Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

The Boundary Element Method in elastodynamics

As is well known B.E.M. is obtained as a mixture of the integral representation formula of classical elasticity and the discretization philosophy of the finite element method (F.E.M.). The paper presents the application of B.E.M. to elastodynamic problems. Both the transient and steady state solutions are presented as well as some techniques to simplify problems with a free-stress boundary.

Effect of web holes on web crippling strength of cold-formed steel channel sections under end-one-flange loading condition – Part I: Tests and finite element analysis

Web openings could be used in cold-formed steel beam members, such as wall studs or floor joints, to facilitate ease of services in buildings. In this paper, a combination of tests and non-linear finite element analyses is used to investigate the effect of such holes on web crippling under end-one-flange (EOF) loading condition; the cases of both flanges fastened and unfastened to the bearing plates are considered. The results of 74 web crippling tests are presented, with 22 tests conducted on channel sections without web openings and 52 tests conducted on channel sections with web openings. In the case of the tests with web openings, the hole was either located centred above the bearing plates or having a horizontal clear distance to the near edge of the bearing plates. A good agreement between the tests and finite element analyses was obtained in term of both strength and failure modes.

Finite Element Simulations of stretch-blow moulding with experimental validation over a broad process window

Injection stretch blow moulding is a well-established method of forming thin-walled containers and has been extensively researched for numerous years. This paper is concerned with validating the finite element analysis of the free-stretch-blow process in an effort to progress the development of injection stretch blow moulding of poly(ethylene terephthalate). Extensive data was obtained experimentally over a wide process window accounting for material temperature and air flow rate, while capturing cavity pressure, stretch-rod reaction force and preform surface strain. This data was then used to assess the accuracy of the correlating FE simulation constructed using ABAQUS/Explicit solver and an appropriate viscoelastic material subroutine. Results reveal that the simulation is able to give good quantitative correlation for conditions where the deformation was predominantly equal biaxial whilst qualitative correlation was achievable when the mode of deformation was predominantly sequential biaxial. Overall the simulation was able to pick up the general trends of how the pressure, reaction force, strain rate and strain vary with the variation in preform temperature and air flow rate. The knowledge gained from these analyses provides insight into the mechanisms of bottle formation, subsequently improving the blow moulding simulation and allowing for reduction in future development costs.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Photoelastic And Finite Element Analyses Of Occlusal Loads In Mandibular Body.

This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.

Finite-element Analysis Of 3 Situations Of Trauma In The Human Edentulous Mandible.

Maxillofacial trauma resulting from falls in elderly patients is a major social and health care concern. Most of these traumatic events involve mandibular fractures. The aim of this study was to analyze stress distributions from traumatic loads applied on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible using finite-element analysis (FEA). Computerized tomographic analysis of an edentulous macerated human mandible of a patient approximately 65 years old was performed. The bone structure was converted into a 3-dimensional stereolithographic model, which was used to construct the computer-aided design (CAD) geometry for FEA. The mechanical properties of cortical and cancellous bone were characterized as isotropic and elastic structures, respectively, in the CAD model. The condyles were constrained to prevent free movement in the x-, y-, and z-axes during simulation. This enabled the simulation to include the presence of masticatory muscles during trauma. Three different simulations were performed. Loads of 700 N were applied perpendicular to the surface of the cortical bone in the symphyseal, parasymphyseal, and mandibular body regions. The simulation results were evaluated according to equivalent von Mises stress distributions. Traumatic load at the symphyseal region generated low stress levels in the mental region and high stress levels in the mandibular neck. Traumatic load at the parasymphyseal region concentrated the resulting stress close to the mental foramen. Traumatic load in the mandibular body generated extensive stress in the mandibular body, angle, and ramus. FEA enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) in response to 3 different traumatic load conditions. This knowledge can help guide emergency responders as they evaluate patients after a traumatic event.

Keratoconus prediction using a finite element model of the cornea with local biomechanical properties

PURPOSE: The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye-care professional. We have developed a finite element model of the cornea, that tries to predicts keratoconus-like behavior and its evolution based on material properties of the corneal tissue. METHODS: Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye model. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. RESULTS: The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized protuberance and increase in curvature when compared to the remaining portion of the cornea. CONCLUSIONS: This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented model has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.

