Local stresses and strains in axially cracked cylindrical shells

A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where . The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging.

The determination of the local conditions for void initiation in front of a crack tip for materials with second-phase particles

A procedure is proposed to determine, for second-phase particles near a crack tip, the maximum particle stresses at the moment of void initiation by either particle fracture or particle/matrix interface separation. A digital image analysis system is applied to perform a quantitative analysis of corresponding fracture surface regions from stereo image pairs taken in the scanning electron microscope. The fracture surface analysis is used to measure, for individual particles, the crack tip opening displacement at the moment of void initiation and the particle location with respect to the crack tip. From these data, the stress tensor at the moment of void initiation is calculated from the Hutchinson–Rice–Rosengren (HRR) field theory. The corresponding average local stresses within the particle are evaluated by a non-linear Mori–Tanaka-type approach. These stresses are compared to estimates according to the models by Argon et al. [A.S. Argon, J. Im, R. Safoglu, Metall. Trans. 6 (1975) 825] and Beremin [F.M. Beremin, Metall. Trans. 12 (1981) 723]. The procedure is demonstrated on an Al6061–10% Al2O3 metal matrix composite.

Elasto-plastic contact stress analysis of joints subjected to cyclic loading

Rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading is carried out. An incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis. For the case of the interference fit, the analysis sequentially carries out insertion of the pin and application of the load on the joint, covering possible initiation of separation (and/or yielding) and progressively the receding/advancing contact at the pin-plate interface. Deformations of both the plate and the pin are considered in the analysis. Numerical examples are presented for the case of an interference fit pin in a large plate under remote cyclic tension, and for an interference fit pin lug joint subjected to cyclic loading. A detailed study is carried out for the latter problem considering the effect of change in contact/separation at the pin-plate interface on local stresses, strains and redistribution of these stresses with the spread of a plastic zone. The results of the study are a useful input for the estimation of the fatigue life of joints. Copyright (C) 1996 Elsevier Science Ltd

Modulação da expressão dos componentes da matriz extracelular e a modulação celular na regeneração da fratura óssea padronizada em tíbia de ratos

O propósito do presente trabalho foi investigar a participação da proliferação celular e da expressão dos componentes da matriz extracelular na cascata de eventos do processo de reparo da fratura óssea, empregando as técnicas histológica, imunohistoquímica e morfométrica, em um modelo experimental padronizado para a indução da lesão na tíbia de ratos a partir do método empregado por Yuehuei e Friedman7. É importante padronizar um modelo de indução da fratura, para posterior investigação da participação das células e dos componentes da matriz extracelular no processo de reparo da fratura, considerando que o tempo de consolidação depende significantemente da natureza e do tipo da lesão produzida. Quarenta (n = 40) ratos Wistar foram submetidos a fratura . Os animais foram avaliados em oito (n = 8) grupos de cinco (n = 5) animais, cada grupo emperimental com 12, 24, 48, 72, 96, 144, 192 e 240 horas após a fratura (12h até 10 dias). As fraturas foram classificadas de acordo com o sistema de classificação internacional de fratura de Muller100, AO (Associação para Osteosíntese). Foram encontradas fraturas simples em 86% do total, sendo 68% de fraturas transversas e 18% de fraturas obliquas, 14% do total de fraturas foram complexas, sendo 8% de fraturas irregulares e 6% de fraturas segmentares. Esses resultados demonstram que o aparelho permite padronizar radiológicamente o tipo de fratura, caracterizado pela linha que separa os fragmentos ósseos. Os resultados qualitativos dos componentes da matriz extracelular para TGF-β, VEGF, colágeno I e II, osteopontina, proteoglicanos, fibras do sistema elástico com a coloração de resorcina funcsina de Weigert, e para proliferação celular pelo PCNA, assim como os resultados morfométricos, sugerem que a modulação da expressão dos componentes da matriz extracelular e a proliferação celular durante o processo de reparo da fratura não é homogênea para todos os componentes teciduais, dependendo significantemente das tensões locais geradas pelo tipo da linha de fratura que pode ser determinante no tempo de regeneração do osso e na qualidade da restauração das propriedades biomecânica. Nossos achados podem contribuir para melhor compreensão da reparo de fratura óssea e para novas abordagens terapêuticas que considerem as propriedades biomecânicas do tecido ósseo em reparo nas suas diferentes etapas

