Finite elements in structural analysis : a bibliography with abstracts.

Mode of access: Internet.

Influence of charge size distribution on net-power draw of tumbling mill based on DEM modelling

Modelling and optimization of the power draw of large SAG/AG mills is important due to the large power draw which modern mills require (5-10 MW). The cost of grinding is the single biggest cost within the entire process of mineral extraction. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions which are not within the model database boundaries. Also, due to its static nature, the impact of the changing conditions within the mill on the power draw cannot be determined using such models. Despite advances in computing power, discrete element method (DEM) modelling of large mills with many thousands of particles could be a time consuming task. The speed of computation is determined principally by two parameters: number of particles involved and material properties. The computational time step is determined by the size of the smallest particle present in the model and material properties (stiffness). In the case of small particles, the computational time step will be short, whilst in the case of large particles; the computation time step will be larger. Hence, from the point of view of time required for modelling (which usually corresponds to time required for 3-4 mill revolutions), it will be advantageous that the smallest particles in the model are not unnecessarily too small. The objective of this work is to compare the net power draw of the mill whose charge is characterised by different size distributions, while preserving the constant mass of the charge and mill speed. (C) 2004 Elsevier Ltd. All rights reserved.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Modelling comminution patterns within a pilot scale AG/SAG mill

The patterns of rock comminution within tumbling mills, as well as the nature of forces, are of significant practical importance. Discrete element modelling (DEM) has been used to analyse the pattern of specific energy applied to rock, in terms of spatial distribution within a pilot AG/SAG mill. We also analysed in some detail the nature of the forces, which may result in rock comminution. In order to examine the distribution of energy applied within the mill, the DEM models were compared with measured particle mass losses, in small scale AG and SAG mill experiments. The intensity of contact stresses was estimated using the Hertz theory of elastic contacts. The results indicate that in the case of the AG mill, the highest intensity stresses and strains are likely to occur deep within the charge, and close to the base. This effect is probably more pronounced for large AG mills. In the SAG mill case, the impacts of the steel balls on the surface of the charge are likely to be the most potent. In both cases, the spatial pattern of medium-to-high energy collisions is affected by the rotational speed of the mill. Based on an assumed damage threshold for rock, in terms of specific energy introduced per single collision, the spatial pattern of productive collisions within each charge was estimated and compared with rates of mass loss. We also investigated the nature of the comminution process within AG vs. SAG mill, in order to explain the observed differences in energy utilisation efficiency, between two types of milling. All experiments were performed using a laboratory scale mill of 1.19 m diameter and 0.31 m length, equipped with 14 square section lifters of height 40 mm. (C) 2006 Elsevier Ltd. All rights reserved.

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.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

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.

The Mechanics of the drawing of polygonal sections from round at elevated temperature

Economic factors such as the rise in cost of raw materials, labour and power, are compelling manufacturers of cold-drawn polygonal sections, to seek new production routes which will enable the expansion in the varieties of metals used and the inclusion of difficult-to-draw materials. One such method generating considerable industrial interest is the drawing of polygonal sections from round at elevated temperature. The technique of drawing mild steel, medium carbon steel and boron steel wire into octagonal, hexagonal and square sections from round at up to 850 deg C and 50% reduction of area in one pass has been established. The main objective was to provide a basic understanding of the process, with particular emphasis being placed on modelling using both experimental and theoretical considerations. Elevated temperature stress-strain data was obtained using a modified torsion testing machine. Data were used in the upper bound solution derived and solved numerically to predict drawing stress strain, strain-rate, temperature and flow stress distribution in the deforming zone for a range of variables. The success of this warm working process will, of course, depend on the use of a satisfactory elevated temperature lubricant, an efficient cooling system, a suitable tool material having good wear and thermal shock resistance and an efficient die profile design which incorporates the principle of least work. The merits and demerits of die materials such as tungsten carbide, chromium carbide, Syalon and Stellite are discussed, principally from the standpoint of minimising drawing force and die wear. Generally, the experimental and theoretical results were in good agreement, the drawing stress could be predicted within close limits and the process proved to be technically feasible. Finite element analysis has been carried out on the various die geometries and die materials, to gain a greater understanding of the behaviour of these dies under the process of elevated temperature drawing, and to establish the temperature distribution and thermal distortion in the deforming zone, thus establishing the optimum die design and die material for the process. It is now possible to predict, for the materials already tested, (i) the optimum drawing temperature range, (ii) the maximum possible reduction of area per pass, (iii) the optimum drawing die profiles and die materials, (iv) the most efficient lubricant in terms of reducing the drawing force and die wear.

