Modeling dynamic behavior in tilting pad gas journal bearings

Thisresearch deals with the dynamic modeling of gas lubricated tilting pad journal bearings provided with spring supported pads, including experimental verification of the computation. On the basis of a mathematical model of a film bearing, a computer program has been developed, which can be used for the simulation of a special type of tilting pad gas journal bearing supported by a rotary spring under different loading conditions time dependently (transient running conditions due to geometry variations in time externally imposed). On the basis of literature, different transformations have been used in the model to achieve simpler calculation. The numerical simulation is used to solve a non-stationary case of a gasfilm. The simulation results were compared with literature results in a stationary case (steady running conditions) and they were found to be equal. In addition to this, comparisons were made with a number of stationary and non-stationary bearing tests, which were performed at Lappeenranta University of Technology using bearings designed with the simulation program. A study was also made using numerical simulation and literature to establish the influence of the different bearing parameters on the stability of the bearing. Comparison work was done with literature on tilting pad gas bearings. This bearing type is rarely used. One literature reference has studied the same bearing type as that used in LUT. A new design of tilting pad gas bearing is introduced. It is based on a stainless steel body and electron beam welding of the bearing parts. It has good operation characteristics and is easier to tune and faster to manufacture than traditional constructions. It is also suitable for large serial production.

Reducing contact resistance in graphene devices

In this thesis, the contact resistance of graphene devices was investigated because high contact resistance is detrimental to the performance of graphene field-effect transistors (GFET). Method for increasing so-called edge-contact area was applied in device fabrication process, as few nanometers thick Ni layer was used as a catalytic etchant during the annealing process. Finally, Ni was also used as a metal for contact. GFETs were fabricated using electron beam lithography using graphene fabricated by chemical vapor deposition (CVD). Critical part of the fabrication process was to preserve the high quality of the graphene channel while etching the graphene at contact areas with Ni during the annealing. This was achieved by optimizing the combination of temperature and gas flows. The structural properties of graphene were studied using scanning electron microscopy, scanning confocal μ-Raman spectroscopy and optical microscopy. Evaluation of electric transport properties including contact resistance was carried out by transmission line method and four-probe method. The lowest contact resistance found was about at 350 Ωμm. In addition, different methods to transfer CVD graphene synthesized on copper were studied. Typical method using PMMA as a supporting layer leaves some residues after its removal, thus effecting on the performance of a graphene devices. In a metal assisted transfer method, metal is used as an interfacial layer between PMMA and graphene. This allows more effective removal of PMMA. However, Raman spectra of graphene transferred by metal assisted method showed somewhat lower quality than the PMMA assisted method

Kuparin hitsaus kattavilla laatuvaatimuksilla

Kuparin ja kupariseosten hitsaus eroaa merkittävästi esimerkiksi terästen hitsauksesta. Suuri lämmönjohtavuus, lämpölaajeneminen, pehmeneminen ja kuparin taipumus liuottaa kaasuja sulaan asettavat hitsaukselle haasteita. Kuparia on perinteisesti hitsattu kaasuhitsaamalla ja kaasukaarihitsausprosesseilla, mutta uudemmat menetelmät kuten laserhitsaus, elektronisuihkuhitsaus ja FSW-hitsaus tarjoavat uudenlaisia käyttökohteita korkealla laadulla. ISO 3834-2 asettaa noudatettavat vaatimukset hitsaustoiminnalle laatuvaatimusten ollessa kattavia. Ydinvoimalaitoksella hitsauksessa tulee lisäksi noudattaa Säteilyturvakeskuksen YVL-ohjeita, joissa on määritetty lisävaatimuksia liitosten materiaalivalinnoille, pätevöittämiselle ja tarkastamiselle. Tässä työssä tutkittiin kuparimetallien hitsauksen mahdollisuutta Loviisan ydinvoimalaitoksella juottamisen sijasta siten, että kattavat laatuvaatimukset täyttyisivät. Hitsauskokeissa ja laboratoriotutkimuksissa testattiin hitsausta erilaisilla hitsausaineilla ja hitsausprosesseilla. Koetulosten pohjalta toteutettiin hitsausmenetelmä deoksidoidun kupariputken ja tinapronssilaipan TIG-hitsaukselle.

