Elemental analysis of wood materials by external millibeam thick target PIXE

PIXE (Particle Induce X-ray Emission spectrometry) was used for analysing stem bark and stem wood of Scots pine, Norway spruce and Silver birch. Thick samples were irradiated, in laboratory atmosphere, with 3 MeV protons and the beam current was measured indirectly using a photo multiplicator (PM) tube. Both point scans and bulk analyses were performed with the 1 mm diameter proton beam. In bulk analyses, whole bark and sectors of discs of the stem wood were dry ashed at 550 ˚C. The ashes were homogenised by shaking and prepared to target pellets for PIXE analyses. This procedure generated representative samples to be analysed, but the enrichment also enabled quantification of some additional trace elements. The ash contents obtained as a product of the sample preparation procedure also showed to be of great importance in the evaluation of results in environmental studies. Spot scans from the pith of pine wood outwards, showed clearly highest concentrations of manganese, calcium and zinc in the first spot irradiated, or 2-3 times higher than in the surrounding wood. For stem wood from the crown part of a pine this higher concentration level was found in the first four spots/mms, including the pith and the two following growth rings. Zinc showed increasing concentrations outwards in sapwood of the pine stem, with the over-all lowest concentrations in the inner half of the sapwood. This could indicate emigration of this element from sapwood being under transformation to heartwood. Point scans across sapwood of pine and spruce showed more distinct variations in concentrations relative to hearth wood. Higher concentrations of e.g. zinc, calcium and manganese were found in earlywood than in denser latewood. Very high concentrations of iron and copper were also seen for some earlywood increments. The ash content of stem bark is up to and order higher than for the stem wood. However, when the elemental concentration in ashes of bark and wood of the same disc were compared, these are very similar – this when trees are growing at spots with no anthropogenic contamination from the atmosphere. The largest difference was obtained for calcium which appeared at two times high concentrations in ashes of bark than in ashes of the wood (ratio of 2). Pine bark is often used in monitoring of atmospheric pollution, where concentrations in bark samples are compared. Here an alternative approach is suggested: Bark and the underlying stem wood of a pine trees are dry ashed and analysed. The elemental concentration in the bark ash is then compared to the concentration of the same element in the wood ash. Comparing bark to wood includes a normalisation for the varying availability of an element from the soil at different sites. When this comparison is done for the ashes of the materials, a normalisation is also obtained for the general and locally different enrichment of inorganic elements from wood to bark. Already a ratio >2 between the concentration in the bark ash and the concentration in the wood ash could indicate atmospheric pollution. For monitoring where bark is used, this way of “inwards” comparison is suggested - instead of comparing to results from analyses of bark from other trees (read reference areas), growing at sites with different soil and, locally, different climate conditions. This approach also enables evaluation of atmospheric pollution from sampling of only relative few individual trees –preferable during forest felling.

The Possibilities and Dosimetric Limitations of MLC-Based Intensity-Modulated Radiotherapy Delivery and Optimization Techniques

The use of intensity-modulated radiotherapy (IMRT) has increased extensively in the modern radiotherapy (RT) treatments over the past two decades. Radiation dose distributions can be delivered with higher conformality with IMRT when compared to the conventional 3D-conformal radiotherapy (3D-CRT). Higher conformality and target coverage increases the probability of tumour control and decreases the normal tissue complications. The primary goal of this work is to improve and evaluate the accuracy, efficiency and delivery techniques of RT treatments by using IMRT. This study evaluated the dosimetric limitations and possibilities of IMRT in small (treatments of head-and-neck, prostate and lung cancer) and large volumes (primitive neuroectodermal tumours). The dose coverage of target volumes and the sparing of critical organs were increased with IMRT when compared to 3D-CRT. The developed split field IMRT technique was found to be safe and accurate method in craniospinal irradiations. By using IMRT in simultaneous integrated boosting of biologically defined target volumes of localized prostate cancer high doses were achievable with only small increase in the treatment complexity. Biological plan optimization increased the probability of uncomplicated control on average by 28% when compared to standard IMRT delivery. Unfortunately IMRT carries also some drawbacks. In IMRT the beam modulation is realized by splitting a large radiation field to small apertures. The smaller the beam apertures are the larger the rebuild-up and rebuild-down effects are at the tissue interfaces. The limitations to use IMRT with small apertures in the treatments of small lung tumours were investigated with dosimetric film measurements. The results confirmed that the peripheral doses of the small lung tumours were decreased as the effective field size was decreased. The studied calculation algorithms were not able to model the dose deficiency of the tumours accurately. The use of small sliding window apertures of 2 mm and 4 mm decreased the tumour peripheral dose by 6% when compared to 3D-CRT treatment plan. A direct aperture based optimization (DABO) technique was examined as a solution to decrease the treatment complexity. The DABO IMRT technique was able to achieve treatment plans equivalent with the conventional IMRT fluence based optimization techniques in the concave head-and-neck target volumes. With DABO the effective field sizes were increased and the number of MUs was reduced with a factor of two. The optimality of a treatment plan and the therapeutic ratio can be further enhanced by using dose painting based on regional radiosensitivities imaged with functional imaging methods.

