EFFECT – Efficient finite element code

The theme of this dissertation is the finite element method applied to mechanical structures. A new finite element program is developed that, besides executing different types of structural analysis, also allows the calculation of the derivatives of structural performances using the continuum method of design sensitivities analysis, with the purpose of allowing, in combination with the mathematical programming algorithms found in the commercial software MATLAB, to solve structural optimization problems. The program is called EFFECT – Efficient Finite Element Code. The object-oriented programming paradigm and specifically the C ++ programming language are used for program development. The main objective of this dissertation is to design EFFECT so that it can constitute, in this stage of development, the foundation for a program with analysis capacities similar to other open source finite element programs. In this first stage, 6 elements are implemented for linear analysis: 2-dimensional truss (Truss2D), 3-dimensional truss (Truss3D), 2-dimensional beam (Beam2D), 3-dimensional beam (Beam3D), triangular shell element (Shell3Node) and quadrilateral shell element (Shell4Node). The shell elements combine two distinct elements, one for simulating the membrane behavior and the other to simulate the plate bending behavior. The non-linear analysis capability is also developed, combining the corotational formulation with the Newton-Raphson iterative method, but at this stage is only avaiable to solve problems modeled with Beam2D elements subject to large displacements and rotations, called nonlinear geometric problems. The design sensitivity analysis capability is implemented in two elements, Truss2D and Beam2D, where are included the procedures and the analytic expressions for calculating derivatives of displacements, stress and volume performances with respect to 5 different design variables types. Finally, a set of test examples were created to validate the accuracy and consistency of the result obtained from EFFECT, by comparing them with results published in the literature or obtained with the ANSYS commercial finite element code.

A distinct element involved in the lipopolysaccharide activation of the tumor necrosis factor -alpha promoter in a promonocytic cell line, THP-1

TNF-α is a pleiotropic cytokine involved in normal homeostasis and plays a key role in defending the host from infection and malignancy. However when deregulated, TNF-α can lead to various disease states. Therefore, understanding the mechanisms by which TNF-α is regulated may aid in its control. In spite of the knowledge gained regarding the transcriptional regulation of TNF-α further characterization of specific TNF-α promoter elements remains to be elucidated. In particular, the T&barbelow;NF-α A&barbelow;P-1/C&barbelow;RE-like (TAC) element of the TNF-α promoter has been shown to be important in the regulation of TNF-α in lymphocytes. Activating transcription factor-2 (ATF-2) and c-Jun were shown to bind to and transactivate the TAC element However, the role of TAC and transcription factors ATF-2 and c-Jun in the regulation of TNF-α in monocytes is not as well characterized. Lipopolysaccharide (LPS), a potent activator of TNF-α in monocytes, provides a good model to study the involvement of TAC in TNF-α regulation. On the other hand, all-tram retinoic acid (ATRA), a physiological monocyte-differentiation agent, is unable to induce TNF-α protein release. ^ To delineate the functional role of TAC, we transfected the wildtype or the TAC deleted TNF-α promoter-CAT construct into THP-1 promonocytic cells before stimulating them with LPS. CAT activity was induced 17-fold with the wildtype TNF-α promoter, whereas the CAT activity was uninducible when the TAC deletion mutant was used. This daft suggests that TAC is vital for LPS to activate the TNF-α promoter. Electrophoretic mobility shift assays using the TAC element as a probe showed a unique pattern for LPS-activated cells: the disappearance of the upper band of a doublet seen in untreated and ATRA treated cells. Supershift analysis identified c-Jun and ATF-2 as components of the LPS-stimulated binding complex. Transient transfection studies using dominant negative mutants of JNK, c-Jun, or ATF-2 suggest that these proteins we important for LPS to activate the TNF-α promoter. Furthermore, an increase in phosphorylated or activated c-Jun was bound to the TAC element in LPS-stimulated cells. Increased c-Jun activation was correlated with increased activity of Jun N-terminal kinase (JNK), a known upstream stimulator of c-Jun and ATF-2, in LPS-stimulated monocytes. On the other hand, ATRA did not induce TNF-α protein release nor changes in the phosphorylation of c-Jun or JNK activity, suggesting that pathways leading to ATRA differentiation of monocytic cells are independent of TNF-α activation. Together, the induction of TNF-α gene expression seems to require JNK activation, and activated c-Jun binding to the TAC element of the TNF-α promoter in THP-1 promonocytic cells. ^

Finite element code-based modeling of a multi-feature isolation system and passive alleviation of possible inner pounding

