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This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.

Producción Científica, A robust approach for clustering functional directional data is proposed. The proposal adapts “impartial trimming” techniques to this particular framework. Impartial trimming uses the dataset itself to tell us which appears to be the most outlying curves. A feasible algorithm is proposed for its practical implementation justified by some theoretical properties. A “warping” approach is also introduced which allows including controlled time warping in that robust clustering procedure to detect typical “templates”. The proposed methodology is illustrated in a real data analysis problem where it is applied to cluster aircraft trajectories., Centro para el Desarrollo Tecnológico Industrial y Ministerio de Economía y Empresa (FEDER) (grant IDI-20150616, CIEN 2015), Ministerio de Asuntos Económicos y Transformación Digital (grants MTM2017-86061-C2-1-P and MTM2017-86061-C2-2-P), Junta de Castilla y León - Fondo Europeo de Desarrollo Regional (grants VA005P17 and VA002G18), Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

The nonlinear dynamics of a thin tube under the action of a harmonic external load is addressed in the paper. Use is made of a beam-like model which extends the Timoshenko beam model with further kinematic descriptors, related to the change in shape of the cross section. The external load is applied in half cap of the pipe, directly triggering both the bending of the axis-line and the flattening of the cross sections. The equations of motion are projected on a reduced basis constituted by the first three linear modes, and then the solutions are sought via the multiple scale method, for two different external resonance conditions. Internal resonances among the modes are considered as well. The outcomes, compared with pure numerical solutions, highlight the possible energy exchange between local modes, i.e., those describing flattening and warping of the cross sections, and global modes, i.e., those related to bending of the axis-line and rotation of the cross section of the pipe.

International audience; Exact solutions for coupled warping beam problem are developed in the present paper. The torsion and shear warping problems are considered together, and three beam formulations are considered, regarding the influence of the bi-moment and bi-shear terms. In the first case, where the bi-moment and bi-shear terms are neglected, the exact solutions have a simple polynomial form. In the second and third cases, the exact solution have a more elaborate form, consisting of hyperbolic terms. The coupling between the modes results from the lack of symmetry of the cross-section and is captured in the exact solution for all modes.

Currently, the use of light steel thin-walled structures from roll-formed sections in industrial and civil construction is increasing. Studies of the strength properties of these structures will lead to the development of the entire industry, including the aviation industry, which includes the development, manufacture and installation of structures using thin-walled bent profiles. The study tested of the influence of deplanation of the cross-section of thin-sheet plates on their use by various methods: FEM-modeling of static thin-sheet samples (plates) with various stress concentrators, imitating structural notches and / or operational defects of structural elements, structural or stimulating stress-strain. fuselage of transport aircraft, analytical calculation and carrying out a full-scale experiment. On the basis of the results obtained and their comparison, conclusions are drawn about the peculiarities of using each of them in the study of the phenomenon of warping on the load of thin-walled elements., Проведено дослідження впливу депланації поперечного перерізу тонколистових пластинок на їх НДС використовуючи різні методики: МКЕ-моделювання статичного навантаження тонколистових зразків (пластинок) з різними концентраторами напруг, що імітують конструкційні вирізи та/або експлуатаційні дефекти елементів конструкції, наявні фюзеляжу транспортних літаків, аналітичний розрахунок та проведенням натурного експерименту. На основі отриманих результатів та їх порівняння зроблено висновки про особливості використання кожної з моделей при дослідженні явища депланації на навантаження тонкостінних елементів.

In this paper, the static response and normal/shear stresses of axially functionally graded exact super-elliptical beams are presented via a warping-included mixed finite element method. Super-elliptical axis geometry is derived over the exact functions of planar curves. The constitutive equations are obtained from three-dimensional elasticity theory. The mixed finite element formulation is enhanced by including the warping deformations via displacement-type finite elements on the cross-section. The two-noded curved mixed finite element has twenty-four degrees of freedom in total. Satisfactory results are obtained for the warping-included normal/shear stresses, displacements and reactional forces of axially functionally graded exact super-elliptical beams even with lesser degrees of freedom compared to the three-dimensional behavior of brick finite elements. As benchmark examples, the influences of high axial curvature, cross-sectional geometry and material gradation on the static response and stresses of axially functionally graded exact super-elliptical beams are investigated.

Continuously Variable Transmissions (CVT) can serve as subsystems for a variety of machineries and robotic systems. A compliant CVT mechanism based on the warping of twisting beams is presented here. The design works based on the demonstrated fact that the twist on one side of a beam can be transferred via sectional warping and propagate across a rotational constraint in the middle of the beam to create a reverse twist on the opposite side. In the proposed compliant CVT the transmission ratio is dependent on the position of the middle rotational constraint which can vary in a continuous range. We have demonstrated this concept and its relation to the twisting beam's warping constant, as well as its functionality for different transmission ratios of 1:4 to 4:1. An analytical model as well as a Finite Element Analysis (FEA) and experiments are employed to characterize and verify the concept and its relation to the warping constant.

Fused filament fabrication (FFF) is gaining attention as an efficient way to create parts and replacements on demand using thermoplastics. This technology requires the development of new materials with a reliable printability that satisfies the requirement of final parts. In this context, a series of composites based on acrylonitrile styrene acrylate (ASA) reinforced with basalt fiber (BF) are reported in this work. First, several surface modification treatments are applied onto the BF to increase their compatibility with the ASA matrix. Then, once the best treatment is identified, the mechanical properties, coefficient of thermal expansion (CTE) and warping distortion of the different specimens designed and prepared by FFF are studied. It was found that the silanized BF is appropriate for an adequate printing, obtaining composites with higher stiffness, tensile strength, low CTE and a significant reduction in part distortion. These composites are of potential interest in the design and manufacturing of final products by FFF, as they show much lower CTE values than pure ASA, which is essential to successfully fabricate large objects using this technique.

