Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Loudness scattering due to vibro-acoustic model variability

The use of numerical simulation in the design and evaluation of products performance is ever increasing. To a greater extent, such estimates are needed in a early design stage, when physical prototypes are not available. When dealing with vibro-acoustic models, known to be computationally expensive, a question remains, which is related to the accuracy of such models in view of the well-know variability inherent to the mass manufacturing production techniques. In addition, both academia and industry have recently realized the importance of actually listening to a products sound, either by measurements or by virtual sound synthesis, in order to assess its performance. In this work, the scatter of significant parameter variations on a simplified vehicle vibro-acoustic model is calculated on loudness metrics using Monte Carlo analysis. The mapping from the system parameters to sound quality metric is performed by a fully-coupled vibro-acoustic finite element model. Different loudness metrics are used, including overall sound pressure level expressed in dB and Specific Loudness in Sones. Sound quality equivalent sources are used to excite this model and the sound pressure level at the driver's head position is acquired to be evaluated according to sound quality metrics. No significant variation has been perceived when evaluating the system using regular sound pressure level expressed in in dB and dB(A). This happens because of the third-octave filters that averages the results under some frequency bands. On the other hand, Zwicker Loudness presents important variations, arguably, due to the masking effects.

Structural stability of flexible lines in catenary configuration under torsion

Catenary risers can present during installation a very low tension close to seabed, which combined with torsion moment can lead to a structural instability, resulting in a loop. This is undesirable once it is possible that the loop turns into a kink, creating damage. This work presents a numerical methodology to analyze the conditions of loop formation in catenary risers. Stability criteria were applied to finite element models, including geometric nonlinearities and contact constraint due to riser-seabed interaction. The classical Greenhill's formula was used to predict the phenomenon and parametric analysis shows a “universal plot” able to predict instability in catenaries using a simple equation that can be applied for typical risers installation conditions and, generically, for catenary lines under torsion.

Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Numerical analysis of Dielectric Barrier Discharge

A numerical investigation of dielectric barrier discharge aimed to simulate the electro hydro dynamic interaction is presented. A discharge drift diffusive model according to the Townsend avalanche is described and used to duplicate the plasma kinetics of a DBD actuator. The discharge characteristics dependence upon dielectric material and applied voltage are simulated and the EHD force field according to a simplified approach is presented and discussed. The coupling of DBD results with a fluid dynamic code is also shown. Finally, a new non invasive diagnostic technique for EHD interaction based on Schlieren imaging is computationally validated.

Micro-FEM models based on micro-CT reconstructions for the in vitro characterization of the elastic properties of trabecular bone tissue.

This master’s thesis describes the research done at the Medical Technology Laboratory (LTM) of the Rizzoli Orthopedic Institute (IOR, Bologna, Italy), which focused on the characterization of the elastic properties of the trabecular bone tissue, starting from october 2012 to present. The approach uses computed microtomography to characterize the architecture of trabecular bone specimens. With the information obtained from the scanner, specimen-specific models of trabecular bone are generated for the solution with the Finite Element Method (FEM). Along with the FEM modelling, mechanical tests are performed over the same reconstructed bone portions. From the linear-elastic stage of mechanical tests presented by experimental results, it is possible to estimate the mechanical properties of the trabecular bone tissue. After a brief introduction on the biomechanics of the trabecular bone (chapter 1) and on the characterization of the mechanics of its tissue using FEM models (chapter 2), the reliability analysis of an experimental procedure is explained (chapter 3), based on the high-scalable numerical solver ParFE. In chapter 4, the sensitivity analyses on two different parameters for micro-FEM model’s reconstruction are presented. Once the reliability of the modeling strategy has been shown, a recent layout for experimental test, developed in LTM, is presented (chapter 5). Moreover, the results of the application of the new layout are discussed, with a stress on the difficulties connected to it and observed during the tests. Finally, a prototype experimental layout for the measure of deformations in trabecular bone specimens is presented (chapter 6). This procedure is based on the Digital Image Correlation method and is currently under development in LTM.