The existing seismic isolation systems are based on well-known and accepted physical principles, but they are still having some functional drawbacks. As an attempt of improvement, the Roll-N-Cage (RNC) isolator has been recently proposed. It is designed to achieve a balance in controlling isolator displacement demands and structural accelerations. It provides in a single unit all the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, resistance to low service loads and minor vibration, and hysteretic energy dissipation characteristics. It is characterized by two unique features that are a self-braking (buffer) and a self-recentering mechanism. This paper presents an advanced representation of the main and unique features of the RNC isolator using an available finite element code called SAP2000. The validity of the obtained SAP2000 model is then checked using experimental, numerical and analytical results. Then, the paper investigates the merits and demerits of activating the built-in buffer mechanism on both structural pounding mitigation and isolation efficiency. The paper addresses the problem of passive alleviation of possible inner pounding within the RNC isolator, which may arise due to the activation of its self-braking mechanism under sever excitations such as near-fault earthquakes. The results show that the obtained finite element code-based model can closely match and accurately predict the overall behavior of the RNC isolator with effectively small errors. Moreover, the inherent buffer mechanism of the RNC isolator could mitigate or even eliminate direct structure-tostructure pounding under severe excitation considering limited septation gaps between adjacent structures. In addition, the increase of inherent hysteretic damping of the RNC isolator can efficiently limit its peak displacement together with the severity of the possibly developed inner pounding and, therefore, alleviate or even eliminate the possibly arising negative effects of the buffer mechanism on the overall RNC-isolated structural responses.

Application of X-ray microtomography to numerical simulations of agglomerate breakage by distinct element method

Computer-aided tomography has been used for many years to provide significant information about the internal properties of an object, particularly in the medical fraternity. By reconstructing one-dimensional (ID) X-ray images, 2D cross-sections and 3D renders can provide a wealth of information about an object's internal structure. An extension of the methodology is reported here to enable the characterization of a model agglomerate structure. It is demonstrated that methods based on X-ray microtomography offer considerable potential in the validation and utilization of distinct element method simulations also examined.

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm3 potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.

Discrete element modelling of power draw of tumbling mills

The power required to operate large mills is typically 5-10 MW. Hence, optimisation of power consumption will have a significant impact on overall economic performance and environmental impact. Power draw modelling results using the discrete element code PFC3D have been compared with results derived from the widely used empirical Model of Morrell. This is achieved by calculating the power draw for a range of operating conditions for constant mill size and fill factor using two modelling approaches. fThe discrete element modelling results show that, apart from density, selection of the appropriate material damping ratio is critical for the accuracy of modelling of the mill power draw. The relative insensitivity of the power draw to the material stiffness allows selection of moderate stiffness values, which result in acceptable computation time. The results obtained confirm that modelling of the power draw for a vertical slice of the mill, of thickness 20% of the mill length, is a reliable substitute for modelling the full mill. The power draw predictions from PFC3D show good agreement with those obtained using the empirical model. Due to its inherent flexibility, power draw modelling using PFC3D appears to be a viable and attractive alternative to empirical models where necessary code and computer power are available.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.

Regional subsidence modelling in Murcia city (SE Spain) using 1-D vertical finite element analysis and 2-D interpolation of ground surface displacements

Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982–1984, 1992–1995 and 2004–2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.

Determination of lifter design, speed and filling effects in AG mills by 3D DEM

The power required to operate large gyratory mills often exceeds 10 MW. Hence, optimisation of the power consumption will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. In most of the published models of tumbling mills (e.g. [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Mineral Processing Ext. Metall.) 105, C54-C62. Austin, L.G., 1990. A mill power equation for SAG mills. Miner. Metall. Process. 57-62]), the effect of lifter design and its interaction with mill speed and filling are not incorporated. Recent experience suggests that there is an opportunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. Although some work has recently been published using DEM simulations, it was basically. limited to 2D. The discrete element code, Particle Flow Code 3D (PFC3D), has been used in this work to model the effects of lifter height (525 cm) and mill speed (50-90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous (AG) mill. It was found that the distribution of the impact energy is affected by the number of lifters, lifter height, mill speed and mill filling. Interactions of lifter design, mill speed and mill filling are demonstrated through three dimensional distinct element methods (3D DEM) modelling. The intensity of the induced stresses (shear and normal) on lifters, and hence the lifter wear, is also simulated. (C) 2004 Elsevier Ltd. All rights reserved.

Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault

Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.

