A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

Kinematic description of the rupture from strong motion data: strategies for a robust inversion

We present a non linear technique to invert strong motion records with the aim of obtaining the final slip and rupture velocity distributions on the fault plane. In this thesis, the ground motion simulation is obtained evaluating the representation integral in the frequency. The Green’s tractions are computed using the discrete wave-number integration technique that provides the full wave-field in a 1D layered propagation medium. The representation integral is computed through a finite elements technique, based on a Delaunay’s triangulation on the fault plane. The rupture velocity is defined on a coarser regular grid and rupture times are computed by integration of the eikonal equation. For the inversion, the slip distribution is parameterized by 2D overlapping Gaussian functions, which can easily relate the spectrum of the possible solutions with the minimum resolvable wavelength, related to source-station distribution and data processing. The inverse problem is solved by a two-step procedure aimed at separating the computation of the rupture velocity from the evaluation of the slip distribution, the latter being a linear problem, when the rupture velocity is fixed. The non-linear step is solved by optimization of an L2 misfit function between synthetic and real seismograms, and solution is searched by the use of the Neighbourhood Algorithm. The conjugate gradient method is used to solve the linear step instead. The developed methodology has been applied to the M7.2, Iwate Nairiku Miyagi, Japan, earthquake. The estimated magnitude seismic moment is 2.6326 dyne∙cm that corresponds to a moment magnitude MW 6.9 while the mean the rupture velocity is 2.0 km/s. A large slip patch extends from the hypocenter to the southern shallow part of the fault plane. A second relatively large slip patch is found in the northern shallow part. Finally, we gave a quantitative estimation of errors associates with the parameters.

Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

Behaviour and applications of elastic waves in structures and metamaterials

The present thesis focuses on elastic waves behaviour in ordinary structures as well as in acousto-elastic metamaterials via numerical and experimental applications. After a brief introduction on the behaviour of elastic guided waves in the framework of non-destructive evaluation (NDE) and structural health monitoring (SHM) and on the study of elastic waves propagation in acousto-elastic metamaterials, dispersion curves for thin-walled beams and arbitrary cross-section waveguides are extracted via Semi-Analytical Finite Element (SAFE) methods. Thus, a novel strategy tackling signal dispersion to locate defects in irregular waveguides is proposed and numerically validated. Finally, a time-reversal and laser-vibrometry based procedure for impact location is numerically and experimentally tested. In the second part, an introduction and a brief review of the basic definitions necessary to describe acousto-elastic metamaterials is provided. A numerical approach to extract dispersion properties in such structures is highlighted. Afterwards, solid-solid and solid-fluid phononic systems are discussed via numerical applications. In particular, band structures and transmission power spectra are predicted for 1P-2D, 2P-2D and 2P-3D phononic systems. In addition, attenuation bands in the ultrasonic as well as in the sonic frequency regimes are experimentally investigated. In the experimental validation, PZTs in a pitch-catch configuration and laser vibrometric measurements are performed on a PVC phononic plate in the ultrasonic frequency range and sound insulation index is computed for a 2P-3D phononic barrier in the sonic frequency range. In both cases the numerical-experimental results comparison confirms the existence of the numerical predicted band-gaps. Finally, the feasibility of an innovative passive isolation strategy based on giant elastic metamaterials is numerically proved to be practical for civil structures. In particular, attenuation of seismic waves is demonstrated via finite elements analyses. Further, a parametric study shows that depending on the soil properties, such an earthquake-proof barrier could lead to significant reduction of the superstructure displacement.

Design and development of new pressure sensors for aerodynamic applications

This artwork reports on two different projects that were carried out during the three years of Doctor of the Philosophy course. In the first years a project regarding Capacitive Pressure Sensors Array for Aerodynamic Applications was developed in the Applied Aerodynamic research team of the Second Faculty of Engineering, University of Bologna, Forlì, Italy, and in collaboration with the ARCES laboratories of the same university. Capacitive pressure sensors were designed and fabricated, investigating theoretically and experimentally the sensor’s mechanical and electrical behaviours by means of finite elements method simulations and by means of wind tunnel tests. During the design phase, the sensor figures of merit are considered and evaluated for specific aerodynamic applications. The aim of this work is the production of low cost MEMS-alternative devices suitable for a sensor network to be implemented in air data system. The last two year was dedicated to a project regarding Wireless Pressure Sensor Network for Nautical Applications. Aim of the developed sensor network is to sense the weak pressure field acting on the sail plan of a full batten sail by means of instrumented battens, providing a real time differential pressure map over the entire sail surface. The wireless sensor network and the sensing unit were designed, fabricated and tested in the faculty laboratories. A static non-linear coupled mechanical-electrostatic simulation, has been developed to predict the pressure versus capacitance static characteristic suitable for the transduction process and to tune the geometry of the transducer to reach the required resolution, sensitivity and time response in the appropriate full scale pressure input A time dependent viscoelastic error model has been inferred and developed by means of experimental data in order to model, predict and reduce the inaccuracy bound due to the viscolelastic phenomena affecting the Mylar® polyester film used for the sensor diaphragm. The development of the two above mentioned subjects are strictly related but presently separately in this artwork.