En el projecte següent es detallaran cinc casos quirúrgics. En cada cas es cercarà optimitzar els fitxers STL originals i trobar una configuració de paràmetres d'impressió que permeti imprimir els prototips estalviant la major quantitat de temps i material. Els materials que es faran servir seran PLA i ABS. Materials molt diferents entre si. L'ABS és més delicat i susceptible a la diferència de temperatura ambiental. El motiu és trobar òptims paràmetres d'impressió per a tots dos materials. Addicionalment, es plantejaran solucions per als diferents problemes d'impressió que puguin sorgir per la complexitat de cada cas clínic. També es faran servir dos models d'impressores. Ja que es requereix extrusió doble i extrusió amb un sol extrusor. D'aquesta manera s'obtindran valors i paràmetres recomanats segons el material amb què voleu imprimir. Tot seguit es farà una anàlisi de l'abast que tenen els prototips fabricats en els casos quirúrgics. Posteriorment s'elaborarà l'anàlisi econòmica de cada peça, la factibilitat mediambiental del projecte i finalment les conclusions. En el siguiente proyecto se detallarán cinco casos quirúrgicos. En cada caso se buscará optimizar los archivos STL originales y hallar una configuración de parámetros de impresión que permita imprimir los prototipos ahorrando la mayor cantidad de tiempo y material. Los materiales que se utilizarán serán PLA y ABS. Materiales muy distintos entre sí. Siendo el ABS más delicado y susceptible a la diferencia de temperatura ambiental. El motivo es encontrar parámetros de impresión óptimos para ambos materiales. Adicionalmente se plantearán soluciones para los distintos problemas de impresión que puedan surgir por la complejidad de cada caso clínico. También se usarán dos modelos de impresoras. Ya que se requiere extrusión doble y extrusión con un solo extrusor. Se obtendrán, de este modo, valores y parámetros recomendados según el material con el que se desee imprimir. Seguidamente se hará un análisis del alcance que tienen los prototipos fabricados en los casos quirúrgicos. Posteriormente se elaborará el análisis económico de cada pieza, la factibilidad medioambiental del proyecto y finalmente las conclusiones. In the following project, five surgical cases will be detailed. In each case, the original STL files will be optimized and configuration of printing parameters that allows printing the prototypes saving the greatest amount of time and material will be find. The materials to be used will be PLA and ABS. Which are very different materials. ABS being more delicate and susceptible to the difference in environmental temperature. The reason is to find optimal printing parameters for both materials. Additionally, solutions will be proposed for the different printing problems that may arise due to the complexity of each clinical case. Two models of printers will also be used. As double extrusion might be required in some of the cases. In this way, recommended values and parameters will be obtained according to the material with which the user wants to print. Next, an analysis will be made of the scope of the prototypes manufactured in surgical cases. Subsequently, the economic analysis of each piece, the environmental feasibility of the project and finally the conclusions will be elaborated.

This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping displacement field, and without introducing any additional kinematic variables. The present beam model also facilitates the recovery of the distributions of longitudinal normal stresses and transverse shear stresses. The authors postulate that the bending and shear terms in first-order shear deformation theory represent the first two terms in an infinite series that would constitute an ideal one-dimensional beam model, and it is suggested that the present beam model constitutes the first four terms in this hypothetical infinite series. The present beam model is solved for several example beams, and the results are compared with those of existing classical and higher-order beam models, as well as computational results from finite element analyses. It is shown that the present beam model is able to accurately represent deformed shapes and stress distributions pertaining to beams that exhibit non-trivial shear compliance as well as non-trivial shear-warping stiffness. In the case of laminated composite beams comprising a large number of laminae, the present beam model offers a level of analytical fidelity that is comparable to that of existing zigzag beam models; however, unlike zigzag beam models, the present beam model is equally well suited for the analyses of beams comprising any number of laminae.

The study presents an analysis of steel I-beam warping. The calculations were made for hot-rolled IPE200 hinged beams with different lengths. After determining load-bearing capacity using the GMNIA method, the beams were strengthened with bimoment restraints at each end. The changes in critical moment and load-bearing capacity were then evaluated. The study presents the manner in which the material and geometric imperfections have been determined. The GMNIA calculations were conducted using the Finite Element Method in Abaqus software. The results were then compared to results obtained with traditional methods and acquired from LT Beam software.

Composite box girder bridges may be a competitive solution under certain constraints due to their efficiency and torsional capacity. However, the cross section deflects transversally, creating longitudinal stresses which reduce the capacity of the section. Those stresses may be controlled using cross-frames, but the detailing of those elements may become expensive. The procedure described herein provides a useful tool for an efficient design of cross frames based on the well-known BEF theory. It may be implemented using a commercial software and the formulation provided increases the accuracy of the existing one.