大别山硬玉石英岩带中的水

The Dabie Mountains is a collisional orogenic belt between the North China and Yantze Continental plates. It is the eastern elongation of the Tongbai and Qingling orogen, and is truncated at its east end by the Tan-Lu fault. Jadeite-quartzite belt occurs in the eastern margin of UHPMB from the Dabie Mountains. Geochemical features indicate that the protoliths of the jadeite-quartzite and associated eclogite to be supracrustal rocks. The occurrence of micro-inclusions of coesite in jadeite and garnet confirmed that the continental crust can be subducted to great depth (8 0-100km) and then exhumed rapidly with its UHP mineral signature fairly preserved. Therefore, study of UHP jadeite-quartzite provides important information on subduction of continental crustal rocks and their exhumation histories, as well as the dynamics of plate tectonic processes at convergent margins. The purpose of this paper is to investigate the presence of hydrous component in the jadeite-quartzite belt, significant natural variations in the hydrous component content of UHP minerals and to discuss the role of water in petrology, geochemistry and micro-tectonic. On the basis of our previous studies, some new geological evidences have been found in the jadeite-quartzite belt by researches on petrography, mineralogy, micro-tectonic, hydrous component content of UHP minerals and combined with the study on rheology of materials using microprob, ER, TEM. By research and analysis of these phenomenona, the results obtained are as follows: 1. The existence of fluid during ultra-high pressure metamorphic process. Jadeites, omphacite, garnet, rutile, coesite and quartz from the jadeite-quartzite belt have been investigated by Fourier transform infrared spectrometer and TEM. Results show that all of these minerals contain trace amount of water which occur as hydroxyl and free-water in these minerals. The two-type hydrous components in UHP minerals are indicated stable in the mantle-depth. The results demonstrated that these ultra-high pressure metamorphic minerals, which were derived from continental crust protoliths, they could bring water into the mantle depth during the ultra-high pressure metamorphism. The clusters of water molecules within garnet are very important evidence of the existence of fluid during ultra-high pressure metamorphic process. It indicated that the metamorphic system was not "dry"during the ultra-high pressure stage. 2.The distribution of hydrous component in UHP minerals of jadeite-quartzite. The systematic distribution of hydrous components in UHP minerals are a strong indication that water in these minerals, are controlled by some factors and that the observed variations are not of a random nature. The distribution and concentration of hydrous component is not only correlated with composition of minerals, but also a function of geological environment. Therefore, the hydrous component in the minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transported water molecules with decreasing pressure during their exhumation. And these water molecules can not only promote the deformation of jadeite through hydrolytic weakening, but also may be the part of the retrograde metamorphic fluid. 3.The role of water in the deformed UHP minerals. The jadeite, omphacite, garnet are strong elongated deformation in the jadeite-quartzite from the Dabie Mountains. They are (1) they are developed strong plastic deformation; (2) developed dislocation loop, dislocation wall; (3) the existence of clusters of water molecular in the garnet; and (4) the evolution of micero-tectonic from clusters of water molecular-dislocation loop in omphacite. That indicated that the water weakening controlled the mechanism of deformed minerals. Because the data presented here are not only the existence of clusters of water molecular in the garnet, but also developed strong elongation, high density of dislocation and high aspect ratios, adding microprobe data demonstrate the studied garnet crystals no compositional zoning. Therefore, this indicates that the diffusion process of the grain boundary mobility did not take place in these garnets. On the basis of above features, we consider that it can only be explained by plastic deformation of the garnets. The clusters of water molecules present in garnet was directly associated with mechanical weakening and inducing in plastic deformation of garnet by glissile dislocations. Investigate of LPO, strain analysis, TEM indicated that these clinopyroxenes developed strong elongation, high aspect ratios, and developed dislocation loop, dislocation wall and free dislocations. These indicated that the deformation mechanism of the clinopyroxenes plastically from the Dabie Mountains is dominant dislocation creep under the condition of the UHP metamorphic conditions. There are some bubbles with dislocation loops attached to them in the omphacite crystal. The bubbles attached to the dislocation loops sometimes form a string of bubble beads and some loops are often connected to one another via a common bubble. The water present in omphacite was directly associated with hydrolitic weakening and inducing in plastic deformation of omphacite by dislocations. The role of water in brittle deformation. Using microscopy, deformation has been identified as plastic deformation and brittle deformation in UHP minerals from the Dabie Mountains. The study of micro-tectonic on these minerals shows that the brittle deformation within UHP minerals was related to local stresses. The brittle deformation is interpreted as being caused by an interaction of high fluid pressure, volume changes. The hydroxyl within UHP minerals transported water molecules with decreasing pressure due to their exhumation. However, under eclogite facies conditions, the litho-static pressure is extreme, but a high fluid pressure will reduce the effective stress and make brittle deformation possible. The role of water in prograde metamorphism. Geochemical research on jadeite-quartzite and associated eclogite show that the protoliths of these rocks are supracrustal rocks. With increasing of temperature and pressure, the chlorite, biotite, muscovite was dehydrous reaction and released hydrous component during the subduction of continental lithosphere. The supracrustal rocks were transformed UHP rocks and formed UHP facies assemblage promotely by water introduction, and was retained in UHP minerals as hydrous component. The water within UHP minerals may be one of the retrograde metamorphic fluids. Petrological research on UHP rocks of jadeite-quartzite belt shows that there was existence of local fluids during early retrograde metamorphism. That are: (1) coronal textures and symplectite around relict UHP minerls crystals formed from UHP minerls by hydration reactions; (2) coronal textures of albite around ruitle; and (3) micro-fractures in jadeite or garnet were filled symplectite of Amp + PI + Mt. That indicated that the reactions of early retrograde metamorphism dependent on fluid introduction. These fluids not only promoted retrograde reaction of UHP minerals, but also were facilitate to diffuse intergranular and promote growth in minerals. Therefore, the hydrous component in the UHP minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transport water molecules with decreasing pressure and may take part in the retrograde metamorphic fluid during their exhumation. 7. The role of water in geochemistry of UHP jadeite-quartzite. Geochemical research show that there are major, trace and rare earth element geochemical variations in the jadeite-quartzite from the Changpu district of Dabie Mountains, during retrograde metamorphic processes from the jadeite-quartzite--gneiss. The elements such as SiO_2、FeO、Ba、Zr、Ga、La、Ce、PTN Nd% Sm and Eu increase gradually from the jadeite-quartzite to retrograded jadeite-quartzite and to gneiss, whilst TiO_2. Na_2CK Fe2O_3、Rb、Y、Nb、Gd、Tb、Dy、Ho、Er、Tm、Yb decrease gradually. And its fO_2 keep nearly unchanged during early retrograde metamorphism, but decreased obviously during later retrograde metamorphism. These indicate that such changes are not only controlled by element transformation between mineralogical phases, but also closely relative to fluid-rock interaction in the decompression retrograde metamorphic processes.