Detecting interfaces in a parabolic-elliptic problem from surface measurements

Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we develop an adaptation of the factorization method to this time-dependent problem. In particular this shows that the locations of the interfaces are uniquely determined by boundary measurements. The method also yields to a numerical algorithm to recover the inclusions and thus the interfaces. We demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method, and finally we present some numerical results for the inverse problem.

Experimental and Numerical Analysis of Gas Forced Convection through Microtubes and Micro Heat Exchangers

The last decade has witnessed very fast development in microfabrication technologies. The increasing industrial applications of microfluidic systems call for more intensive and systematic knowledge on this newly emerging field. Especially for gaseous flow and heat transfer at microscale, the applicability of conventional theories developed at macro scale is not yet completely validated; this is mainly due to scarce experimental data available in literature for gas flows. The objective of this thesis is to investigate these unclear elements by analyzing forced convection for gaseous flows through microtubes and micro heat exchangers. Experimental tests have been performed with microtubes having various inner diameters, namely 750 m, 510 m and 170 m, over a wide range of Reynolds number covering the laminar region, the transitional zone and also the onset region of the turbulent regime. The results show that conventional theory is able to predict the flow friction factor when flow compressibility does not appear and the effect of fluid temperature-dependent properties is insignificant. A double-layered microchannel heat exchanger has been designed in order to study experimentally the efficiency of a gas-to-gas micro heat exchanger. This microdevice contains 133 parallel microchannels machined into polished PEEK plates for both the hot side and the cold side. The microchannels are 200 µm high, 200 µm wide and 39.8 mm long. The design of the micro device has been made in order to be able to test different materials as partition foil with flexible thickness. Experimental tests have been carried out for five different partition foils, with various mass flow rates and flow configurations. The experimental results indicate that the thermal performance of the countercurrent and cross flow micro heat exchanger can be strongly influenced by axial conduction in the partition foil separating the hot gas flow and cold gas flow.

Finite element modeling of the cement-bone interface beneath the tibial tray of a total knee arthroplasty: Study of the stress shielding effect (modellazione agli elementi finiti dell'interfaccia cemento-osso sotto il piatto tibiale di protesi totale di ginocchio: Analisi dello stress shielding)

The goal of this thesis was the study of the cement-bone interface in the tibial component of a cemented total knee prosthesis. One of the things you can see in specimens after in vivo service is that resorption of bone occurs in the interdigitated region between bone and cement. A stress shielding effect was investigated as a cause to explain bone resorption. Stress shielding occurs when bone is loaded less than physiological and therefore it starts remodeling according to the new loading conditions. µCT images were used to obtain 3D models of the bone and cement structure and a Finite Element Analysis was used to simulate different kind of loads. Resorption was also simulated by performing erosion operations in the interdigitated bone region. Finally, 4 models were simulated: bone (trabecular), bone with cement, and two models of bone with cement after progressive erosions of the bone. Compression, tension and shear test were simulated for each model in displacement-control until 2% of strain. The results show how the principal strain and Von Mises stress decrease after adding the cement on the structure and after the erosion operations. These results show that a stress shielding effect does occur and rises after resorption starts.

"Offshore tower or platform foundations: numerical analysis of a laterally loaded single pile or pile group in soft clay and analysis of actions on a jacket structure"