In dieser Arbeit wird eine Methode f��r die Sch��tzung von elastischen Formmittelwerten von offenen und planaren Kurven vorgestellt. Dazu wurden die Konzepte des full Procrustes Mittelwerts f��r Landmark Konfigurationen mit dem square-root-velocity Framework f��r die elastische Analyse von Funktionen kombiniert, um elastische full Procrustes Mittelwerte zu berechnen. Die Sch��tzung dieses Mittelwerts h��ngt eng mit der komplexen Kovarianzoberfl��che der beobachteten Kurven zusammen, welche durch Ber��cksichtigung ihrer Symmetrieeigenschaften effizient gesch��tzt werden kann (siehe Cederbaum, Scheipl und Greven 2018). In Kombination mit den Methoden f��r elastische Mittelwertberechnung in Steyer, St��cker und Greven 2021 ist dieser Ansatz besonders passend Kurven mit nur wenigen, unregelm����ig verteilten Beobachtungspunkten. Die vorgestellte Methode und ihre Implementierung wurde auf zwei Testdatens��tzen ��berpr��ft. ��ber den in der Sch��tzung verwendeten Strafparameter (penalty) kann die Gl��tte des Mittelwerts kontrolliert werden, wobei eine penalty erster oder zweiter Ordnung auch in Bereichen mit wenig Beobachtungen zu stabilen Sch��tzungen f��hrt. Die Beobachtungen k��nnen ��ber ihre elastischen full Procrustes Fits gemeinsam mit dem Mittelwert visualisiert werde, wobei der gesch��tzte Mittelwert aber nicht als ein naiver funktionaler Mittelwert der Fits interpretiert werden kann. Au��erdem ist der elastische full Procrustes Mittelwert robust gegen��ber Ausrei��ern, da diese tendenziell so skaliert werden, das ihr Einfluss auf die Sch��tzung eingeschr��nkt wird. Die Methode wurde benutzt um die Variabilit��t von Zungenkonturen bei der Artikulation von Konsonanten zu analysieren. Hierbei scheint der Vokalkontext den gr����ten Effekt auf die Zungenkontur zu haben, w��hrend der Einfluss des ausgesprochen Konsonanten zwischen den Sprechern unterscheidet., This thesis proposes a method for elastic shape mean estimation of open planar curves. It combines the concept of the full Procrustes mean with the square-root-velocity framework to estimate elastic full Procrustes means. This mean can be shown to be related to an eigenfunction problem over the complex covariance surface of the observed curves, which can be estimated efficiently by accounting for its symmetry (Cederbaum, Scheipl and Greven 2018). These methods, in combination with the methods for elastic mean estimation in Steyer, St��cker and Greven 2021, make the proposed estimation procedure especially suitable to sparse and irregular observations. The method and its implementation were validated over toy datasets, where it was shown that the estimated shape mean is elastic and invariant with respect to shape preserving transformations of the input curves. The penalty used in the estimation provides stable estimates in regions where observations are sparse and consistently good results were achieved for first and second order penalties. The estimated mean may be plotted together with the elastic full Procrustes fits, however, care has to be taken when interpreting these plots, as the estimated mean curve is not a simple functional mean of the aligned curves. Furthermore, the elastic full Procrustes mean is quite robust to outliers, as they tend to get shrunk towards zero, restricting their influence on the mean estimation. Finally, the method was used to analyse variability in an empirical dataset of tongue contours during consonant articulation. Here it was found that the vowel context has the largest influence on the tongues shape, while the effect of the spoken consonant seems to vary between speakers.

A model for describing warp—characterized as a systematic, large-scale deviation from the intended flat shape—in corrugated board based on Kirchhoff plate theory is proposed. It is based on established homogenization techniques and only a minimum of model assumptions. This yields general results applicable to any kind of corrugated cardboard. Since the model is intended to be used with industrial data, basic material properties which are usually not measured in practice are summarized to a few parameters. Those parameters can easily be fitted to the measurement data, allowing the user to systematically identify ways to reduce warp in a given situation in practice. In particular, the model can be used both as a filter to separate the warp from other surface effects such as washboarding, and to interpolate between discrete sample points scattered across the surface of a corrugated board sheet. Applying the model only requires height measurements of the corrugated board at several known (not necessarily exactly predetermined) locations across the corrugated board and acts as an interpolation or regression method between those points. These data can be acquired during production in a cost-efficient way and do not require any destructive testing of the board. The principle of an algorithm for fitting measured data to the model is presented and illustrated with examples taken from ongoing measurements. Additionally, the case of warp-free board is analyzed in more detail to deduce additional theoretical conditions necessary to reach this state.

The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method.

Leafsprings are commonly used in flexure mechanisms to enable repeatable motion and provide support stiffness. In various applications, the torsional stiffness needs to be increased. This paper presents the concept of using warping constraints distributed along the leafspring to increase the torsional stiffness relative to the stiffness in other directions. A beam-based model of nonuniform torsion is used to estimate the relationship between the geometrical design parameters and the expected increase in torsional stiffness. The model predicts that an order of magnitude increase in stiffness is feasible. Compared to other solutions, the distributed warping constraints have a less obtrusive shape that offer more design freedom.

Leafsprings are commonly used in flexure mechanisms to enable repeatable motion and provide support stiffness. In various applications, the torsional stiffness needs to be increased. This paper presents the concept of using warping constraints distributed along the leafspring to increase the torsional stiffness relative to the stiffness in other directions. A beam-based model of nonuniform torsion is used to estimate the relationship between the geometrical design parameters and the expected increase in torsional stiffness. The model predicts that an order of magnitude increase in stiffness is feasible. Compared to other solutions, the distributed warping constraints have a less obtrusive shape that offer more design freedom.

Reinforced concrete core walls form the backbone of millions of buildings internationally, bracing the structure against wind and earthquake loading. Due largely to plan asymmetry, a torsional response of a building is possible, where the core wall will resist the twisting actions. There is currently no evidence for the torsional capacity of reinforced concrete U-shaped core walls, which are a popular wall geometry used in construction practice. An experimental campaign will be soon conducted in the laboratory LEMSC of the institute iMMC at UCLouvain, Belgium, to test three large-scale reinforced concrete U-shaped walls subjected to different combinations of flexure and torsion. A blind prediction competition was organised by the authors to estimate salient behaviour and performance characteristics of the walls subjected to pure flexure and pure torsion. This paper presents a summary of the experimental campaign and some blind predictions by the authors using finite element modelling. These predictions, as well as others submitted for the competition, will be compared to the experimental results during the conference presentation.