Characterisation of Laser Beam and Paper Material Interaction

It is known already from 1970´s that laser beam is suitable for processing paper materials. In this thesis, term paper materials mean all wood-fibre based materials, like dried pulp, copy paper, newspaper, cardboard, corrugated board, tissue paper etc. Accordingly, laser processing in this thesis means all laser treatments resulting material removal, like cutting, partial cutting, marking, creasing, perforation etc. that can be used to process paper materials. Laser technology provides many advantages for processing of paper materials: non-contact method, freedom of processing geometry, reliable technology for non-stop production etc. Especially packaging industry is very promising area for laser processing applications. However, there are only few industrial laser processing applications worldwide even in beginning of 2010´s. One reason for small-scale use of lasers in paper material manufacturing is that there is a shortage of published research and scientific articles. Another problem, restraining the use of laser for processing of paper materials, is colouration of paper material i.e. the yellowish and/or greyish colour of cut edge appearing during cutting or after cutting. These are the main reasons for selecting the topic of this thesis to concern characterization of interaction of laser beam and paper materials. This study was carried out in Laboratory of Laser Processing at Lappeenranta University of Technology (Finland). Laser equipment used in this study was TRUMPF TLF 2700 carbon dioxide laser that produces a beam with wavelength of 10.6 μm with power range of 190-2500 W (laser power on work piece). Study of laser beam and paper material interaction was carried out by treating dried kraft pulp (grammage of 67 g m-2) with different laser power levels, focal plane postion settings and interaction times. Interaction between laser beam and dried kraft pulp was detected with different monitoring devices, i.e. spectrometer, pyrometer and active illumination imaging system. This way it was possible to create an input and output parameter diagram and to study the effects of input and output parameters in this thesis. When interaction phenomena are understood also process development can be carried out and even new innovations developed. Fulfilling the lack of information on interaction phenomena can assist in the way of lasers for wider use of technology in paper making and converting industry. It was concluded in this thesis that interaction of laser beam and paper material has two mechanisms that are dependent on focal plane position range. Assumed interaction mechanism B appears in range of average focal plane position of 3.4 mm and 2.4 mm and assumed interaction mechanism A in range of average focal plane position of 0.4 mm and -0.6 mm both in used experimental set up. Focal plane position 1.4 mm represents midzone of these two mechanisms. Holes during laser beam and paper material interaction are formed gradually: first small hole is formed to interaction area in the centre of laser beam cross-section and after that, as function of interaction time, hole expands, until interaction between laser beam and dried kraft pulp is ended. By the image analysis it can be seen that in beginning of laser beam and dried kraft pulp material interaction small holes off very good quality are formed. It is obvious that black colour and heat affected zone appear as function of interaction time. This reveals that there still are different interaction phases within interaction mechanisms A and B. These interaction phases appear as function of time and also as function of peak intensity of laser beam. Limit peak intensity is the value that divides interaction mechanism A and B from one-phase interaction into dual-phase interaction. So all peak intensity values under limit peak intensity belong to MAOM (interaction mechanism A one-phase mode) or to MBOM (interaction mechanism B onephase mode) and values over that belong to MADM (interaction mechanism A dual-phase mode) or to MBDM (interaction mechanism B dual-phase mode). Decomposition process of cellulose is evolution of hydrocarbons when temperature is between 380- 500°C. This means that long cellulose molecule is split into smaller volatile hydrocarbons in this temperature range. As temperature increases, decomposition process of cellulose molecule changes. In range of 700-900°C, cellulose molecule is mainly decomposed into H2 gas; this is why this range is called evolution of hydrogen. Interaction in this range starts (as in range of MAOM and MBOM), when a small good quality hole is formed. This is due to “direct evaporation” of pulp via decomposition process of evolution of hydrogen. And this can be seen can be seen in spectrometer as high intensity peak of yellow light (in range of 588-589 nm) which refers to temperature of ~1750ºC. Pyrometer does not detect this high intensity peak since it is not able to detect physical phase change from solid kraft pulp to gaseous compounds. As interaction time between laser beam and dried kraft pulp continues, hypothesis is that three auto ignition processes occurs. Auto ignition of substance is the lowest temperature in which it will spontaneously ignite in a normal atmosphere without an external source of ignition, such as a flame or spark. Three auto ignition processes appears in range of MADM and MBDM, namely: 1. temperature of auto ignition of hydrogen atom (H2) is 500ºC, 2. temperature of auto ignition of carbon monoxide molecule (CO) is 609ºC and 3. temperature of auto ignition of carbon atom (C) is 700ºC. These three auto ignition processes leads to formation of plasma plume which has strong emission of radiation in range of visible light. Formation of this plasma plume can be seen as increase of intensity in wavelength range of ~475-652 nm. Pyrometer shows maximum temperature just after this ignition. This plasma plume is assumed to scatter laser beam so that it interacts with larger area of dried kraft pulp than what is actual area of beam cross-section. This assumed scattering reduces also peak intensity. So result shows that assumably scattered light with low peak intensity is interacting with large area of hole edges and due to low peak intensity this interaction happens in low temperature. So interaction between laser beam and dried kraft pulp turns from evolution of hydrogen to evolution of hydrocarbons. This leads to black colour of hole edges.