Localized mechanics of dentin self-etching adhesive system

The bond strength of composite resins (CRs) to dentin is influenced by the interfacial microstructure of the hybrid layer (HL) and the resin tags (TAG). The contemporary self-etching primer adhesive systems overcame the inconvenient of the etch-and-rinse protocol. Studies, however, have demonstrated that HL thickness and TAG length vary according to the wetting time and additional use of acid-etching prior to self-etching primers. This study investigated the localized stress distribution in the HL and the dentin/adhesive interface. Two HL thicknesses (3 or 6 mu m), two TAG lengths (13 or 17 mu m) and two loading conditions (perpendicular and oblique-25 degrees) were investigated by the finite element (FE) analysis. Five two-dimensional FE models (M) of a dentin specimen restored with CR (38 x 64 mu m) were constructed: M1 - no HL and no TAG; M2 - 3 mu m of HL and 13 mu m of TAG; M3 - 3 mu m of HL and 17 mu m of TAG; M4 - 6 mu m of HL and 13 mu m of TAG; and M5 - 6 mu m of HL and 17 mu m of TAG. Two distributed loadings (L) (20N) were applied on CR surface: L1 - perpendicular, and L2 - oblique (25 degrees). Fixed interfacial conditions were assigned on the border of the dentin specimen. Ansys 10.0 (Ansys (R), Houston, PA, USA) software was used to calculate the stress fields. The peak of von Mises (sigma(vM)) and maximum principal stress (sigma(max)) was higher in L2 than in L1. Microstructures (HL and TAG) had no effect on local stresses for L1. Decreasing HL decreased sigma(vM) and sigma(max) in all structures for L2, but the TAG length had influence only on the peributular dentin. The thickness of HL had more influence on the sigma(vM) and sigma(max) than TAG length. The peritubular dentin and its adjacent structures showed the highest sigma(vM) and sigma(max), mainly in the oblique loading.