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Evoluzione Morfotettonica delle Aree Alpine "Sempione" e "Brennero" attraverso Studi Termocronologici di bassa temperatura

E’ mostrata l’analisi e la modellazione di dati termocronologici di bassa temperatura da due regioni Alpine: il Sempione ed il Brennero. Le faglie distensive presenti bordano settori crostali profondi appartenenti al dominio penninico: il duomo metamorfico Lepontino al Sempione e la finestra dei Tauri al Brennero. I dati utilizzati sono FT e (U-Th)/He su apatite. Per il Sempione i dati provengono dalla bibliografia; per il Brennero si è provveduto ad un nuovo campionamento, sia in superficie che in sotterraneo. Gli attuali lavori per la galleria di base del Brennero (BBT), hanno consentito, per la prima volta, di raccogliere dati di FT e (U-Th)/He in apatite in sottosuolo per la finestra dei Tauri occidentale. Le analisi sono state effettuate tramite un codice a elementi finiti, Pecube, risolvente l’equazione di diffusione del calore per una topografia evolvente nel tempo. Il codice è stato modificato per tener conto dei dati sotterranei. L’inversione dei dati è stata effettuata usando il Neighbourhood Algorithm (NA), per ottenere il più plausibile scenario di evoluzione morfotettonico. I risultati ottenuti per il Sempione mostrano: ipotetica evoluzione dello stile tettonico della faglia del Sempione da rolling hinge a low angle detachment a 6.5 Ma e la cessazione dell’attività a 3 Ma; costruzione del rilievo fino a 5.5 Ma, smantellamento da 5.5 Ma ad oggi, in coincidenza dei cambiamenti climatici Messiniani e relativi all’inizio delle maggiori glaciazioni; incremento dell’esumazione da 0–0.6 mm/anno a 0.6–1.2 mm/anno a 2.4 Ma nell’emisfero settentrionale. I risultati al Brennero mostrano: maggiore attività tettonica della faglia del Brennero (1.3 mm/anno), maggiore attività esumativa (1–2 mm/anno) prima dei 10 Ma; crollo dell’attività della faglia del Brennero fra 10 Ma e oggi (0.1 mm/anno) e dell’attività esumativa nello stesso periodo (0.1–0.3 mm/anno); nessun aumento del tasso esumativo o variazioni topografiche negli ultimi 5 Ma.

Modelling the dynamic response of rockfall protection barriers

Mountainous areas are prone to natural hazards like rockfalls. Among the many countermeasures, rockfall protection barriers represent an effective solution to mitigate the risk. They are metallic structures designed to intercept rocks falling from unstable slopes, thus dissipating the energy deriving from the impact. This study aims at providing a better understanding of the response of several rockfall barrier types, through the development of rather sophisticated three-dimensional numerical finite elements models which take into account for the highly dynamic and non-linear conditions of such events. The models are built considering the actual geometrical and mechanical properties of real systems. Particular attention is given to the connecting details between the structural components and to their interactions. The importance of the work lies in being able to support a wide experimental activity with appropriate numerical modelling. The data of several full-scale tests carried out on barrier prototypes, as well as on their structural components, are combined with results of numerical simulations. Though the models are designed with relatively simple solutions in order to obtain a low computational cost of the simulations, they are able to reproduce with great accuracy the test results, thus validating the reliability of the numerical strategy proposed for the design of these structures. The developed models have shown to be readily applied to predict the barrier performance under different possible scenarios, by varying the initial configuration of the structures and/or of the impact conditions. Furthermore, the numerical models enable to optimize the design of these structures and to evaluate the benefit of possible solutions. Finally it is shown they can be also used as a valuable supporting tool for the operators within a rockfall risk assessment procedure, to gain crucial understanding of the performance of existing barriers in working conditions.

On Designing Compliant Actuators Based On Dielectric Elastomers

Dielectric Elastomers (DE) are incompressible dielectrics which can experience deviatoric (isochoric) finite deformations in response to applied large electric fields. Thanks to the strong electro-mechanical coupling, DE intrinsically offer great potentialities for conceiving novel solid-state mechatronic devices, in particular linear actuators, which are more integrated, lightweight, economic, silent, resilient and disposable than equivalent devices based on traditional technologies. Such systems may have a huge impact in applications where the traditional technology does not allow coping with the limits of weight or encumbrance, and with problems involving interaction with humans or unknown environments. Fields such as medicine, domotic, entertainment, aerospace and transportation may profit. For actuation usage, DE are typically shaped in thin films coated with compliant electrodes on both sides and piled one on the other to form a multilayered DE. DE-based Linear Actuators (DELA) are entirely constituted by polymeric materials and their overall performance is highly influenced by several interacting factors; firstly by the electromechanical properties of the film, secondly by the mechanical properties and geometry of the polymeric frame designed to support the film, and finally by the driving circuits and activation strategies. In the last decade, much effort has been focused in the devolvement of analytical and numerical models that could explain and predict the hyperelastic behavior of different types of DE materials. Nevertheless, at present, the use of DELA is limited. The main reasons are 1) the lack of quantitative and qualitative models of the actuator as a whole system 2) the lack of a simple and reliable design methodology. In this thesis, a new point of view in the study of DELA is presented which takes into account the interaction between the DE film and the film supporting frame. Hyperelastic models of the DE film are reported which are capable of modeling the DE and the compliant electrodes. The supporting frames are analyzed and designed as compliant mechanisms using pseudo-rigid body models and subsequent finite element analysis. A new design methodology is reported which optimize the actuator performances allowing to specifically choose its inherent stiffness. As a particular case, the methodology focuses on the design of constant force actuators. This class of actuators are an example of how the force control could be highly simplified. Three new DE actuator concepts are proposed which highlight the goodness of the proposed method.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.