Elasto-plastic impact of fine particles and fragmentation of small agglomerates

Surface deposition of dense aerosol particles is of major concern in the nuclear industry for safety assessment. This study presents theoretical investigations and computer simulations of single gas-born U3O8 particles impacting with the in-reactor surface and the fragmentation of small agglomerates. A theoretical model for elasto-plastic spheres has been developed and used to analyse the force-displacement and force-time relationships. The impulse equations, based on Newton's second law, are applied to govern the tangential bouncing behaviour. The theoretical model is then incorporated into the Distinct Element Method code TRUBAL in order to perform computer simulated tests of particle collisions. A comparison of simulated results with both theoretical predictions and experimental measurements is provided. For oblique impacts, the results in terms of the force-displacement relationship, coefficients of restitution, trajectory of the impacting particle, and distribution of kinetic energy and work done during the process of impact are presented. The effects of Poisson's ratio, friction, plastic deformation and initial particle rotation on the bouncing behaviour are also discussed. In the presence of adhesion an elasto-plastic collision model, which is an extension to the JKR theory, is developed. Based on an energy balance equation the critical sticking velocity is obtained. For oblique collisions computer simulated results are used to establish a set of criteria determining whether or not the particle bounces off the target plate. For impact velocities above the critical sticking value, computer simulated results for the coefficients of restitution and rebound angles of the particle are presented. Computer simulations of fracture/fragmentation resulting from agglomerate-wall impact have also been performed, where two randomly generated agglomerates (one monodisperse, the other polydisperse), each consisting of 50 primary particles are used. The effects of impact angle, local structural arrangements close to the impact point, and plastic deformation at the contacts on agglomerate damage are examined. The simulated results show a significant difference in agglomerate strength between the two assemblies. The computer data also shows that agglomerate damage resulting from an oblique impact is determined by the normal velocity component rather than the impact speed.

Metodologia para análise da confiabilidade estrutural de escavações em rocha.

A methodology for rock-excavation structural-reliability analysis that uses Distinct Element Method numerical models is presented. The methodology solves the problem of the conventional numerical models that supply only punctual results and use fixed input parameters, without considering its statistical errors. The analysis of rock-excavation stability must consider uncertainties from geological variability, from uncertainty in the choice of mechanical behaviour hypothesis, and from uncertainties in parameters adopted in numerical model construction. These uncertainties can be analyzed in simple deterministic models, but a new methodology was developed for numerical models with results of several natures. The methodology is based on Monte Carlo simulations and uses principles of Paraconsistent Logic. It will be presented in the analysis of a final slope of a large-dimensioned surface mine.

Prediction of rock alteration patterns: a potential tool in mineral exploration

Hydrothermal alteration of a quartz-K-feldspar rock is simulated numerically by coupling fluid flow and chemical reactions. Introduction of CO2 gas generates an acidic fluid and produces secondary quartz, muscovite and/or pyrophyllite at constant temperature and pressure of 300 degrees C and 200 MPa. The precipitation and/or dissolution of the secondary minerals is controlled by either mass-action relations or rate laws. In our simulations the mass of the primary elements are conserved and the mass-balance equations are solved sequentially using an implicit scheme in a finite-element code. The pore-fluid velocity is assumed to be constant. The change of rock volume due to the dissolution or precipitation of the minerals, which is directly related to their molar volume, is taken into account. Feedback into the rock porosity and the reaction rates is included in the model. The model produces zones of pyrophyllite quartz and muscovite due to the dissolution of K-feldspar. Our model simulates, in a simplified way, the acid-induced alteration assemblages observed in various guises in many significant mineral deposits. The particular aluminosilicate minerals produced in these experiments are associated with the gold deposits of the Witwatersrand Basin.

Blast loading of masonry infills: testing and simulation

This work intends to present a newly developed test setup for dynamic out-of-plane loading using underWater Blast Wave Generators (WBWG) as loading source. Underwater blasting operations have been, during the last decades, subject of research and development of maritime blasting operations (including torpedo studies), aquarium tests for the measurement of blasting energy of industrial explosives and confined underwater blast wave generators. WBWG allow a wide range for the produced blast impulse and surface area distribution. It also avoids the generation of high velocity fragments and reduces atmospheric sound wave. A first objective of this work is to study the behavior of masonry infill walls subjected to blast loading. Three different masonry walls are to be studied, namely unreinforced masonry infill walls and two different reinforcement solutions. These solutions have been studied previously for seismic action mitigation. Subsequently, the walls will be simulated using an explicit finite element code for validation and parametric studies. Finally, a tool to help designers to make informed decisions on the use of infills under blast loading will be presented.