Um estudo da estabilidade mecânica de poços a partir de perfis geofísicos em formações pouco consolidadas

A análise da estabilidade mecânica de um poço pode ser feita a partir do cálculo de parâmetros elásticos da formação utilizando a densidade do meio e as velocidades de propagação das ondas compressional e cisalhante na formação rochosa, os quais podem ser obtidos de perfis geofísicos do poço. Em formações sedimentares pouco consolidadas as ferramentas de perfilagem sônica convencionais (monopolares) não conseguem registrar com acuidade a velocidade da onda cisalhante pois a primeira chegada dessa onda é camuflada pela chegada de outras ondas que podem ser mais rápidas que a onda cisalhante num poço perfurado neste tipo de formação. Medidas das velocidades sônicas são feitas em laboratório em amostras da formação, sob condições semelhantes às condições in situ, servindo como ajuste das velocidades registradas no poço pela ferramenta de perfilagem sônica. Para a análise de estabilidade da formação, perfis auxiliares são necessários como o perfil de porosidade, saturação de fluidos e perfis de composição mineralógica da formação rochosa. Exige-se ainda dados de testes de avaliação da formação e de condições do reservatório, mas que são comuns em poços de petróleo, como o teste de formação e os testes de pressurização do poço, tais como o teste de micro-fraturamento hidráulico ou o teste de absorção. A avaliação das tensões principais efetivas que atuam distante do poço, e que não são afetadas pela sua presença, é feita através da associação de um modelo de deformação elástica apropriado e o resultado do teste de pressurização disponível para o poço em estudo. Utilizando resultados clássicos da teoria da elasticidade geral pode-se calcular o campo de tensões modificado na vizinhança da parede do poço devido ao efeito da própria presença do poço ali perfurado e da diferença de pressão existente entre o interior do poço e a formação rochosa. A determinação das propriedades mecânicas da formação a partir das velocidades sônicas e a avaliação do campo de tensões assumindo um modelo elástico de deformação, supõem o meio rochoso no qual as ondas se propagam como elástico, homogêneo e isotrópico. Esta suposição representa a principal aproximação assumida pela metodologia descrita neste trabalho. De posse das propriedades mecânicas da formação e do campo de tensões que age na vizinhança do poço resta definir o critério segundo o qual a rocha sofre instabilidade mecânica quando submetida aquele campo de tensões. Isto permite determinar se, nas condições avaliadas do poço e da formação, haverá quebra da parede do poço por excesso de tensão e, se houver, qual a sua extensão. Assim o problema é como analisar o comportamento mecânico de um poço em uma formação pouco consolidada a partir de perfis geofísicos os quais podem ter problemas no registro das propriedades físicas do meio em formações deste tipo. A metodologia proposta é aplicada a dois intervalos de profundidade pertencentes a dois poços onde arenitos e folhelhos se intercalam e nos quais todos os dados necessários estão disponíveis. Os resultados obtidos mostram que, exceto quando outros mecanismos de quebra da parede do poço agem na formação, a metodologia proposta consegue com sucesso detectar zonas de ocorrência de instabilidade mecânica do poço provocadas por um campo de tensões que excede a resistência mecânica da formação.

Behaviour of displacement piles in sand under cyclic axial loading

Field experiments have demonstrated that piles driven into sand can respond to axial cyclic loading in Stable, Unstable or Meta-Stable ways, depending on the combinations of mean and cyclic loads and the number of cycles. An understanding of the three styles of responses is provided by experiments involving a highly instrumented model displacement pile and an array of soil stress sensors installed in fine sand in a pressurised calibration chamber. The different patterns of effective stress developing on and around the shaft are reported, along with the results of static load tests that track the effects on shaft capacity. The interpretation links these observations to the sand's stress strain behaviour. The interface-shear characteristics, the kinematic yielding, the local densification, the growth of a fractured interface-shear zone and the restrained dilatancy at the pile soil interface are all found to be important. The model tests are shown to be compatible with the full-scale behaviour and to provide key information for improving the modelling and the design rules. (C) 2012 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Influence of advanced load simulation models on fatigue design of jackets for offshore wind turbines.

Constant developments in the field of offshore wind energy have increased the range of water depths at which wind farms are planned to be installed. Therefore, in addition to monopile support structures suitable in shallow waters (up to 30 m), different types of support structures, able to withstand severe sea conditions at the greater water depths, have been developed. For water depths above 30 m, the jacket is one of the preferred support types. Jacket represents a lightweight support structure, which, in combination with complex nature of environmental loads, is prone to highly dynamic behavior. As a consequence, high stresses with great variability in time can be observed in all structural members. The highest concentration of stresses occurs in joints due to their nature (structural discontinuities) and due to the existence of notches along the welds present in the joints. This makes them the weakest elements of the jacket in terms of fatigue. In the numerical modeling of jackets for offshore wind turbines, a reduction of local stresses at the chord-brace joints, and consequently an optimization of the model, can be achieved by implementing joint flexibility in the chord-brace joints. Therefore, in this work, the influence of joint flexibility on the fatigue damage in chord-brace joints of a numerical jacket model, subjected to advanced load simulations, is studied.