[EN] The use of filaments made of recycled materials such as PET on fused deposition modelling (FDM) is aspired to be one of the innovative techniques for sustainable and environmentally friendly production. However, to carry out such a development, it is crucial to understand the behaviour of virgin PET and optimise the printing parameters to obtain the best results. Research of the effect that FDM technology can have on the mechanical properties of 3D-printed products made of polyethylene terephthalate (PET) filaments has been carried out. The bed temperature of the printer is one of the most important parameters to be controlled since by increasing the temperature from 70 ºC to 100 ºC, the polymer crystallizes (cold crystallization) and the fragility of the specimens is increased. The same observation happens with injected specimens by increasing the mould temperature from 25 ºC to 85 ºC, where the ductility of the specimen decreases. Using differential scanning calorimetry, the crystallinity degree of each specimen was measured. Through a scanning electron microscope, the printing parameters influence on the quality of structure and filament adhesion were observed. Optimization of process parameters is required to obtain amorphous specimens that can reach the mechanical performance of injected PET specimens. [ES] El uso de filamentos elaborados con materiales reciclados como el PET en la tecnología de impresión 3D, aspira ser una de las técnicas innovadoras para una producción sostenible y ambientalmente favorable. Sin embargo, para llevar a cabo tal desarrollo es imprescindible conocer el comportamiento del PET virgen, así como los parámetros de procesado que permitan obtener las mejores prestaciones de este material. El trabajo se centra en la investigación del efecto que la tecnología FDM tiene en las propiedades mecánicas de productos hechos con filamento de polietilén tereftalato (PET). La temperatura de la cama de la impresora es de los parámetros más importantes para controlar ya que al subir la temperatura de 70 ºC a 100 ºC, el producto cristaliza (cristalización en frío) y la fragilidad de las probetas aumenta. Lo mismo ocurre en el caso de probetas inyectadas al subir la temperatura del molde de 25 ºC a 85ºC, donde la ductilidad de las probetas decrece. Aplicando la calorimetría diferencial de barrido, se ha determinado el grado de cristalinidad, encontrándose un gradiente de cristalinidad en el espesor de la probeta. Con la microscopia electrónica de barrido se ha observado la influencia que tienen la temperatura y el patrón de impresión en la calidad de la misma. Se requiere la optimización de los parámetros de procesado en impresión 3D para obtener probetas amorfas que se acerquen a la resistencia mecánica de las probetas de PET inyectadas.

This research focuses on thermal deformations of thermoplast during three-dimensional printing. A filament acrylonitrile butadiene styrene was used, and the main focus was put on warping. Twenty-seven cuboids divided in six categories by their length, height, surface area, color, nozzle temperature and bed temperature were printed by Fused Filament Fabrication 3D printer. The whole process was captured by a thermal camera and the movies were used to analyze the temperature distribution during printing. All printouts were measured and scanned with a 3D scanner in order to highlight any abbreviations from the original digital models. The obtained results were used to formulate some general conclusions on the influence of selected parameters on the warping process. Based on the outcomes of the study, a set of guidelines on how to minimalize warping was proposed.

The article analyses the method of enhancing a steel beam by adding additional steel members like ribs. They are rigidly connected with both flanges in a plane parallel to the web. That plates reduces warping during in-plane bending of steel beam under lateral-torsional bucking. Different thicknesses of steel plates used as ribs and different cross-sections were taken into account. Calculations were conducted using FEM and ABAQUS CAE environment. The outcomes were compared with ones from previous studies which concerned an influence of endplates on load-bearing capacity of an I-beam.

This study deals with the analysis of multilayer composite and functionally graded materials (FGM) structures. The material properties of the FGM beam are assumed to vary according to the power law distribution of its constituent’s volume fraction over the cross section. The analytical analysis seems to be cumbersome. A finite element approach is investigated in this work for the static and free vibration behaviors of the 2D FGM beams with variable constituents over the cross section. The analyses are carried out in arbitrary axes and the axial, bending and shear couplings are considered. In this study, the classical beam theory, Timoshenko first-order and higher order shear models are described and implemented. The different models are compared to benchmark solutions found in the literature. Effects of boundary conditions, slenderness ratio, and the FGM power law parameter are investigated under static and free vibration analyses. FGM and multilayer sandwich beams are also analyzed. It is proven that the axial bending and shear coupling affect the behavior of the FGM beams in both statics and dynamics. In the presence of short beams, shear effect is important and leads to cross-section warping. The classical beam theory fails in this context. All models are close in the case of slender beams.

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are assumed. Isogeometric tools (NURBS) are employed in order to obtain the results for the 1D formulation and 3D shell models are developed in FEM commercial software for composite cross sections with diaphragms. The number of intermediate diaphragms according to bridges design specifications is compared to the analyzed diaphragmatic arrangements in order to assess the overall structural behavior of bridges decks. For this purpose, examples of curved beam models with open or closed cross sections and various arrangements of diaphragms have been studied.

In this paper, we investigate the coupling of Poisson’s and warping effect for a general asymmetric cross-section of Cosserat beam. We present the challenges and inconsistencies observed as a result of our attempt to couple the two effects. The fully-coupled Poisson’s transformation is then developed to describe the in-plane deformation for the prismatic beam. A comprehensive kinematic treatment of geometrically exact and nonlinear Cosserat beam subjected to large deformation and finite strain is finally obtained that extensively captures the deformation due to multiple curvatures, torsion, shear, axial deformation, warping and a fully-coupled Poisson’s effect in the cross-section, all while maintaining the single manifold nature of the problem. The contributions to the strain vector and the deformation gradient tensor due to various deformation effects are interpreted and explained in detail. In the final part of the paper, we use the kinematics developed to establish a measurement model of discrete and finite length strain gauges attached to the surface of the beam (or embedded into the beam). We investigate the relationship between the scalar strain measurement of the strain gauge and the local finite strain parameters of the beam.

A new mixed-dimension coupling method is formulated for members with (bi-symmetric) wide flange cross sections based on the idea of least squares transformations between two sets of point clouds. This coupling method imposes the minimum number of constraint equations required to link the displacement, rotation, and torsion-warping degrees-of-freedom of the dependent node. At the heart of the formulation is the solution of a 4 x 4 eigenvalue problem and the deduction of torsion-warping deformations. The proposed method is implemented and validated for nonlinear finite element analysis and the source code is made publicly available. Examples demonstrate that the proposed coupling method can improve interface stress distributions over alternative methods and is suitable for the coupling of elastic continuum finite elements.

n fused layer modeling (FLM) manufacturing technology, there is an increased demand for semi-crystalline materials due to their favorable mechanical properties, such as high strength and toughness. The reasons for their limited use are process-related residual stresses and reduced interlayer bonding, resulting in component distortion, warping and poor strength. Addressing these problems, this paper presents the development and implementation of a rotary print head that enables local laser pre-deposition heating and forced air cooling in the 2.5-dimensional FLM process. Samples of polypropylene are fabricated to investigate the effects of the modified process on residual stresses and interlayer bonding. The investigations show that local laser pre-deposition heating can positively influence the interlayer bonding. In combination with a reduction of the extrusion temperature and additional cooling, it is possible to considerably reduce the residual stresses. The results of this research show that pre-deposition heating and forced air cooling significantly improve the processability of semi-crystalline thermoplastics in the FLM process., Journal of manufacturing and materials processing;Vol. 5. 2021, 3, art. 82