Laser Cutting of Austenitic Stainless Steel with a High Quality Laser Beam

The thin disk and fiber lasers are new solid-state laser technologies that offer a combinationof high beam quality and a wavelength that is easily absorbed by metal surfacesand are expected to challenge the CO2 and Nd:YAG lasers in cutting of metals ofthick sections (thickness greater than 2mm). This thesis studied the potential of the disk and fiber lasers for cutting applications and the benefits of their better beam quality. The literature review covered the principles of the disk laser, high power fiber laser, CO2 laser and Nd:YAG laser as well as the principle of laser cutting. The cutting experiments were made with thedisk, fiber and CO2 lasers using nitrogen as an assist gas. The test material was austenitic stainless steel of sheet thickness 1.3mm, 2.3mm, 4.3mm and 6.2mm for the disk and fiber laser cutting experiments and sheet thickness of 1.3mm, 1.85mm, 4.4mm and 6.4mm for the CO2 laser cutting experiments. The experiments focused on the maximum cutting speeds with appropriate cut quality. Kerf width, cutedge perpendicularity and surface roughness were the cut characteristics used to analyze the cut quality. Attempts were made to draw conclusions on the influence of high beam quality on the cutting speed and cut quality. The cutting speeds were enormous for the disk and fiber laser cutting experiments with the 1.3mm and 2.3mm sheet thickness and the cut quality was good. The disk and fiber laser cutting speeds were lower at 4.3mm and 6.2mm sheet thickness but there was still a considerable percentage increase in cutting speeds compared to the CO2 laser cutting speeds at similar sheet thickness. However, the cut quality for 6.2mm thickness was not very good for the disk and fiber laser cutting experiments but could probably be improved by proper selection of cutting parameters.

A computationally efficient shear deformable beam element for large deformation multibody applications

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Automated formulation of optimisation models for steel beam structures

Over 70% of the total costs of an end product are consequences of decisions that are made during the design process. A search for optimal cross-sections will often have only a marginal effect on the amount of material used if the geometry of a structure is fixed and if the cross-sectional characteristics of its elements are property designed by conventional methods. In recent years, optimalgeometry has become a central area of research in the automated design of structures. It is generally accepted that no single optimisation algorithm is suitable for all engineering design problems. An appropriate algorithm, therefore, mustbe selected individually for each optimisation situation. Modelling is the mosttime consuming phase in the optimisation of steel and metal structures. In thisresearch, the goal was to develop a method and computer program, which reduces the modelling and optimisation time for structural design. The program needed anoptimisation algorithm that is suitable for various engineering design problems. Because Finite Element modelling is commonly used in the design of steel and metal structures, the interaction between a finite element tool and optimisation tool needed a practical solution. The developed method and computer programs were tested with standard optimisation tests and practical design optimisation cases. Three generations of computer programs are developed. The programs combine anoptimisation problem modelling tool and FE-modelling program using three alternate methdos. The modelling and optimisation was demonstrated in the design of a new boom construction and steel structures of flat and ridge roofs. This thesis demonstrates that the most time consuming modelling time is significantly reduced. Modelling errors are reduced and the results are more reliable. A new selection rule for the evolution algorithm, which eliminates the need for constraint weight factors is tested with optimisation cases of the steel structures that include hundreds of constraints. It is seen that the tested algorithm can be used nearly as a black box without parameter settings and penalty factors of the constraints.