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.

Disc Filter External Models in an Integrated Simulation Environment

Työssä tutkittiin kiekkosuodattimeen liittyviä ulkoisia simulointimalleja integroidussa simulointiympäristössä. Työn tarkoituksena oli parantaa olemassa olevaa mekanistista kiekkosuodatinmallia. Malli laadittiin dynaamiseen paperiteollisuuden tarpeisiin tehtyyn simulaattoriin (APMS), jossa olevaan alkuperäiseen mekanistiseen malliin tehtiin ulkoinen lisämalli, joka käyttää hyväkseen kiekkosuodatinvalmistajan mittaustuloksia. Laitetiedon saatavuutta suodattimien käyttäjille parannettiin luomalla Internetissä sijaitsevalle palvelimelle kiekkosuodattimen laitetietomäärittelyt. Suodatinvalmistaja voi palvella asiakkaitaan viemällä laitetiedot palvelimelle ja yhdistämällä laitetiedon simulointimalliin. Tämä on mahdollista Internetin ylitse käytettävän integroidun simulointiympäristön avulla, jonka on tarkoitus kokonaisvaltaisesti yhdistää simulointi ja prosessisuunnittelu. Suunnittelijalle tarjotaan työkalut, joilla dynaaminen simulointi, tasesimulointi ja kaavioiden piirtäminen onnistuu prosessilaitetiedon ollessa saatavilla. Nämä työkalut on tarkoitus toteuttaa projektissa nimeltä Galleria, jossa luodaan prosessimalli- ja laitetietopalvelin Internetiin. Gallerian käyttöliittymän avulla prosessisuunnittelija voi käyttää erilaisia simulointiohjelmistoja ja niihin luotuja valmiita malleja, sekä saada käsiinsä ajan tasalla olevaa laitetietoa. Ulkoinen kiekkosuodatinmalli laskee suodosvirtaamat ja suodosten pitoisuudet likaiselle, kirkkaalle ja superkirkkaalle suodokselle. Mallin syöttöparametrit ovat kiekkojen pyörimisnopeus, sisään tulevan syötön pitoisuus, suotautuvuus (freeness) ja säätöparametri, jolla säädetään likaisen ja kirkkaan suodoksen keskinäinen suhde. Suotautuvuus kertoo mistä massasta on kyse. Mitä suurempi suotautuvuus on, sitä paremmin massa suodattuu ja sitä puhtaampia suodokset yleensä ovat. Mallin parametrit viritettiin regressioanalyysillä ja valmistajan palautetta apuna käyttäen. Käyttäjä voi valita haluaako hän käyttää ulkoista vai alkuperäistä mallia. Alkuperäinen malli täytyy ensin alustaa antamalla sille nominaaliset toimintapisteet virtaamille ja pitoisuuksille tietyllä pyörimisnopeudella. Ulkoisen mallin yhtälöitä voi käyttää alkuperäisen mallin alustamiseen, jos alkuperäinen malli toimii ulkoista paremmin. Ulkoista mallia voi käyttää myös ilman simulointiohjelmaa Galleria-palvelimelta käsin. Käyttäjälle avautuu näin mahdollisuus tarkastella kiekkosuodattimien parametreja ja nähdä suotautumistulokset oman työasemansa ääreltä mistä tahansa, kunhan Internetyhteys on olemassa. Työn tuloksena kiekkosuodattimien laitetiedon saatavuus käyttäjille parani ja alkuperäisen simulointimallin rajoituksia ja puutteita vähennettiin.

