Application of the Boundary Method to the determination of the properties of the beam cross-sections

Using the 3-D equations of linear elasticity and the asylllptotic expansion methods in terms of powers of the beam cross-section area as small parameter different beam theories can be obtained, according to the last term kept in the expansion. If it is used only the first two terms of the asymptotic expansion the classical beam theories can be recovered without resort to any "a priori" additional hypotheses. Moreover, some small corrections and extensions of the classical beam theories can be found and also there exists the possibility to use the asymptotic general beam theory as a basis procedure for a straightforward derivation of the stiffness matrix and the equivalent nodal forces of the beam. In order to obtain the above results a set of functions and constants only dependent on the cross-section of the beam it has to be computed them as solutions of different 2-D laplacian boundary value problems over the beam cross section domain. In this paper two main numerical procedures to solve these boundary value pf'oblems have been discussed, namely the Boundary Element Method (BEM) and the Finite Element Method (FEM). Results for some regular and geometrically simple cross-sections are presented and compared with ones computed analytically. Extensions to other arbitrary cross-sections are illustrated.

Método multigrid algébrico: reutilização das estruturas multigrid no transporte de contaminantes

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas.

Advanced interpretation of subsidence in Murcia (SE Spain) using A-DInSAR data – modelling and validation

Subsidence is a natural hazard that affects wide areas in the world causing important economic costs annually. This phenomenon has occurred in the metropolitan area of Murcia City (SE Spain) as a result of groundwater overexploitation. In this work aquifer system subsidence is investigated using an advanced differential SAR interferometry remote sensing technique (A-DInSAR) called Stable Point Network (SPN). The SPN derived displacement results, mainly the velocity displacement maps and the time series of the displacement, reveal that in the period 2004–2008 the rate of subsidence in Murcia metropolitan area doubled with respect to the previous period from 1995 to 2005. The acceleration of the deformation phenomenon is explained by the drought period started in 2006. The comparison of the temporal evolution of the displacements measured with the extensometers and the SPN technique shows an average absolute error of 3.9±3.8 mm. Finally, results from a finite element model developed to simulate the recorded time history subsidence from known water table height changes compares well with the SPN displacement time series estimations. This result demonstrates the potential of A-DInSAR techniques to validate subsidence prediction models as an alternative to using instrumental ground based techniques for validation.

Finite elements in structural analysis : a bibliography with abstracts.

Mode of access: Internet.

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.

Focused, eight-element transceive phased array coil for parallel magnetic resonance imaging of the chest-theoretical considerations

A new transceive system for chest imaging for MRI applications is presented. A focused, eight-element transceive torso phased array coil is designed to investigate transmitting a focused radiofrequency field deep within the torso and to enhance signal homogeneity in the heart region. The system is used in conjunction with the SENSE reconstruction technique to enable focused parallel imaging. A hybrid finite-difference-time-domain/method-of-moments method is used to accurately predict the radiofrequency behavior inside the human torso. The simulation results reported herein demonstrate the feasibility of the design concept, which shows that radiofrequency field focusing with SENSE reconstruction is theoretically achievable. (c) 2005 Wiley-Liss, Inc.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Evaluation of parameters effective in FRP shear strengthening of RC beams using FE method

Shear strengthening is required when an RC beam is found deficient in shear, or when its shear capacity falls below its flexural capacity after flexural strengthening. A recent technique for the shear strengthening of RC beams is to provide additional FRP web reinforcement, commonly in the form of bonded external FRP strips/sheets. Over the last few years, several experimental studies have been conducted on this new strengthening technique, which has established its effectiveness. While experimental methods of investigation are extremely useful in obtaining information about the composite behaviour of FRP and reinforced concrete, the use of numerical models such as the one presented in this paper helps in developing a good understanding of the behaviour at lower costs. In the study presented in this paper, ANSYS finite element program is used to examine the response of beams strengthened in shear by FRPs. The FE model is calibrated against test results performed at the University of Kentucky. Once validated, the model is used to examine the influence of fibre orientation, compressive strength of concrete, area of tensile and compressive reinforcements, and amount and distance between stirrups on the strength and ductility of FRP strengthened beam.

Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project

To foster ongoing international cooperation beyond ACES (APEC Cooperation for Earthquake Simulation) on the simulation of solid earth phenomena, agreement was reached to work towards establishment of a frontier international research institute for simulating the solid earth: iSERVO = International Solid Earth Research Virtual Observatory institute (http://www.iservo.edu.au). This paper outlines a key Australian contribution towards the iSERVO institute seed project, this is the construction of: (1) a typical intraplate fault system model using practical fault system data of South Australia (i.e., SA interacting fault model), which includes data management and editing, geometrical modeling and mesh generation; and (2) a finite-element based software tool, which is built on our long-term and ongoing effort to develop the R-minimum strategy based finite-element computational algorithm and software tool for modelling three-dimensional nonlinear frictional contact behavior between multiple deformable bodies with the arbitrarily-shaped contact element strategy. A numerical simulation of the SA fault system is carried out using this software tool to demonstrate its capability and our efforts towards seeding the iSERVO Institute.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Indagine modellistica sulla tenuta idraulica delle difese arginali deputate alla protezione idraulica del territorio