Fabrication and characterization of silicon position sensitive particle detectors

Position sensitive particle detectors are needed in high energy physics research. This thesis describes the development of fabrication processes and characterization techniques of silicon microstrip detectors used in the work for searching elementary particles in the European center for nuclear research, CERN. The detectors give an electrical signal along the particles trajectory after a collision in the particle accelerator. The trajectories give information about the nature of the particle in the struggle to reveal the structure of the matter and the universe. Detectors made of semiconductors have a better position resolution than conventional wire chamber detectors. Silicon semiconductor is overwhelmingly used as a detector material because of its cheapness and standard usage in integrated circuit industry. After a short spread sheet analysis of the basic building block of radiation detectors, the pn junction, the operation of a silicon radiation detector is discussed in general. The microstrip detector is then introduced and the detailed structure of a double-sided ac-coupled strip detector revealed. The fabrication aspects of strip detectors are discussedstarting from the process development and general principles ending up to the description of the double-sided ac-coupled strip detector process. Recombination and generation lifetime measurements in radiation detectors are discussed shortly. The results of electrical tests, ie. measuring the leakage currents and bias resistors, are displayed. The beam test setups and the results, the signal to noise ratio and the position accuracy, are then described. It was found out in earlier research that a heavy irradiation changes the properties of radiation detectors dramatically. A scanning electron microscope method was developed to measure the electric potential and field inside irradiated detectorsto see how a high radiation fluence changes them. The method and the most important results are discussed shortly.

Metallien laserporaus

Lasertarkkuusporauksella on tämän hetken teollisuudessa useita sovelluksia, kuten esimerkiksi mustesuihkukirjoittimet, dieselmoottoreiden polttoainesuuttimet, lääketieteen instrumentit, turbiinien lapojen jäähdytysreiät ja stensiilit. Tässä työssä on tutkittu laserporauksen mahdollisuuksia 99,9 % kupariin sekä EN 1.4301 ruostumattomaan teräkseen (vastaava AISI 304). Ainepaksuuksia oli käytettävissä kolmea: 0,1 mm, 0,5 mm ja 1,0 mm. Vertailun vuoksi valittiin tutkimukseen mukaan ainepaksuudeltaan 1,0 mm EN 1.4432 haponkestävää terästä (vastaava AISI 316L). Tutkimuksessa käytettiin kolmea eritehoista 1,064 µm aallonpituuden Nd:YAG – laseria ja yhtä CO2 – laseria. Poratut reiät kuvattiin elektronimikroskoopilla ja jokaisesta reiästä mitattiin halkaisija, ympyrämäisyys ja kartiokkuus. Lisäksi reiän laatua arvioitaessa tarkasteltiin purseen määrää reikien ympärillä. Tutkimus osoitti, että eri materiaaleihin voidaan porata, laserin säteen laadusta ja aallonpituudesta riippuen, hyvin erikokoisia reikiä. Kartiokkuuteen havaittiin voitavan vaikuttaa polttopisteen paikkaa siirtämällä.

Wet Oxidation of Paper Mill Evaporation Concentrates

Tämän työn tarkoituksena oli tutkia lämpötilan pH:n ja vetyperoksidin vaikutusta kuorimoveden haihdutuskonsentraatin märkähapetuksessa. Kirjallisuusosassa esitellään massan ja paperin valmistusta sekä kuorintaprosessi. Lisäksi tarkastellaan kuoren kemiallista koostumusta, jäteveden ja prosessiveden käsittelymenetelmiä sekä märkähapetuksen periaatteita. Kokeellinen osa käsittää erään suomalaisen paperitehtaan kuorimoveden haihdutuskonsentraatin märkähapetuskokeet. Hapetuskokeet tehtiin useammassa eri lämpötilassa, pH:ssa ja vetyperoksidikonsentraatiossa. Em. muuttujien vaikutusta tutkittiin kemialliseen hapenkulutukseen (COD), biologiseen hapenkulutukseen (BOD), välittömästi saatavana olevan biologiseen hapenkulutukseen (IABOD), orgaaniseen kokonaishiileen (TOC) ja tanniini/ligniini pitoisuuteen. Koetulokset osoittivat, että korkeimmat COD- ja TOC-reduktiot saavutettiin H2O2-katalysoidulla märkähapetuksella jäteveden alkuperäisessä pH:ssa (60 % reduktio COD:lla ja 45 % reduktio TOC:lla lämpötilassa 170 °C ja 0.2 g H2O2/g COD). Toisaalta, parhaat tulokset biohajoavuuden paranemisen suhteen saavutettiin emäksisissä olosuhteissa, jossa 170 °C:ssa saavutettiin BOD/COD-arvo 76 %. Emäksisissä olosuhteissa saavutettiin lähes täydellinen tanniinin reduktio lämpötila-alueella 130-170 °C, mutta näissä lämpötiloissa orgaanisen kuorman alenemista ei havaittu.

