Prediction of bendig load capacity of timber beams by finite element method simulation of knots and grain deviation

A finite element model was used to simulate timberbeams with defects and predict their maximum load in bending. Taking into account the elastoplastic constitutive law of timber, the prediction of fracture load gives information about the mechanisms of timber failure, particularly with regard to the influence of knots, and their local graindeviation, on the fracture. A finite element model was constructed using the ANSYS element Plane42 in a plane stress 2D-analysis, which equates thickness to the width of the section to create a mesh which is as uniform as possible. Three sub-models reproduced the bending test according to UNE EN 408: i) timber with holes caused by knots; ii) timber with adherent knots which have structural continuity with the rest of the beam material; iii) timber with knots but with only partial contact between knot and beam which was artificially simulated by means of contact springs between the two materials. The model was validated using ten 45 × 145 × 3000 mm beams of Pinus sylvestris L. which presented knots and graindeviation. The fracture stress data obtained was compared with the results of numerical simulations, resulting in an adjustment error less of than 9.7%

Goal-oriented self-adaptive hp-strategies for finite element analysis of electromagnetic scattering and radiation problems

In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an user-prescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

Analysis of the stress state of a halved and tabled traditional timber scarf joint with the Finite Element Method

The purpose of this study is to determine the stress distribution in the carpentry joint of halved and tabled scarf joint with the finite element method (FEM) and its comparison with the values obtained using the theory of Strength of Materials. The stress concentration areas where analyzed and the influence of mesh refinement was studied on the results in order to determine the mesh size that provides the stress values more consistent with the theory. In areas where stress concentration is lower, different mesh sizes show similar stress values. In areas where stress concentration occurs, the same values increase considerably with the refinement of the mesh. The results show a central symmetry of the isobar lines distribution where the centre of symmetry corresponds to the geometric centre of the joint. Comparison of normal stress levels obtained by the FEM and the classical theory shows small differences, except at points of stress concentration.

Finite Element Analysis Model of a Contactless Transformer for Battery Chargers in Electric Vehicles

A contactless transformer model is proposed in this paper using Finite Element Analysis (FEA). This model can be used to simulate Inductive Coupling Power Transfer (ICPT) systems with good accuracy of the transformer and reduce the fabrication time of these systems. The model not only takes into account the geometry of the windings but also the frequency effects in them. As the transformer does not have a magnetic core, it is complicated to model because the flux is expanded in the area around the windings. In order to obtain a very accurate model, it is necessary to use a 2D/3D field solver.

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry.

Finite element simulation of sandwich panels of laminated plaster and rockwool under mixed mode fracture

Sandwich panels of laminated gypsum and rock wool have shown large pathology of cracking due to excessive slabs deflection. Currently the most widespread use of this material is as vertical elements of division or partition, with no structural function, what justifies that there are no studies on the mechanism of fracture and mechanical properties related to it. Therefore, and in order to reduce the cracking problem, it is necessary to progress in the simulation and prediction of the behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability.

Finite element simulation of sandwich panels of plasterboard and rock wool under mixed mode fracture

This paper presents the results of research on mixed mode fracture of sandwich panels of plasterboard and rock wool. The experimental data of the performed tests are supplied. The specimens were made from commercial panels. Asymmetrical three-point bending tests were performed on notched specimens. Three sizes of geometrically similar specimens were tested for studying the size effect. The paper also includes the numerical simulation of the experimental results by using an embedded cohesive crack model.The involved parameters for modelling are previously measured by standardised tests.

Generación de modelos físicos personalizados y segmentación de la pared arterial y el trombo intraluminal en imágenes de aneurismas aórticos abdominales

