On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.

Fatigue analysis of brackets with and without scallop for bridge and other deck structure using effective notch stress.

Due to functional requirement of a structural detail brackets with and without scallop are frequently used in bridges, decks, ships and offshore structure. Scallops are designed to serve as passage way for fluids, to reduce weld length and plate distortions. Moreover, scallops are used to avoid intersection of two or more welds for the fact that there is the presence of inventible inherent initial crack except for full penetrated weld and the formation of multi-axial stress state at the weld intersection. Welding all around the scallop corner increase the possibility of brittle fracture even for the case the bracket is not loaded by primary load. Avoiding of scallop will establish an initial crack in the corner if bracket is welded by fillet welds. If the two weld run pass had crossed, this would have given a 3D residual stress situation. Therefore the presences and absence of scallop necessitates the 3D FEA fatigue resistance of both types of brackets using effective notch stress approach ( ). FEMAP 10.1 with NX NASTRAN was used for the 3D FEA. The first and main objective of this research was to investigate and compare the fatigue resistance of brackets with and without scallop. The secondary goal was the fatigue design of scallops in case they cannot be avoided for some reason. The fatigue resistance for both types of brackets was determined based on approach using 1 mm fictitiously rounded radius based on IIW recommendation. Identical geometrical, boundary and loading conditions were used for the determination and comparison of fatigue resistance of both types of brackets using linear 3D FEA. Moreover the size effect of bracket length was also studied using 2D SHELL element FEA. In the case of brackets with scallop the flange plate weld toe at the corner of the scallop was found to exhibit the highest and made the flange plate weld toe critical for fatigue failure. Whereas weld root and weld toe at the weld intersections were the highly stressed location for brackets without scallop. Thus weld toe for brackets with scallop, and weld root and weld toe for brackets without scallop were found to be the critical area for fatigue failure. Employing identical parameters on both types of brackets, brackets without scallop had the highest except for full penetrated weld. Furthermore the fatigue resistance of brackets without scallop was highly affected by the lack of weld penetration length and it was found out that decreased as the weld penetration was increased. Despite the fact that the very presence of scallop reduces the stiffness and also same time induce stress concentration, based on the 3D FEA it is worth concluding that using scallop provided better fatigue resistance when both types of brackets were fillet welded. However brackets without scallop had the highest fatigue resistance when full penetration weld was used. This thesis also showed that weld toe for brackets with scallop was the only highly stressed area unlike brackets without scallop in which both weld toe and weld root were the critical locations for fatigue failure when different types of boundary conditions were used. Weld throat thickness, plate thickness, scallop radius, lack of weld penetration length, boundary condition and weld quality affected the fatigue resistance of both types of brackets. And as a result, bracket design procedure, especially welding quality and post weld treatment techniques significantly affect the fatigue resistance of both type of brackets.

Spatial multicriteria decision analysis for the siting of on-shore wind power in Kemiönsaari

Wind power is a low-carbon energy production form that reduces the dependence of society on fossil fuels. Finland has adopted wind energy production into its climate change mitigation policy, and that has lead to changes in legislation, guidelines, regional wind power areas allocation and establishing a feed-in tariff. Wind power production has indeed boosted in Finland after two decades of relatively slow growth, for instance from 2010 to 2011 wind energy production increased with 64 %, but there is still a long way to the national goal of 6 TWh by 2020. This thesis introduces a GIS-based decision-support methodology for the preliminary identification of suitable areas for wind energy production including estimation of their level of risk. The goal of this study was to define the least risky places for wind energy development within Kemiönsaari municipality in Southwest Finland. Spatial multicriteria decision analysis (SMCDA) has been used for searching suitable wind power areas along with many other location-allocation problems. SMCDA scrutinizes complex ill-structured decision problems in GIS environment using constraints and evaluation criteria, which are aggregated using weighted linear combination (WLC). Weights for the evaluation criteria were acquired using analytic hierarchy process (AHP) with nine expert interviews. Subsequently, feasible alternatives were ranked in order to provide a recommendation and finally, a sensitivity analysis was conducted for the determination of recommendation robustness. The first study aim was to scrutinize the suitability and necessity of existing data for this SMCDA study. Most of the available data sets were of sufficient resolution and quality. Input data necessity was evaluated qualitatively for each data set based on e.g. constraint coverage and attribute weights. Attribute quality was estimated mainly qualitatively by attribute comprehensiveness, operationality, measurability, completeness, decomposability, minimality and redundancy. The most significant quality issue was redundancy as interdependencies are not tolerated by WLC and AHP does not include measures to detect them. The third aim was to define the least risky areas for wind power development within the study area. The two highest ranking areas were Nordanå-Lövböle and Påvalsby followed by Helgeboda, Degerdal, Pungböle, Björkboda, and Östanå-Labböle. The fourth aim was to assess the recommendation reliability, and the top-ranking two areas proved robust whereas the other ones were more sensitive.

Linear prediction in optical spectroscopy

A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.

Conventional and nonconventional Kramers-Kronig analysis in optical spectroscopy

This Master’s Thesis is dedicated to the investigation and testing conventional and nonconventional Kramers-Kronig relations on simulated and experimentally measured spectra. It is done for both linear and nonlinear optical spectral data. Big part of attention is paid to the new method of obtaining complex refractive index from a transmittance spectrum without direct information of the sample thickness. The latter method is coupled with terahertz tome-domain spectroscopy and Kramers-Kronig analysis applied for testing the validity of complex refractive index. In this research precision of data inversion is evaluated by root-mean square error. Testing of methods is made over different spectral range and implementation of this methods in future is considered.