Laser processing effect on magnetic properties of amorphous wires

A study was conducted to observe the laser processing effects on the magnetic properties of amorphous wires. Weekly interacting heterogeneous structures with different magnetic properties were formed by the local annealing by argon laser. Favourable changes were observed due to the creation of local stresses and structural interfaces.

Theoretical study on the (1-012) deformation twinning and cracking in coarse-grained magnesium alloys

This paper theoretically and systematically investigates: (1) the effect of local transformed strains within deformation twinning on twin intersection; (2) the fracture mode based on type I co-zone tensile twin intersection in coarse-grained magnesium alloys, as well as the impacts of twin intersection and grain diameter on interfacial crack nucleation along twin boundaries; and (3) the influence of the local stresses arising from the encountered twin bands on crack growth. A novel dislocation-based strain nucleus model and a Green's function method, which are applicable to any material with local transformations in which elastic properties are reasonably approximated as isotropic, are specifically employed to model the concentrated transformed strain and calculate the local stress field resulting from deformation twinning and the stress intensity factors at crack tips in the magnesium alloys, respectively. In addition, an electron backscatter diffraction (EBSD) measurement is provided for crack nucleation originating from Type I co-zone tensile twin intersection. The theoretical modeling indicates: (i) the local strains within barrier twins strongly dictate the growth of incident twins and enhance the twin propagation stress; (ii) larger grains favor brittle fracture. More specifically, the dislocation reactions and pile-ups at the junctions between tensile twins can result in interfacial crack nucleation and growth along the twin boundaries, which is a brittle fracture mode based on lower twinning stress and stress concentration in the coarse-grained magnesium alloys; and (iii) the direction of crack propagation is easily changed by high-density twin bands and twin intersections owing to the local strains.

Path independent limiting criteria in sheet metal forming

The Forming Limit Diagram (FLD) is a conventional failure diagram to estimate necking limits of sheet metal for proportional loading conditions. Previous studies reveal that the FLD is not suitable for predicting the influence of nonlinear strain paths. This paper presents methodical comparison among all common available strain path independent strain/stress based limiting criteria. All the strain path independent strain based limiting criteria (Traditional Failure Diagram (TFD), Extended Forming Limit Diagram (XFLD), Extended Stress Ratio Based Forming Limit Diagram (ESRFLD), and Polar Effective Plastic StrainDiagram (PEPSD)) and stress based limiting criteria (Traditional Stress based Failure Diagram (TFSD), Stress Based Forming Limit Diagram (FLSD), Stress Ratio and Stress Based Forming Limit Diagram (SRFLSD), Extended Stress Based Forming Limit Diagram (XFLSD), and Polar Effective Stress Diagram (PESSD)) are approximately path-independent for smaller amount of pre-straining and path dependent for large pre-straining conditions. From advance image correlation technique precisely determination of local strains near necked area is possible today. However direct determination of local stresses near necked area is not possible. Therefore, local stresses and equivalent stress are determined by employing both yield criterion and strain-hardening law. Similarly equivalent strain is calculated by the use of yield criterion. Therefore, the choice of yield criterion has an impact on the results for TFD, XFLD, ESRFLD and PEPSD. However, selections of both yield criterion and strain-hardening law have substantial influence on the results for TFSD, FLSD, SRFLSD, XFLSD and PESSD. The inherent calculation error can be minimized by generation of experimental data for each material and then selection of representable yield criterion and strain-hardening law. Improvement of experimental techniques and generation of rigorous material data bank in various strain paths may help researchers to diagnose and resolve the issue. TFD, TFSD and XFLSD have inherent variables to take care the effect of through thickness stress, however rigorous experimental verification is needed before the field application.

Analytical benchmark solutions for steel frame structures subject to local buckling effects

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. This paper contains a comprehensive set of analytical benchmark solutions for steel frames comprising non-compact sections, which can be used to verify the accuracy of simplified concentrated plasticity methods of advanced analysis. The analytical benchmark solutions were obtained using a distributed plasticity shell finite element model that explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. A brief description and verification of the shell finite element model is provided in this paper.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.