Characterisation of pigment particles by scanning electron microscope and image analysis programs

Coating and filler pigments have strong influence to the properties of the paper. Filler content can be even over 30 % and pigment content in coating is about 85-95 weight percent. The physical and chemical properties of the pigments are different and the knowledge of these properties is important for optimising of optical and printing properties of the paper. The size and shape of pigment particles can be measured by different analysers which can be based on sedimentation, laser diffraction, changes in electric field etc. In this master's thesis was researched particle properties especially by scanning electron microscope (SEM) and image analysis programs. Research included nine pigments with different particle size and shape. Pigments were analysed by two image analysis programs (INCA Feature and Poikki), Coulter LS230 (laser diffraction) and SediGraph 5100 (sedimentation). The results were compared to perceive the effect of particle shape to the performance of the analysers. Only image analysis programs gave parameters of the particle shape. One part of research was also the sample preparation for SEM. Individual particles should be separated and distinct in ideal sample. Analysing methods gave different results but results from image analysis programs corresponded even to sedimentation or to laser diffraction depending on the particle shape. Detailed analysis of the particle shape required high magnification in SEM, but measured parameters described very well the shape of the particles. Large particles (ecd~1 µm) could be used also in 3D-modelling which enabled the measurement of the thickness of the particles. Scanning electron microscope and image analysis programs were effective and multifunctional tools for particle analyses. Development and experience will devise the usability of analysing method in routine use.

Tautomerism and Fragmentation of Biologically Active Hetero Atom (O, N)-Containing Acyclic and Cyclic Compounds Under Electron Ionization

In this thesis a total of 86 compounds containing the hetero atoms oxygen and nitrogen were studied under electron ionization mass spectrometry (EIMS). These compounds are biologically active and were synthesized by various research groups. The main attention of this study was paid on the fragmentations related to different tautomeric forms of 2- phenacylpyridines, 2-phenacylquinolines, 8-aryl-3,4-dioxo-2H,8H-6,7-dihydroimidazo- [2,1-c][1,2,4]triazines and aryl- and benzyl-substituted 2,3-dihydroimidazo[1,2-a]pyrimidine-5,7-(1H,6H)-diones. Also regio/stereospecific effects on fragmentations of pyrrolo- and isoindoloquinazolinones and naphthoxazine, naphthpyrrolo-oxazinone and naphthoxazino-benzoxazine derivatives were screened. Results were compared with NMR data, when available. The first part of thesis consists of theory and literature review of different types of tautomerism and fragmentation mechanisms in EIMS. The effects of tautomerism in biological systems are also briefly reviewed. In the second part of the thesis the own results of the author, based on six publications,are discussed. For 2-phenacylpyridines and 2-phenacylquinolines the correlation of different Hammett substituent constants to the relative abundances (RA) or total ion currents (% TIC) of selected ions were investigated. Although it was not possible to assign most of the ions formed unambiguously to the different tautomers, the linear fits of their RAs and % TICs can be related to changing contributions of different tautomeric forms. For dioxoimidazotriazines and imidazopyrimidinediones the effects of substituents were rather weak. The fragmentations were also found useful for obtaining structural information. Some stereoisomeric pairs of pyrrolo- and isoindoloquinazolines and regiomeric pairs of naphtoxazine derivatives showed clear differences in thir mass spectra. Some mechanisms are suggested for their fragmentations.

Electric field calibration method for scanning electron microscope

This paper proposes a calibration method which can be utilized for the analysis of SEM images. The field of application of the developed method is a calculation of surface potential distribution of biased silicon edgeless detector. The suggested processing of the data collected by SEM consists of several stages and takes into account different aspects affecting the SEM image. The calibration method doesn’t pretend to be precise but at the same time it gives the basics of potential distribution when the different biasing voltages applied to the detector.

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

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.