Kinematic bending of profiles allows to manufacture parts with high flexibility concerning the geometry. Still, the production of profiles with asymmetric cross-sections regarding the force application axis using kinematic bending processes offers challenges regarding springback and warping. These geometric deviations can be reduced by partial, cross-sectional heating during the process as it lowers the flow stress locally. In this work, the influence of partial, cross-sectional heating during a three-roll push-bending process on the warping and springback of L-profiles is investigated. Numerical and experimental methods reveal the influence of temperature on warping and springback. A newly developed analytical model predicts the warping and bending moment in the design phase and assists to understand the effect of warping reduction through partial heating during plastic bending. With increasing temperature of the heated profile area, the warping is reduced up to 76% and the springback of the bend profiles is decreased up to 44%. The warping reduction is attributed to a shift in stress free fiber due to the temperature gradient between heated and room temperature areas. The shift of stress-free fiber leads to an adapted shear center position, resulting in an approximated “quasi-symmetric” bending case.

Micro-computed tomography (µCT) provides non-destructive three-dimensional (3D) imaging of soft tissue microstructures. Specific features in µCT images can be identified using correlated two-dimensional (2D) histology images allowing manual segmentation. However, this is very time-consuming and requires specialist knowledge of the tissue and imaging modalities involved. Using a custom-designed µCT system optimized for imaging unstained formalin-fixed paraffin-embedded soft tissues, we imaged human lung tissue at isotropic voxel sizes less than 10 µm. Tissue sections were stained with haematoxylin and eosin or cytokeratin 18 in columnar airway epithelial cells using immunofluorescence (IF), as an exemplar of this workflow. Novel utilization of tissue autofluorescence allowed automatic alignment of 2D microscopy images to the 3D µCT data using scripted co-registration and automated image warping algorithms. Warped IF images, which were accurately aligned with the µCT datasets, allowed 3D segmentation of immunoreactive tissue microstructures in the human lung. Blood vessels were segmented semi-automatically using the co-registered µCT datasets. Correlating 2D IF and 3D µCT data enables accurate identification, localization and segmentation of features in fixed soft lung tissue. Our novel correlative imaging workflow provides faster and more automated 3D segmentation of µCT datasets. This is applicable to the huge range of formalin-fixed paraffin-embedded tissues held in biobanks and archives.

There is an increasing number of rainfall products available over Africa and globally. Rainfall has considerable socio-economic impacts in sub-Saharan Africa, and the sparse gauge and radar networks make such estimates particularly valuable. They are used in many important applications such as drought/flood forecasting, water management or climate monitoring. The choice of which one to use has a significant influence on the output and performance of such applications. The large number of available rainfall products makes it difficult to select the “best” one for one’s need. Among the rainfall products, there is an increasing number of satellite-based estimates with ever finer resolution. They are particularly valuable in Africa where the gauge network is not dense enough to represent the high variability of the rainfall during the monsoon season. However, there are substantial differences between them. Rainfall events are moving systems which can be described by their positions and timings beside of their intensity. A position or timing error will also lead to mismatches in the rainfall occurrence or intensity. This is especially true for localized rainfall events such as the convective rainstorms occurring during the rainy season in sub-Saharan Africa. However, rainfall is mainly evaluated with respect to its intensity or occurrence, while position and timing errors are rarely studied.

There is an increasing number of rainfall products available over Africa and globally. Rainfall has considerable socio-economic impacts in sub-Saharan Africa, and the sparse gauge and radar networks make such estimates particularly valuable. They are used in many important applications such as drought/flood forecasting, water management or climate monitoring. The choice of which one to use has a significant influence on the output and performance of such applications. The large number of available rainfall products makes it difficult to select the “best” one for one’s need. Among the rainfall products, there is an increasing number of satellite-based estimates with ever finer resolution. They are particularly valuable in Africa where the gauge network is not dense enough to represent the high variability of the rainfall during the monsoon season. However, there are substantial differences between them. Rainfall events are moving systems which can be described by their positions and timings beside of their intensity. A position or timing error will also lead to mismatches in the rainfall occurrence or intensity. This is especially true for localized rainfall events such as the convective rainstorms occurring during the rainy season in sub-Saharan Africa. However, rainfall is mainly evaluated with respect to its intensity or occurrence, while position and timing errors are rarely studied.

We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation) from the amplitude variation ("vertical" variation) is crucial in order to properly conduct further analyses, which otherwise can be severely distorted. We determine precise nonparametric conditions under which the two forms of variation are identifiable. These show that the identifiability delicately depends on the underlying rank. By means of several counterexamples, we demonstrate that our conditions are sharp if one wishes a genuinely nonparametric setup; and in doing so we caution that popular remedies such as structural assumptions or roughness penalties can easily fail. We then propose a nonparametric registration method based on a "local variation measure", the main element in elucidating identifiability. A key advantage of the method is that it is free of any tuning or penalisation parameters regulating the amount of alignment, thus circumventing the problem of over/under-registration often encountered in practice. We provide asymptotic theory for the resulting estimators under the identifiable regime, but also under mild departures from identifiability, quantifying the resulting bias in terms of the amplitude variation's spectral gap., Comment: 54 pages (Accepted for publication in Bernoulli)

This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

Torsional vibrations in beams are damped by discrete, axial viscous dampers in configurations constituting bimoments. The bimoments act on warping displacements and partial restraining of warping suggests the inclusion of a flexibility parameter, calibrated from numerical results. Correcting for distortion is incorporated in a similar manner. The use of the governing differential equation with calibrated parameters as an alternative to a full complex analysis by a FE model is justified by an example. It is demonstrated that the differential equation determines the damped frequencies and damping ratios with great accuracy. Significant damping ratios of the lowest torsional mode are obtained.

