear tests were performed on specimens with geometry designed to investigate the effects of high shear across the joint. The curved-bolt connection not only provides the necessary compressive stress across the transverse joint but also makes future replacement of a single deck panel possible without replacing the entire deck. Load-deflection, shear-deflection curves were obtained using the experimental tests and were used to compare with the values obtained from finite element analysis. In flexure, the ultimate load predicted by the finite element model was lower than the experimental ultimate load by 1% for the post-tensioned connection and 3% for the curved-bolt connection. The shear models predicted the ultimate shear reached, within 5% of the experimental values. The cracking pattern also matched closely. The yield and cracking moment of the curved-bolt connection predicted by the finite element model were lower by 13% and 2%, respectively, compared to the post-tensioned connection in flexure.

Indiana University-Purdue University Indianapolis (IUPUI) / Traumatic Brain Injuries (TBI) are one of the most apprehensive issues today. In recent years a lot of research has been done for reducing the risk of TBI, but no concrete solution exists yet. Helmets are one of the protective devices that are used to prevent human beings from mild TBI. For many years some kind of foam has been used in helmets for energy absorption. But, in recent years non-traditional solutions other than foam are being explored by different groups. Focus of this thesis is to develop a completely new concept of energy absorption for helmet liner by diverting the impact forces in radial directions normal to the direction of impact. This work presents a new design of an advanced layered composite (ALC) for energy dissipation through action of a 3D array of compliant mechanisms. The ALC works by diverting incoming forces in multiple radial directions and also has design provisions for reducing rotational forces. Design of compliant mechanism is optimized using multi-material topology optimization algorithm considering rigid and flexible material phases together with void. The design proposed here needs to be manufactured using the advanced polyjet printing additive manufacturing process. A general and parametric design procedure is explained which can be used to produce variants of the designs for different impact conditions and different applications. Performance of the designed ALC is examined through a benchmark example in which a comparison is made between the ALC and the traditional liner foam. An impact test is carried out in this benchmark example using dynamic Finite Element Analysis in LS DYNA. The comparison parameters under consideration are gradualness of energy absorption and peak linear force transmitted from the ALC to the body in contact with it. The design in this article is done particularly for the use in sports helmets. However, the ALC may find applications in other energy absorbing structures such as vehicle crashworthy components and protective gears. The ultimate goal of this research is to provide a novel design of energy absorbing structure which reduces the risk of head injury when the helmet is worn.