Laterally loaded piles are a typical situation for a large number of cases in which deep foundations are used. Dissertation herein reported, is a focus upon the numerical simulation of laterally loaded piles. In the first chapter the best model settings are largely discussed, so a clear idea about the effects of interface adoption, model dimension, refinement cluster and mesh coarseness is reached. At a second stage, there are three distinct parametric analyses, in which the model response sensibility is studied for variation of interface reduction factor, Eps50 and tensile cut-off. In addition, the adoption of an advanced soil model is analysed (NGI-ADP). This was done in order to use the complex behaviour (different undrained shear strengths are involved) that governs the resisting process of clay under short time static loads. Once set a definitive model, a series of analyses has been carried out with the objective of defining the resistance-deflection (P-y) curves for Plaxis3D (2013) data. Major results of a large number of comparisons made with curves from API (America Petroleum Institute) recommendation are that the empirical curves have almost the same ultimate resistance but a bigger initial stiffness. In the second part of the thesis a simplified structural preliminary design of a jacket structure has been carried out to evaluate the environmental forces that act on it and on its piles foundation. Finally, pile lateral response is studied using the empirical curves.

Hydrodynamic induced by an array of wave energy converters. Experimental and numerical analysis

The thesis analyses the hydrodynamic induced by an array of Wave energy Converters (WECs), under an experimental and numerical point of view. WECs can be considered an innovative solution able to contribute to the green energy supply and –at the same time– to protect the rear coastal area under marine spatial planning considerations. This research activity essentially rises due to this combined concept. The WEC under exam is a floating device belonging to the Wave Activated Bodies (WAB) class. Experimental data were performed at Aalborg University in different scales and layouts, and the performance of the models was analysed under a variety of irregular wave attacks. The numerical simulations performed with the codes MIKE 21 BW and ANSYS-AQWA. Experimental results were also used to calibrate the numerical parameters and/or to directly been compared to numerical results, in order to extend the experimental database. Results of the research activity are summarized in terms of device performance and guidelines for a future wave farm installation. The device length should be “tuned” based on the local climate conditions. The wave transmission behind the devices is pretty high, suggesting that the tested layout should be considered as a module of a wave farm installation. Indications on the minimum inter-distance among the devices are provided. Furthermore, a CALM mooring system leads to lower wave transmission and also larger power production than a spread mooring. The two numerical codes have different potentialities. The hydrodynamics around single and multiple devices is obtained with MIKE 21 BW, while wave loads and motions for a single moored device are derived from ANSYS-AQWA. Combining the experimental and numerical it is suggested –for both coastal protection and energy production– to adopt a staggered layout, which will maximise the devices density and minimize the marine space required for the installation.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Influence of Smoothing on Voxel-Based Mesh Accuracy in Micro-Finite Element

The interest in automatic volume meshing for finite element analysis (FEA) has grown more since the appearance of microfocus CT (μCT), due to its high resolution, which allows for the assessment of mechanical behaviour at a high precision. Nevertheless, the basic meshing approach of generating one hexahedron per voxel produces jagged edges. To prevent this effect, smoothing algorithms have been introduced to enhance the topology of the mesh. However, whether smoothing also improves the accuracy of voxel-based meshes in clinical applications is still under question. There is a trade-off between smoothing and quality of elements in the mesh. Distorted elements may be produced by excessive smoothing and reduce accuracy of the mesh. In the present work, influence of smoothing on the accuracy of voxel-based meshes in micro-FE was assessed. An accurate 3D model of a trabecular structure with known apparent mechanical properties was used as a reference model. Virtual CT scans of this reference model (with resolutions of 16, 32 and 64 μm) were then created and used to build voxel-based meshes of the microarchitecture. Effects of smoothing on the apparent mechanical properties of the voxel-based meshes as compared to the reference model were evaluated. Apparent Young’s moduli of the smooth voxel-based mesh were significantly closer to those of the reference model for the 16 and 32 μm resolutions. Improvements were not significant for the 64 μm, due to loss of trabecular connectivity in the model. This study shows that smoothing offers a real benefit to voxel-based meshes used in micro-FE. It might also broaden voxel-based meshing to other biomechanical domains where it was not used previously due to lack of accuracy. As an example, this work will be used in the framework of the European project ContraCancrum, which aims at providing a patient-specific simulation of tumour development in brain and lungs for oncologists. For this type of clinical application, such a fast, automatic, and accurate generation of the mesh is of great benefit.