Many satellite-based estimates use gauge information for bias correction. In general, bias-correction methods are focused on the intensity error and do not explicitly correct possible position or timing errors. However, position and timing errors in rainfall estimates can also lead to errors in the rainfall occurrence or the intensity. This is especially true for localized rainfall events such as the convective rainstorms occurring during the rainy season in sub-Saharan Africa. We investigated the use of warping to correct such errors. The goal was to gauge-adjust satellite-based estimates with respect to the position and the timing of the rain event, instead of its intensity. Warping is a field-deformation method that transforms an image into another one. We compared two methods, spatial warping focusing on the position errors and time warping for the timing errors. They were evaluated on two case studies: a synthetic rainfall event represented by an ellipse and a rain event in southern Ghana during the monsoon season. In both cases, the two warping methods reduced significantly the respective targeted (position or timing) errors. In the southern Ghana case, the average position error was decreased by about 45 km by the spatial warping and the average timing error was decreased from more than 1 h to 0.2 h by the time warping. Both warping methods also improved the continuous statistics on the intensity: the correlation went from 0.18 to at least 0.62 after warping in the southern Ghana case. The spatial warping seems more interesting because of its positive impact on both position and timing errors.

A beam-like model is proposed to address nonlinear dynamic response of a thin pipe, under the action of a resonant transverse load. The mechanical model consists of a Timoshenko beam enriched with further kinematic and dynamic variables which, besides extension and bending, consistently describe local effects, related to ovalization and warping of the cross-section. The nonlinear equations of motions are derived via the principle of virtual work, and internal resonance between the global and local modes is addressed by the multiple scale method, after a Galerkin projection of the equations on the first significant modes. The softening behavior induced by the local deformation remarkably affects the asymptotic solution, which turns out to be in good agreement with that provided by numerical integration.

This article discusses the possibility of exploratory data analysis of samples described by second-order chromatographic data affected by peak shifts. In particular, the potential of the kernel Gram matrix representation as an alternative to the necessary and time-consuming alignment step is evaluated. It was demonstrated through several simulation studies and comparisons that even small peak shifts can be a substantial source of data variance, and they can easily hamper the interpretation of chromatographic data. When peak shifts are small, their negative effect is far more destructive than the impact of relatively large levels of the Gaussian noise, heteroscedastic noise, and signal&rsquo, s baseline. The Gram principal component analysis approach has proven to be a well-suited tool for exploratory analysis of chromatographic signals collected using the diode-array detector in which sample-to-sample peak shifts were observed.

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design. Web of Science 66 1 255 244

При изготовлении образца нервюры из полимерного композиционного материала (ПКМ) была выяв-лена проблема, которая заключается в избыточном короблении изделия. Т.е. после завершения формова-ния образца и остывания его до комнатной температуры можно было видеть большие деформации изделия, абсолютные значения которых достигали 1 мм и которые не совместимы с использованием из-делия по назначению. Причем выраженные деформации имели изгибные формы. Авторами данной рабо-ты при помощи численных методов, реализованных в ПО MSC/Natran, был проведен анализ причин из-быточных короблений нервюры и разработаны рекомендации к технологии изготовления для обеспече-ния допустимых деформаций при воздействии температурных нагрузок. Допустимые деформации, для данного изделия, составляют δ=0,5мм, When making a rib sample from a polymer composite material (PCM), a problem was identified, which consists in excessive warping of the product. I.e., after the sample was formed and cooled to room temperature, it was possible to see large deformations of the product, the absolute values of which reached 1 mm and which are not compatible with the use of the product for its intended purpose. Moreover, the pronounced deformations had bending forms. The authors of this work, using numerical methods implemented in the MSC/Natran software, analyzed the causes of excessive rib warping and developed recommendations for manufacturing technology to ensure minimal deformations under the influence of temperature loads.