La prima parte di questo lavoro di tesi tratta dell’interazione tra un bacino di laminazione e il sottostante acquifero: è in fase di progetto, infatti, la costruzione di una cassa di espansione sul torrente Baganza, a monte della città di Parma. L’obiettivo di tale intervento è di ridurre il rischio di esondazione immagazzinando temporaneamente, in un serbatoio artificiale, la parte più pericolosa del volume di piena che verrebbe rilasciata successivamente con portate che possono essere agevolmente contenute nel tratto cittadino del torrente. L’acquifero è stato preliminarmente indagato e monitorato permettendone la caratterizzazione litostratigrafica. La stratigrafia si può riassumere in una sequenza di strati ghiaioso-sabbiosi con successione di lenti d’argilla più o meno spesse e continue, distinguendo due acquiferi differenti (uno freatico ed uno confinato). Nel presente studio si fa riferimento al solo acquifero superficiale che è stato modellato numericamente, alle differenze finite, per mezzo del software MODFLOW_2005. L'obiettivo del presente lavoro è di rappresentare il sistema acquifero nelle condizioni attuali (in assenza di alcuna opera) e di progetto. La calibrazione è stata condotta in condizioni stazionarie utilizzando i livelli piezometrici raccolti nei punti d’osservazione durante la primavera del 2013. I valori di conducibilità idraulica sono stati stimati per mezzo di un approccio geostatistico Bayesiano. Il codice utilizzato per la stima è il bgaPEST, un software gratuito per la soluzione di problemi inversi fortemente parametrizzati, sviluppato sulla base dei protocolli del software PEST. La metodologia inversa stima il campo di conducibilità idraulica combinando osservazioni sullo stato del sistema (livelli piezometrici nel caso in esame) e informazioni a-priori sulla struttura dei parametri incogniti. La procedura inversa richiede il calcolo della sensitività di ciascuna osservazione a ciascuno dei parametri stimati; questa è stata valutata in maniera efficiente facendo ricorso ad una formulazione agli stati aggiunti del codice in avanti MODFLOW_2005_Adjoint. I risultati della metodologia sono coerenti con la natura alluvionale dell'acquifero indagato e con le informazioni raccolte nei punti di osservazione. Il modello calibrato può quindi essere utilizzato come supporto alla progettazione e gestione dell’opera di laminazione. La seconda parte di questa tesi tratta l'analisi delle sollecitazioni indotte dai percorsi di flusso preferenziali causati da fenomeni di piping all’interno dei rilevati arginali. Tali percorsi preferenziali possono essere dovuti alla presenza di gallerie scavate da animali selvatici. Questo studio è stato ispirato dal crollo del rilevato arginale del Fiume Secchia (Modena), che si è verificato in gennaio 2014 a seguito di un evento alluvionale, durante il quale il livello dell'acqua non ha mai raggiunto la sommità arginale. La commissione scientifica, la cui relazione finale fornisce i dati utilizzati per questo studio, ha attribuito, con molta probabilità, il crollo del rilevato alla presenza di tane di animali. Con lo scopo di analizzare il comportamento del rilevato in condizioni integre e in condizioni modificate dall'esistenza di un tunnel che attraversa il manufatto arginale, è stato realizzato un modello numerico 3D dell’argine mediante i noti software Femwater e Feflow. I modelli descrivono le infiltrazioni all'interno del rilevato considerando il terreno in entrambe le porzioni sature ed insature, adottando la tecnica agli elementi finiti. La tana è stata rappresentata da elementi con elevata permeabilità e porosità, i cui valori sono stati modificati al fine di valutare le diverse influenze sui flussi e sui contenuti idrici. Per valutare se le situazioni analizzate presentino o meno il verificarsi del fenomeno di erosione, sono stati calcolati i valori del fattore di sicurezza. Questo è stato valutato in differenti modi, tra cui quello recentemente proposto da Richards e Reddy (2014), che si riferisce al criterio di energia cinetica critica. In ultima analisi è stato utilizzato il modello di Bonelli (2007) per calcolare il tempo di erosione ed il tempo rimanente al collasso del rilevato.

Equiangular spiral micro-structured waveguides in lithium niobate

Buried, micro-structured waveguides with an equiangular spiral geometry, which can be formed in a lithium niobate crystal by direct femtosecond laser writing, are analysed with the full-vectorial finite element method. The guiding properties of such waveguides are presented.

The spectral sensitivity of long period gratings fabricated in elliptical core D-shaped optical fibre

Long period gratings (LPGs) were written into a D-shaped optical fibre that has an elliptical core with a W-shaped refractive index profile and the first detailed investigation of such LPGs is presented. The LPGs’ attenuation bands were found to be sensitive to the polarisation of the interrogating light with a spectral separation of about 15 nm between the two orthogonal polarisation states. A finite element method was successfully used to model many of the behavioural features of the LPGs. In addition, two spectrally overlapping attenuation bands corresponding to orthogonal polarisation states were observed; modelling successfully reproduced this spectral feature. The spectral sensitivity of both orthogonal states was experimentally measured with respect to temperature and bending. These LPG devices produced blue and red wavelength shifts depending upon the orientation of the bend with measured maximum sensitivities of -3.56 and +6.51 nm m, suggesting that this type of fibre LPG may be useful as a shape/bend orientation sensor with reduced errors associated with polarisation dependence. The use of neighbouring bands to discriminate between temperature and bending was also demonstrated, leading to an overall curvature error of ±0.14 m-1 and an overall temperature error of ±0.3 °C with a maximum polarisation dependence error of ±8 × 10-2 m-1 for curvature and ±5 × 10-2 °C for temperature.