Rare earth element and yttrium geochemistry applied to the genetic study of cryolite ore at the Pitinga Mine (Amazon, Brazil)

This work aims at the geochemical study of Pitinga cryolite mineralization through REE and Y analyses in disseminated and massive cryolite ore deposits, as well as in fluorite occurrences. REE signatures in fluorite and cryolite are similar to those in the Madeira albite granite. The highest ΣREE values are found in magmatic cryolite (677 to 1345 ppm); ΣREE is lower in massive cryolite. Average values for the different cryolite types are 10.3 ppm, 6.66 ppm and 8.38 ppm (for nucleated, caramel and white types, respectively). Disseminated fluorite displays higher ΣREE values (1708 and 1526ppm) than fluorite in late veins(34.81ppm). Yttrium concentration is higher in disseminated fluorite and in magmatic cryolite. The evolution of several parameters (REEtotal, LREE/HREE, Y) was followed throughout successive stages of evolution in albite granites and associated mineralization. At the end of the process, late cryolite was formed with low REEtotal content. REE data indicate that the MCD was formed by, and the disseminated ore enriched by (additional formation of hydrothermal disseminated cryolite), hydrothermal fluids, residual from albite granite. The presence of tetrads is poorly defined, although nucleated, caramel and white cryolite types show evidence for tetrad effect.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Three-dimensional finite element thermal analysis of dental tissues irradiated with Er,Cr:YSGG laser

In the present study, a finite element model of a half-sectioned molar tooth was developed in order to understand the thermal behavior of dental hard tissues (both enamel and dentin) under laser irradiation. The model was validated by comparing it with an in vitro experiment where a sound molar tooth was irradiated by an Er,Cr:YSGG pulsed laser. The numerical tooth model was conceived to simulate the in vitro experiment, reproducing the dimensions and physical conditions of the typical molar sound tooth, considering laser energy absorption and calculating the heat transfer through the dental tissues in three dimensions. The numerical assay considered the same three laser energy densities at the same wavelength (2.79 mu m) used in the experiment. A thermographic camera was used to perform the in vitro experiment, in which an Er, Cr: YSGG laser (2.79 mu m) was used to irradiate tooth samples and the infrared images obtained were stored and analyzed. The temperature increments in both the finite element model and the in vitro experiment were compared. The distribution of temperature inside the tooth versus time plotted for two critical points showed a relatively good agreement between the results of the experiment and model. The three dimensional model allows one to understand how the heat propagates through the dentin and enamel and to relate the amount of energy applied, width of the laser pulses, and temperature inside the tooth. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2953526]

Alpha element abundances and gradients in the Milky Way bulge from FLAMES-GIRAFFE spectra of 650 K giants

Aims. We present the analysis of the [alpha/Fe] abundance ratios for a large number of stars at several locations in the Milky Way bulge with the aim of constraining its formation scenario. Methods. We obtained FLAMES-GIRAFFE spectra (R = 22 500) at the ESO Very Large Telescope for 650 bulge red giant branch (RGB) stars and performed spectral synthesis to measure Mg, Ca, Ti, and Si abundances. This sample is composed of 474 giant stars observed in 3 fields along the minor axis of the Galactic bulge and at latitudes b = -4 degrees, b = -6 degrees, b = -12 degrees. Another 176 stars belong to a field containing the globular cluster NGC 6553, located at b = -3 degrees and 5 degrees away from the other three fields along the major axis. Stellar parameters and metallicities for these stars were presented in Zoccali et al. (2008, A&A, 486, 177). We have also re-derived stellar parameters and abundances for the sample of thick and thin disk red giants analyzed in Alves-Brito et al. (2010, A&A, 513, A35). Therefore using a homogeneous abundance database for the bulge, thick and thin disk, we have performed a differential analysis minimizing systematic errors, to compare the formation scenarios of these Galactic components. Results. Our results confirm, with large number statistics, the chemical similarity between the Galactic bulge and thick disk, which are both enhanced in alpha elements when compared to the thin disk. In the same context, we analyze [alpha/Fe] vs. [Fe/H] trends across different bulge regions. The most metal rich stars, showing low [alpha/Fe] ratios at b = -4 degrees disappear at higher Galactic latitudes in agreement with the observed metallicity gradient in the bulge. Metal-poor stars ([Fe/H] < -0.2) show a remarkable homogeneity at different bulge locations. Conclusions. We have obtained further constrains for the formation scenario of the Galactic bulge. A metal-poor component chemically indistinguishable from the thick disk hints for a fast and early formation for both the bulge and the thick disk. Such a component shows no variation, neither in abundances nor kinematics, among different bulge regions. A metal-rich component showing low [alpha/Fe] similar to those of the thin disk disappears at larger latitudes. This allows us to trace a component formed through fast early mergers (classical bulge) and a disk/bar component formed on a more extended timescale.

Neutron Activation Analysis: A Primary (Ratio) Method to Determine SI-Traceable Values of Element Content in Complex Samples

The metrological principles of neutron activation analysis are discussed. It has been demonstrated that this method can provide elemental amount of substance with values fully traceable to the SI. The method has been used by several laboratories worldwide in a number of CCQM key comparisons - interlaboratory comparison tests at the highest metrological level - supplying results equivalent to values from other methods for elemental or isotopic analysis in complex samples without the need to perform chemical destruction and dissolution of these samples. The CCOM accepted therefore in April 2007 the claim that neutron activation analysis should have the similar status as the methods originally listed by the CCOM as `primary methods of measurement`. Analytical characteristics and scope of application are given.