This thesis proposes a numerical tool for the static and dynamic study of viscoelastic structures made of Functionally Graded Materials (FGM) for vibration control by passive damping. The objective is to make available to engineers a generic code based on the finite element approach for sizing calculations on FGM sandwich beam with viscoelastic core for applications requiring lightness and good thermal and mechanical resistance such as aerospace, automotive and nuclear. To reach this objective we first proposed a numerical model for the static and free vibration study of FGM sandwich beams with elastic behavior. This finite element model is implemented in the Matlab code environment. Using this code, we compare different beam theories for different geometric properties and boundary conditions. Thus, the limit of the classical beam theory in the study of short structures is highlighted. Also with this numerical model, the study of axial-bending and axial-rotation coupling is possible. From this, it is shown that FGM structures are very sensitive to spatial coupling and warping effects because of the non-symmetrical distribution of the material in their cross sections. In the proposed code, the resolution of the vibration problem is possible using classical eigenvalue and eigenvector problem solving methods. Then to introduce passive damping in the FGM sandwich structure, we proposed a sandwich beam model with FGM materials faces and viscoelastic materials core. This model is also implemented in the Matlab language and proposed as a generic tool. The interest of this numerical tool lies in its ability to compute the modal properties as well as the behavior of the viscoelastic FGM sandwich beam while taking into account the frequency dependence of the viscoelastic behavior, the boundary conditions and the axial-bending and axial-rotation coupling specific to FGM materials. The free vibration problem is non-linear in this case due to the material non-linearity induced by the soft layer. In the proposed code, the resolution of this problem is possible thanks to the coupling of the homotopy technical, the asymptotic numerical method and the automatic differentiation. Through this work, the contribution of FGM materials in the improvement of the damping power of structures is highlighted. In the continuation of the work, we propose a finite element formulation to compute the amplitude of forced vibrations of viscoelastic FGM sandwich structures. The resolution of the forced vibration problem is possible by using the bandwidths method. A study on the contribution of FGM materials in the reduction of vibration amplitudes is carried out for different viscoelastic laws. It is proved in this study that by a direct control of the composition gradient of FGM materials it is possible to optimize the damping power of structures even for low frequency modes for which classical composite materials have a damping power requiring improvement.; On propose par le biais de cette thèse un outil numérique pour l’étude statique et dynamique des structures viscoélastiques constituées de matériaux à gradient de propriétés (FGM) pour le contrôle des vibrations par amortissement passif. L’objectif est de mettre à la disposition des ingénieurs un code générique basé sur l’approche élément fini pour des calculs de dimensionnements sur des poutres sandwich FGM à âme viscoélastique destinées aux applications exigeant la légèreté et une bonne résistance thermique et mécanique comme le domaine de l’aérospatial, de l’automobile et du nucléaire. Pour atteindre cet objectif nous avons d’abord proposé un modèle numérique pour l’étude statique et des vibrations libres des poutres sandwich FGM à comportement élastique. Ce modèle élément fini est implémenté dans l’environnement du code Matlab. A l’aide de ce code nous comparons les différentes théories de poutre pour différentes configurations géométriques et différentes conditions aux limites. Ainsi, la limite de la théorie classique de poutre dans l’étude des structures courtes est soulignée. Aussi, avec ce modèle numérique, l’étude du couplage flexion membrane et rotation membrane est possible. De là, il est montré que les structures FGM sont très sensibles aux effets de couplages spatiaux et du gauchissement à cause de la répartition non symétrique de la matière dans leurs sections droites. Dans le code proposé, la résolution du problème de vibrations est possible grâce à des méthodes classiques de résolution des problèmes aux valeurs propres et vecteurs propres. Pour introduire de l’amortissement passif dans la structure sandwich FGM, nous avons proposé un modèle de poutre sandwich dont les faces sont en matériaux FGM et le cœur en matériaux viscoélastiques. Ce modèle est également implémenté dans le langage de programmation Matlab et proposé sous forme d’un outil générique. L’intérêt de cet outil numérique réside dans sa capacité à calculer les propriétés modales ainsi que le comportement de la structure sandwich FGM viscoélastique tout en prenant en compte la dépendance en fréquence du comportement viscoélastique, les conditions aux limites et le couplage membrane-flexion et membrane-rotation propres aux matériaux FGM. Le problème de vibrations libres est fortement non linéaire dans ce cas à cause de la non linéarité matériaux induite par la couche molle. Dans le code proposé, la résolution de ce problème est possible grâce au couplage de la technique d’homotopie, de la méthode asymptotique numérique et de la différentiation automatique. Par ce travail, l’apport des matériaux FGM dans l’amélioration du pouvoir amortissant des structures est démontré. Dans la suite du travail, nous proposons une formulation élément fini pour calculer l’amplitude des vibrations forcées des structures sandwich FGM viscoélastiques. La résolution du problème de vibration forcée est possible par utilisation de la méthode des bandes passantes. Une étude sur la contribution des matériaux FGM dans la réduction des amplitudes de vibrations est menée pour différentes lois viscoélastiques. Il est prouvé dans cette étude que par un contrôle direct du gradient de composition des matériaux FGM, il est possible d’optimiser le pouvoir amortissant des structures même pour les modes de basses fréquences pour lesquels les matériaux composites classiques présentent un pouvoir amortissant nécessitant des améliorations.

Дипломна робота: 51 с., 38 рис., 1 дод., 7 джерел. Об’єкт дослідження – програмні інструменти спеціалізованого програмного пакету Nuke та набір студійного візуального контенту для реалізації технології морфінгу зображень для цілей кіновиробництва. Метою роботи є аналіз програмних інструментів програми з цифрового композитингу для роботи статичними та динамічними зображеннями (відеороліки) задля проведення процедури морфінгу. Крім цього, необхідно визначити основні програмні підходи, які дозволяють провести операції з варпінгу та морфінгу зображень. У результаті виконання дипломної роботи були створені нодові схеми, які на основі підключення зображень з елементами комп’ютерної графіки та зображень, які отримано в студії, дозволяють виявити усі технічні нюанси роботи з реалізації процедури морфінгу зображень. Галузь застосування: кіновиробництво, цифровий композитинг, програми зі створення візуальних ефектів для кінофільмів. Thesis of bachelor’s: 51 p., 38 fig., 1 appendix, 7 refer. The object of research is the software tools of the specialized software package Nuke and a set of studio visual content for the implementation of image morphing technology for the purposes of film production. The aim of the work is to analyze the software tools of the digital compositing program for working with static and dynamic images (videos) for the morphing procedure. In addition, it is necessary to identify the basic software approaches that allow you to perform operations on warping and morphing images. As a result of the thesis, node schemes were created, which, based on the connection of images with elements of computer graphics and images obtained in the studio, allow to identify all the technical nuances of the implementation of the procedure of image morphing. Field of application: film production, digital compositing, programs for creating visual effects for movies.

Shrinkage and warping of additive manufacturing (AM) parts are two critical issues that adversely influence the dimensional accuracy especially in powder bed fusion processes such as selective laser sintering (SLS). Powder fusion, material solidification, and recrystallization are the key stages causing volumetric changes of polymeric materials during the abrupt heating&ndash, cooling process. In this work, the mechanisms of shrinkage and warping of semi-crystalline polyamide (PA) 12 in SLS are well investigated. Heat-transfer and thermo-mechanical models are established to predict the process-dependent shrinkage and warping. The influence of raw material- and laser-related parameters are considered in the heat-transfer and thermo-mechanical models. Such models are established considering the natural thermal gradient and dynamic recrystallization, which induce internal strain and volumetric change. Moreover, an experimental design via orthogonal approach is introduced to validate the feasibility and accuracy of the proposed models. Finally, the quantitative relationships of process parameters with product shrinkage and warping are established, the dimensional accuracy in part-scale can be well predicted and validated with printed parts in a real experiment.