Esta tesis doctoral está encuadrada dentro del marco general de la ingeniería biomédica aplicada al tratamiento de las enfermedades cardiovasculares, enfermedades que provocan alrededor de 1.9 millones (40%) de muertes al año en la Unión Europea. En este contexto surge el proyecto europeo SCATh-Smart Catheterization, cuyo objetivo principal es mejorar los procedimientos de cateterismo aórtico introduciendo nuevas tecnologías de planificación y navegación quirúrgica y minimizando el uso de fluoroscopía. En particular, esta tesis aborda el modelado y diagnóstico de aneurismas aórticos abdominales (AAA) y del trombo intraluminal (TIL), allí donde esté presente, así como la segmentación de estas estructuras en imágenes preoperatorias de RM. Los modelos físicos específicos del paciente, construidos a partir de imágenes médicas preoperatorias, tienen múltiples usos, que van desde la evaluación preoperatoria de estructuras anatómicas a la planificación quirúrgica para el guiado de catéteres. En el diagnóstico y tratamiento de AAA, los modelos físicos son útiles a la hora de evaluar diversas variables biomecánicas y fisiológicas de las estructuras vasculares. Existen múltiples técnicas que requieren de la generación de modelos físicos que representen la anatomía vascular. Una de las principales aplicaciones de los modelos físicos es el análisis de elementos finitos (FE). Las simulaciones de FE para AAA pueden ser específicas para el paciente y permiten modelar estados de estrés complejos, incluyendo los efectos provocados por el TIL. La aplicación de métodos numéricos de análisis tiene como requisito previo la generación de una malla computacional que representa la geometría de interés mediante un conjunto de elementos poliédricos, siendo los hexaédricos los que presentan mejores resultados. En las estructuras vasculares, generar mallas hexaédricas es un proceso especialmente exigente debido a la compleja anatomía 3D ramificada. La mayoría de los AAA se encuentran situados en la bifurcación de la arteria aorta en las arterias iliacas y es necesario modelar de manera fiel dicha bifurcación. En el caso de que la sangre se estanque en el aneurisma provocando un TIL, éste forma una estructura adyacente a la pared aórtica. De este modo, el contorno externo del TIL es el mismo que el contorno interno de la pared, por lo que las mallas resultantes deben reflejar esta particularidad, lo que se denomina como "mallas conformadas". El fin último de este trabajo es modelar las estructuras vasculares de modo que proporcionen nuevas herramientas para un mejor diagnóstico clínico, facilitando medidas de riesgo de rotura de la arteria, presión sistólica o diastólica, etc. Por tanto, el primer objetivo de esta tesis es diseñar un método novedoso y robusto para generar mallas hexaédricas tanto de la pared aórtica como del trombo. Para la identificación de estas estructuras se utilizan imágenes de resonancia magnética (RM). Deben mantenerse sus propiedades de adyacencia utilizando elementos de alta calidad, prestando especial atención al modelado de la bifurcación y a que sean adecuadas para el análisis de FE. El método tiene en cuenta la evolución de la línea central del vaso en el espacio tridimensional y genera la malla directamente a partir de las imágenes segmentadas, sin necesidad de reconstruir superficies triangulares. Con el fin de reducir la intervención del usuario en el proceso de generación de las mallas, es también objetivo de esta tesis desarrollar un método de segmentación semiautomática de las distintas estructuras de interés. Las principales contribuciones de esta tesis doctoral son: 1. El diseño, implementación y evaluación de un algoritmo de generación de mallas hexaédricas conformadas de la pared y el TIL a partir de los contornos segmentados en imágenes de RM. Se ha llevado a cabo una evaluación de calidad que determine su aplicabilidad a métodos de FE. Los resultados demuestran que el algoritmo desarrollado genera mallas conformadas de alta calidad incluso en la región de la bifurcación, que son adecuadas para su uso en métodos de análisis de FE. 2. El diseño, implementación y evaluación de un método de segmentación automático de las estructuras de interés. La luz arterial se segmenta de manera semiautomática utilizando un software disponible a partir de imágenes de RM con contraste. Los resultados de este proceso sirven de inicialización para la segmentación automática de las caras interna y externa de la pared aórtica utilizando métodos basado en modelos de textura y forma a partir de imágenes de RM sin contraste. Los resultados demuestran que el algoritmo desarrollado proporciona segmentaciones fieles de las distintas estructuras de interés. En conclusión, el trabajo realizado en esta tesis doctoral corrobora las hipótesis de investigación postuladas, y pretende servir como aportación para futuros avances en la generación de modelos físicos de geometrías biológicas. ABSTRACT The frame of this PhD Thesis is the biomedical engineering applied to the treatment of cardiovascular diseases, which cause around 1.9 million deaths per year in the European Union and suppose about 40% of deaths per year. In this context appears the European project SCATh-Smart Catheterization. The main objective of this project is creating a platform which improves the navigation of catheters in aortic catheterization minimizing the use of fluoroscopy. In the framework of this project, the specific field of this PhD Thesis is the diagnosis and modeling of abdominal aortic aneurysm (AAAs) and the intraluminal thrombus (ILT) whenever it is present. Patient-specific physical models built from preoperative imaging are becoming increasingly important in the area of minimally invasive surgery. These models can be employed for different purposes, such as the preoperatory evaluation of anatomic structures or the surgical planning for catheter guidance. In the specific case of AAA diagnosis and treatment, physical models are especially useful for evaluating pressures over vascular structures. There are multiple techniques that require the generation of physical models which represent the target anatomy. Finite element (FE) analysis is one the principal applications for physical models. FE simulations for AAA may be patient-specific and allow modeling biomechanical and physiological variables including those produced by ILT, and also the segmentation of those anatomical structures in preoperative MR images. Applying numeric methods requires the generation of a proper computational mesh. These meshes represent the patient anatomy using a set of polyhedral elements, with hexahedral elements providing better results. In the specific case of vascular structures, generating hexahedral meshes is a challenging task due to the complex 3D branching anatomy. Each patient’s aneurysm is unique, characterized by its location and shape, and must be accurately represented for subsequent analyses to be meaningful. Most AAAs are located in the region where the aorta bifurcates into the iliac arteries and it is necessary to model this bifurcation precisely and reliably. If blood stagnates in the aneurysm and forms an ILT, it exists as a conforming structure with the aortic wall, i.e. the ILT’s outer contour is the same as the wall’s inner contour. Therefore, resulting meshes must also be conforming. The main objective of this PhD Thesis is designing a novel and robust method for generating conforming hexahedral meshes for the aortic wall and the thrombus. These meshes are built using largely high-quality elements, especially at the bifurcation, that are suitable for FE analysis of tissue stresses. The method accounts for the evolution of the vessel’s centerline which may develop outside a single plane, and generates the mesh directly from segmented images without the requirement to reconstruct triangular surfaces. In order to reduce the user intervention in the mesh generation process is also a goal of this PhD. Thesis to develop a semiautomatic segmentation method for the structures of interest. The segmentation is performed from magnetic resonance image (MRI) sequences that have tuned to provide high contrast for the arterial tissue against the surrounding soft tissue, so that we determine the required information reliably. The main contributions of this PhD Thesis are: 1. The design, implementation and evaluation of an algorithm for generating hexahedral conforming meshes of the arterial wall and the ILT from the segmented contours. A quality inspection has been applied to the meshes in order to determine their suitability for FE methods. Results show that the developed algorithm generates high quality conforming hexahedral meshes even at the bifurcation region. Thus, these meshes are suitable for FE analysis. 2. The design, implementation and evaluation of a semiautomatic segmentation method for the structures of interest. The lumen is segmented in a semiautomatic way from contrast filled MRI using an available software. The results obtained from this process are used to initialize the automatic segmentation of the internal and external faces of the aortic wall. These segmentations are performed by methods based on texture and shape models from MRI with no contrast. The results show that the algorithm provides faithful segmentations of the structures of interest requiring minimal user intervention. In conclusion, the work undertaken in this PhD. Thesis verifies the investigation hypotheses. It intends to serve as basis for future physical model generation of proper biological anatomies used by numerical methods.