Computer simulation of form-roll design

Changes in modern structural design have created a demand for products which are light but possess high strength. The objective is a reduction in fuel consumption and weight of materials to satisfy both economic and environmental criteria. Cold roll forming has the potential to fulfil this requirement. The bending process is controlled by the shape of the profile machined on the periphery of the rolls. A CNC lathe can machine complicated profiles to a high standard of precision, but the expertise of a numerical control programmer is required. A computer program was developed during this project, using the expert system concept, to calculate tool paths and consequently to expedite the procurement of the machine control tapes whilst removing the need for a skilled programmer. Codifying the expertise of a human and the encapsulation of knowledge within a computer memory, destroys the dependency on highly trained people whose services can be costly, inconsistent and unreliable. A successful cold roll forming operation, where the product is geometrically correct and free from visual defects, is not easy to attain. The geometry of the sheet after travelling through the rolling mill depends on the residual strains generated by the elastic-plastic deformation. Accurate evaluation of the residual strains can provide the basis for predicting the geometry of the section. A study of geometric and material non-linearity, yield criteria, material hardening and stress-strain relationships was undertaken in this research project. The finite element method was chosen to provide a mathematical model of the bending process and, to ensure an efficient manipulation of the large stiffness matrices, the frontal solution was applied. A series of experimental investigations provided data to compare with corresponding values obtained from the theoretical modelling. A computer simulation, capable of predicting that a design will be satisfactory prior to the manufacture of the rolls, would allow effort to be concentrated into devising an optimum design where costs are minimised.

System identification of linear vibrating structures

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.

A three dimensional numerical investigation of hillslope flow processes

Physically based distributed models of catchment hydrology are likely to be made available as engineering tools in the near future. Although these models are based on theoretically acceptable equations of continuity, there are still limitations in the present modelling strategy. Of interest to this thesis are the current modelling assumptions made concerning the effects of soil spatial variability, including formations producing distinct zones of preferential flow. The thesis contains a review of current physically based modelling strategies and a field based assessment of soil spatial variability. In order to investigate the effects of soil nonuniformity a fully three dimensional model of variability saturated flow in porous media is developed. The model is based on a Galerkin finite element approximation to Richards equation. Accessibility to a vector processor permits numerical solutions on grids containing several thousand node points. The model is applied to a single hillslope segment under various degrees of soil spatial variability. Such variability is introduced by generating random fields of saturated hydraulic conductivity using the turning bands method. Similar experiments are performed under conditions of preferred soil moisture movement. The results show that the influence of soil variability on subsurface flow may be less significant than suggested in the literature, due to the integrating effects of three dimensional flow. Under conditions of widespread infiltration excess runoff, the results indicate a greater significance of soil nonuniformity. The recognition of zones of preferential flow is also shown to be an important factor in accurate rainfall-runoff modelling. Using the results of various fields of soil variability, experiments are carried out to assess the validity of the commonly used concept of `effective parameters'. The results of these experiments suggest that such a concept may be valid in modelling subsurface flow. However, the effective parameter is observed to be event dependent when the dominating mechanism is infiltration excess runoff.

Parametric study of the behaviour of reinforced concrete columns in fire

The research is concerned with the application of the computer simulation technique to study the performance of reinforced concrete columns in a fire environment. The effect of three different concrete constitutive models incorporated in the computer simulation on the structural response of reinforced concrete columns exposed to fire is investigated. The material models differed mainly in respect to the formulation of the mechanical properties of concrete. The results from the simulation have clearly illustrated that a more realistic response of a reinforced concrete column exposed to fire is given by a constitutive model with transient creep or appropriate strain effect The assessment of the relative effect of the three concrete material models is considered from the analysis by adopting the approach of a parametric study, carried out using the results from a series of analyses on columns heated on three sides which produce substantial thermal gradients. Three different loading conditions were used on the column; axial loading and eccentric loading both to induce moments in the same sense and opposite sense to those induced by the thermal gradient. An axially loaded column heated on four sides was also considered. The computer modelling technique adopted separated the thermal and structural responses into two distinct computer programs. A finite element heat transfer analysis was used to determine the thermal response of the reinforced concrete columns when exposed to the ISO 834 furnace environment. The temperature distribution histories obtained were then used in conjunction with a structural response program. The effect of the occurrence of spalling on the structural behaviour of reinforced concrete column is also investigated. There is general recognition of the potential problems of spalling but no real investigation into what effect spalling has on the fire resistance of reinforced concrete members. In an attempt to address the situation, a method has been developed to model concrete columns exposed to fire which incorporates the effect of spalling. A total of 224 computer simulations were undertaken by varying the amounts of concrete lost during a specified period of exposure to fire. An array of six percentages of spalling were chosen for one range of simulation while a two stage progressive spalling regime was used for a second range. The quantification of the reduction in fire resistance of the columns against the amount of spalling, heating and loading patterns, and the time at which the concrete spalls appears to indicate that it is the amount of spalling which is the most significant variable in the reduction of fire resistance.