External Location Factors of Foreign Direct Investment in Russia – Finnish Perspective

Tämän diplomityön tavoitteena on selvittää, mitä alueellisia tekijöitä suomalaiset yritykset ottavat huomioon valitessaan sopivaa sijaintia suoralle investoinnille Venäjän sisällä. Muutamia yrityksen sisäisiä tekijöitä käytetään taustamuuttujina selittämään sijaintitekijöiden painotuksissa havaittavia eroja erilaisten yritysten välillä. Venäjän alueita vertaillaan lopuksi painotusten valossa. Työn ensimmäisessä osassa keskitytään suorien ulkomaisten investointien teoreettiseen taustaan. Aiempia tutkimuksia käydään läpi, jotta tekijät, joilla on havaittu olevan vaikutusta investointien sijoittumiseen maan sisällä, saadaan kartoitettua. Työn jälkimmäinen osa perustuu yrityskyselyn avulla kerättyyn empiiriseen aineistoon. Aineiston avulla selvitetään mitä tekijöitä suomalaisyritykset huomioivat sijaintipäätöstä tehdessään. Tulosten valossa on ilmeistä, että alueen markkinapotentiaali on suomalaisyrityksissä tärkein huomioitava tekijä investoinnin sijainnista päätettäessä. Myös infrastruktuuri ja kustannushyödyt vaikuttavat päätökseen. Erityyppisten yritysten painotukset ovat hyvin samanlaisia. Moskova ja Pietari vastaavat Venäjän alueista parhaiten suomalaisyritysten investoinnin sijainnille asettamia kriteerejä.

Kylmämuovatun putkipalkin väsyminen metsätyökoneen puomirakenteessa

Työssä on tutkittu kylmämuovatun suorakaideputkipalkin väsymistä metsätyökoneen puomirakenteen osana. Kylmämuovatun putkipalkin sisäpintaan syntyy käytössä puristavan ulkoisen kuormituksen vaikutuksesta putkipalkin pituussuunnassa sekä seinämän läpi kasvavia säröjä. Työn tarkoituksena on ollut selvittää rakenteen väsymiskestoikä sekä säröytymisen aiheuttavat tekijät. Työssä on verrattu kestoikälaskentaan ja särönkasvuun sovellettujen murtumismekaniikan ja elementtimenetelmän tuloksia laboratoriokokeista saatuihin tuloksiin. Toisiaan tukevien tulosten perusteella kylmämuovausprosessissa syntyneiden jäännösjännitysten osuus särön ydintymisessä, kasvussa ja sen käyttäytymisessä on ulkoisen kuorman paikallisen vaikutuksen lisänä erittäin merkittävä. Putkipalkin väsyminen onkin jäännösjännityksistä riippuva särönkasvuilmiö.

External Location Factors of Finnish Direct Investment in Central and Eastern European Transitional Economies

Tutkimuksen päätavoitteena oli selvittää suomalaisten suorien investointien maan valintaan vaikuttavia tekijöitä Itä- ja Keski-Euroopan kymmenessä siirtymätaloudessa. Empiirisessä osuudessa tarkasteltiin suomalaisten yritysten tärkeimpiä sijaintitekijöitä alueella ja yrityskohtaisten tekijöiden vaikutusta sijaintitekijöihin. Tutkimuksessa selvitettiin myös yritysten päämotiiveja investoida maihin. Laaditun investointikriteeristön mukaan maat pystyttiin laittamaan paremmuusjärjestykseen suomalaisen investoijan kannalta. Empiirisen osuuden aineisto kerättiin postikyselylomakkeella yrityksiltä, joilla on tai jotka ovat suunnittelemassa investointeja näihin maihin. Tutkimusote oli kvantitatiivinen. Tutkimustulokset osoittavat, että suomalaiset investoijat valitsevat Itä- ja Keski-Euroopan maan investointikohteeksi pääasiassa markkinapotentiaalin ja edullisten kustannusten perusteella. Myös infrastruktuuri vaikuttaa maan valintaan. Eri aloilla toimivien yritysten sijaintitekijöiden painotuksissa havaittiin eroja. Yrityksen koko ja päämotiivi vaikuttivat sijaintitekijöiden painotuksiin. Investointikriteereiden mukaan kaksi parasta investointimaata suomalaisille investoijille ovat Puola ja Viro. Vertailtaessa investointikriteereitä toteutuneisiin investointeihin voidaan todeta, että suomalaiset investoijat eivät ole hyödyntäneet investoinneilla saatavia etuja kaikissa kohdemaissa.

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.