Polyoxymethylene (POM) is one of the most popular thermoplastic polymers used in the industry. Therefore, the interest in its potential applications in rapid prototyping is understandable. Nevertheless, its low dimensional stability causes the warping of 3D prints, limiting its applications. This research aimed to evaluate the effects of POM modification with ethylene-vinyl acetate (EVA) (2.5, 5.0, and 7.5 wt.%) on its processing (by melt flow index), structure (by X-ray microcomputed tomography), and properties (by static tensile tests, surface resistance, contact angle measurements, differential scanning calorimetry, and thermogravimetric analysis), as well as very rarely analyzed emissions of volatile organic compounds (VOCs) (by headspace analysis). Performed modifications decreased stiffness and strength of the material, simultaneously enhancing its ductility, which simultaneously increased the toughness even by more than 50% for 7.5 wt.% EVA loading. Such an effect was related to an improved linear flow rate resulting in a lack of defects inside the samples. The decrease of the melting temperature and the slight increase of thermal stability after the addition of EVA broadened the processing window for 3D printing. The 3D printing trials on two different printers showed that the addition of EVA copolymer increased the possibility of a successful print without defects, giving space for further development.

Comparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

The paper gives an analysis and an assessment of the applicability of the most well-known grades of steels used for making large-sized case-hardening gears. It was found that increasing the hardness of the cemented tooth surface with simultaneous provision and preservation of its specified direction is a complex and important task in the creation of case-hardening gears. The features of the change in the dimensions of parts are studied depending on the degree of their nickel alloying. The use of a new material – steel 20KhN3MA – is proposed, which allows us to increase the strength, accuracy, reliability and life of large-sized gears. Of particular interest is the steel 20KhN3MA, as it is poorly deformed during technological alterations and in operation, it is used for large-sized gears of high-power reduction gear systems and for non-grinding cogwheels, first of all with a circular tooth. The material presented in this paper is of interest and can be useful for scientists and engineering services of the engineering industry.

This paper presents a finite element analysis of flexural-torsional and buckling behaviour of a thin- walled frame with a special focus on the joint warping behaviour. Four different joint types and two different cross-sections are analysed in order to investigate the influence of warping transmission on the overall behaviour of the structure. External loads are assumed to be static and conservative. The material is assumed to be homogenous, isotropic and linear elastic. The analysis is performed using the MSC Nastran shell model consisting of parabolic shell elements. The results obtained in the analysis together with some typical examples are discussed.

In the study of prismatic bars subjected to bending forces, the authors of Strength of Materials generally assume the Navier-Bernoulli simplifying hypothesis which states that flat cross sections (CS) normal to their axes before deformation remain flat and normal to their axes. A more detailed study in terms of Elasticity, however, shows how approximate this hypothesis can be for some basic prismatic bar problems in which displacements can readily be obtained. When or whether the surface remains flat, absolutely flat, or not is a point of debate among engineers and architects alike and even for structural specialists, who look deeper into this kind of issues. This paper proposes a detailed study of said problems and clarifies them. Contrary to what should be expected according to well-established literature, the CS of any bar subjected to pure bending forces does not remain flat after deformation. Our analysis revisits accepted displacement solutions for tension, bending and torque and will hopefully remove the misunderstanding leading to a flat geometry for the deformed CS. It also includes the correct interpretation of the warped geometry from the exact equations we obtain in this paper, which we illustrate with results from finite elastic models. En el estudio de las barras sometidas a flexión, la Resistencia de Materiales asume la hipótesis simplificadora de Navier-Bernoulli. Esta indica que secciones planas transversales (ST) al eje de la pieza antes de la deformación permanecen planas y normales al eje deformado tras ella. Un análisis más detallado en términos de la Elasticidad muestra el carácter aproximado de esta hipótesis para algunos problemas elementales de barras, en los cuales los movimientos se pueden obtener fácilmente. Esta discusión es conocida por arquitectos e ingenieros, pero en muchos casos no está claro, incluso para especialistas estructurales, en qué casos la ST permanece o no "exactamente" plana. El artículo discute los problemas citados y aclara la situación. Como conclusión inesperada se obtiene que, incluso en flexión pura, la ST no permanece plana tras deformarse, como se supone en tratados muy clásicos. El análisis se realiza a partir de soluciones de movimientos conocidas para tracción, flexión y torsión. La discusión aclara el malentendido que conduce a una geometría plana para la ST deformada e incluye la interpretación correcta de su geometría alabeada, a partir de las ecuaciones exactas obtenidas en este artículo e ilustradas con resultados de modelos de elementos finitos elásticos.

Because of the significance of electron microscope tomography in the investigation of biological structure at nanometer scales, ongoing improvement efforts have been continuous over recent years. This is particularly true in the case of software developments. Nevertheless, verification of improvements delivered by new algorithms and software remains difficult. Current analysis tools do not provide adaptable and consistent methods for quality assessment. This is particularly true with images of biological samples, due to image complexity, variability, low contrast and noise. We report an electron tomography (ET) simulator with accurate ray optics modeling of image formation that includes curvilinear trajectories through the sample, warping of the sample and noise. As a demonstration of the utility of our approach, we have concentrated on providing verification of the class of reconstruction methods applicable to wide field images of stained plastic-embedded samples. Accordingly, we have also constructed digital phantoms derived from serial block face scanning electron microscope images. These phantoms are also easily modified to include alignment features to test alignment algorithms. The combination of more realistic phantoms with more faithful simulations facilitates objective comparison of acquisition parameters, alignment and reconstruction algorithms and their range of applicability. With proper phantoms, this approach can also be modified to include more complex optical models, including distance-dependent blurring and phase contrast functions, such as may occur in cryotomography.

Freeform surfaces need to be discretized into manageable sized panels so that the surface can be fabricated in smaller pieces that are then assembled on site. This discretization process comprises numerous challenges; including not only the aesthetic and spatial concerns, but also the structural and constructional needs. The mesh generated has to fit to the surface, without distorting the form; meanwhile the panels have to preserve their planarity in order to prevent any brittle failure due to warping. This study proposes a unique approach to quadrilateral discretization by incorporating the form, material capacities and fabrication challenges in order to obtain a structure that can be realized and constructed. In this paper, quadrilateral discretization of freeform surfaces is studied with the focus of material properties. The possibility of utilizing quadrilateral meshes with limited non-planarity is explored. The capacity of materials against warping is calculated, by structural experiments and simulations to obtain the limiting values that are integrated into design as tolerance of panels to non-planarity. Consequently, the amount of non-planarity becomes a parameter that needs to be considered during the generation of the quadrilateral mesh in order to generate an optimum surface discretization.