An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented

Some consistent finite element formulations of 1-D beam models: a comparative study

A consistent Finite Element formulation was developed for four classical 1-D beam models. This formulation is based upon the solution of the homogeneous differential equation (or equations) associated with each model. Results such as the shape functions, stiffness matrices and consistent force vectors for the constant section beam were found. Some of these results were compared with the corresponding ones obtained by the standard Finite Element Method (i.e. using polynomial expansions for the field variables). Some of the difficulties reported in the literature concerning some of these models may be avoided by this technique and some numerical sensitivity analysis on this subject are presented.

Finite element code-based modeling of a multi-feature isolation system and passive alleviation of possible inner pounding

The existing seismic isolation systems are based on well-known and accepted physical principles, but they are still having some functional drawbacks. As an attempt of improvement, the Roll-N-Cage (RNC) isolator has been recently proposed. It is designed to achieve a balance in controlling isolator displacement demands and structural accelerations. It provides in a single unit all the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, resistance to low service loads and minor vibration, and hysteretic energy dissipation characteristics. It is characterized by two unique features that are a self-braking (buffer) and a self-recentering mechanism. This paper presents an advanced representation of the main and unique features of the RNC isolator using an available finite element code called SAP2000. The validity of the obtained SAP2000 model is then checked using experimental, numerical and analytical results. Then, the paper investigates the merits and demerits of activating the built-in buffer mechanism on both structural pounding mitigation and isolation efficiency. The paper addresses the problem of passive alleviation of possible inner pounding within the RNC isolator, which may arise due to the activation of its self-braking mechanism under sever excitations such as near-fault earthquakes. The results show that the obtained finite element code-based model can closely match and accurately predict the overall behavior of the RNC isolator with effectively small errors. Moreover, the inherent buffer mechanism of the RNC isolator could mitigate or even eliminate direct structure-tostructure pounding under severe excitation considering limited septation gaps between adjacent structures. In addition, the increase of inherent hysteretic damping of the RNC isolator can efficiently limit its peak displacement together with the severity of the possibly developed inner pounding and, therefore, alleviate or even eliminate the possibly arising negative effects of the buffer mechanism on the overall RNC-isolated structural responses.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.