Statistical finite element model for bone shape and biomechanical properties

We present a framework for statistical finite element analysis combining shape and material properties, and allowing performing statistical statements of biomechanical performance across a given population. In this paper, we focus on the design of orthopaedic implants that fit a maximum percentage of the target population, both in terms of geometry and biomechanical stability. CT scans of the bone under consideration are registered non-rigidly to obtain correspondences in position and intensity between them. A statistical model of shape and intensity (bone density) is computed by means of principal component analysis. Afterwards, finite element analysis (FEA) is performed to analyse the biomechanical performance of the bones. Realistic forces are applied on the bones and the resulting displacement and bone stress distribution are calculated. The mechanical behaviour of different PCA bone instances is compared.

MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro

Purpose Femoral fracture is a common medical problem in osteoporotic individuals. Bone mineral density (BMD) is the gold standard measure to evaluate fracture risk in vivo. Quantitative computed tomography (QCT)-based homogenized voxel finite element (hvFE) models have been proved to be more accurate predictors of femoral strength than BMD by adding geometrical and material properties. The aim of this study was to evaluate the ability of hvFE models in predicting femoral stiffness, strength and failure location for a large number of pairs of human femora tested in two different loading scenarios. Methods Thirty-six pairs of femora were scanned with QCT and total proximal BMD and BMC were evaluated. For each pair, one femur was positioned in one-legged stance configuration (STANCE) and the other in a sideways configuration (SIDE). Nonlinear hvFE models were generated from QCT images by reproducing the same loading configurations imposed in the experiments. For experiments and models, the structural properties (stiffness and ultimate load), the failure location and the motion of the femoral head were computed and compared. Results In both configurations, hvFE models predicted both stiffness (R2=0.82 for STANCE and R2=0.74 for SIDE) and femoral ultimate load (R2=0.80 for STANCE and R2=0.85 for SIDE) better than BMD and BMC. Moreover, the models predicted qualitatively well the failure location (66% of cases) and the motion of the femoral head. Conclusions The subject specific QCT-based nonlinear hvFE model cannot only predict femoral apparent mechanical properties better than densitometric measures, but can additionally provide useful qualitative information about failure location.

Results of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

The characteristics of a global set-up of the Finite-Element Sea-Ice Ocean Model under forcing of the period 1958-2004 are presented. The model set-up is designed to study the variability in the deep-water mass formation areas and was therefore regionally better resolved in the deep-water formation areas in the Labrador Sea, Greenland Sea, Weddell Sea and Ross Sea. The sea-ice model reproduces realistic sea-ice distributions and variabilities in the sea-ice extent of both hemispheres as well as sea-ice transport that compares well with observational data. Based on a comparison between model and ocean weather ship data in the North Atlantic, we observe that the vertical structure is well captured in areas with a high resolution. In our model set-up, we are able to simulate decadal ocean variability including several salinity anomaly events and corresponding fingerprint in the vertical hydrography. The ocean state of the model set-up features pronounced variability in the Atlantic Meridional Overturning Circulation as well as the associated mixed layer depth pattern in the North Atlantic deep-water formation areas.

A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail.

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.

A gradient-enhanced continuum damage model with application to fibre-reinforced tissues at finite strains

A non-local gradient-based damage formulation within a geometrically non-linear set- ting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy function which is additively composed by an isotropic neo-Hookean matrix and by an anisotropic fibre-reinforced material based on the model proposed by T. Gasser, R. Ogden, and G. Holzapfel.

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.

Particle swarm optimization with sequential niche technique for dynamic finite element model updating

Peer reviewed

Approximate solution for frequency synchronization in a finite-size Kuramoto model

Peer reviewed

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

A finite element model of perforated panel absorbers including viscothermal effects

Most of the analytical models devoted to determine the acoustic properties of a rigid perforated panel consider the acoustic impedance of a single hole and then use the porosity to determine the impedance for the whole panel. However, in the case of not homogeneous hole distribution or more complex configurations this approach is no longer valid. This work explores some of these limitations and proposes a finite element methodology that implements the linearized Navier Stokes equations in the frequency domain to analyse the acoustic performance under normal incidence of perforated panel absorbers. Some preliminary results for a homogenous perforated panel show that the sound absorption coefficient derived from the Maa analytical model does not match those from the simulations. These differences are mainly attributed to the finite geometry effect and to the spatial distribution of the perforations for the numerical case. In order to confirm these statements, the acoustic field in the vicinities of the perforations is analysed for a more complex configuration of perforated panel. Additionally, experimental studies are carried out in an impedance tube for the same configuration and then compared to previous methods. The proposed methodology is shown to be in better agreement with the laboratorial measurements than the analytical approach.